Market - User contributions [en]

MediaWiki:Sitenotice

2024-09-15T04:47:49Z

Vipul:

Want site search autocompletion? See [[Project:Enabling site search autocompletion|here]] 
Encountering 429 Too Many Requests errors when browsing the site? See [[Project:429 Too Many Requests error|here]]

User:Vipul/Sandbox

2024-09-15T04:46:24Z

Vipul:

Test

<math>\frac{\sqrt{e^{2\pi^3}}}{5 + t^{2/313} + 13}</math>

<math>9^{\sqrt{7 + 2}} = 729</math>

<math>2^{8 - 1} = 128</math>

<math>2^7 - 1 = 127</math>

<math>5^{1 + 2} = 125</math>

<math>(3 + 4)^3 = 343</math>

<math>6^{2 + 1} = 216</math>

<math>3! * 6 = 36</math>

<math>\left(\sqrt{7 + 2}\right)^{\sqrt{9}!} = 729</math>

<math>(7 - 4)! + 4! = 744</math>

<math>3! * 60 = 360</math>

<math>(4/2)^{10} = 1024</math>

<math>\sqrt{7 + 2}!! + 3 = 723</math>

MediaWiki:Sitenotice

2024-09-08T18:07:13Z

Vipul:

'''This site is in the process of being migrated to a new server. Edits made until this notice has been removed may be lost.''' 
Want site search autocompletion? See [[Project:Enabling site search autocompletion|here]] 
Encountering 429 Too Many Requests errors when browsing the site? See [[Project:429 Too Many Requests error|here]]

Market:Enabling site search autocompletion

2024-08-15T05:39:16Z

Vipul:

Content copied from [[Ref:Ref:Enabling site search autocompletion]]. Images used are specific to this site (Market).

Site search autocompletion is currently broken by default on this site. This page includes details on how to get it to work, and what's going on.

==What's wrong with site search autocompletion and how to fix it==

===What's wrong===

When you start typing something in the site search bar, you'll see it stuck at "Loading search suggestions" as shown in the screenshot below:

[[File:Site search autocompletion broken.png]]

Note that the actual search is still working -- you just have to hit Enter after typing the search query and it'll go to the search results page. It's the autocompletion before you hit Enter that is broken.

===How to fix it===

To fix it, you need to follow these steps:

* Write to vipulnaik1@gmail.com asking for a login to the site. Please include the following with your request: preferred username, preferred initial password (you can change it after logging in), real name (if you want it entered), email address to use (if you want an actual email address by which you can be contacted), and whether you want edit access as well. You don't need edit access for enabling site search autocompletion.
* Log in to the site. Then go to [[Special:Preferences]]. Go to the Appearance section and switch the Skin from "Vector (2022)" to "Vector legacy (2010)".
* Make sure to hit "Save" at the bottom.
* Now you can reload the page or load a new page.

Site search autocompletion should now work. Here's an example:

[[File:Site search autocompletion working.png]]

==More background==

We've recently upgraded the MediaWiki version of this wiki from 1.35.13 to 1.41.2 (see [[Special:Version]]). The upgrade allows us to migrate the wiki to a more modern operating system version running PHP 8. With the current setup for MediaWiki 1.41.2, we're in this situation:

* The "Vector legacy (2010)" skin has site search autocompletion working, but it doesn't render well on small screens. Specifically, even on small mobile screens, it still shows the left menu, and doesn't properly use the MobileFrontend extension settings.
* The "Vector (2022)" skin doesn't have site search autocompletion working (see screenshots in preceding section) but it does render fine on mobile devices.

It is possible to set only one default skin (that is applicable to all non-logged-in users and is the default for logged-in users who have not configured a skin for themselves). So, the selection of default skin comes down to whether it's more important for casual users to have the mobile experience working or to have site search autocompletion working. Based on a general understanding of user behavior, we believe that having a usable mobile experience is more important for casual users than having site search autocompletion.

However, for power users who are using the site extensively, site search autocompletion may be important. That's why we've written this page giving guidance on how to set up site search autocompletion.

MediaWiki:Sitenotice

2024-08-15T05:05:03Z

Vipul:

File:Site search autocompletion working.png

2024-08-15T05:04:07Z

Vipul:

File:Site search autocompletion broken.png

2024-08-15T05:03:12Z

Vipul:

Market:429 Too Many Requests error

2024-08-15T04:58:11Z

Vipul: Created page with "This content is copied from Ref:Ref:429 Too Many Requests error. If you get a 429 Too Many Requests error when browsing this site, read on. You're probably seeing this error because a large number of requests have been made from your IP address over a short period of time. That's probably a lot of requests from you or others who share your IP address (such as your home wi-fi network). Waiting a minute and then retrying should generally work. If you are an actual h..."

This content is copied from [[Ref:Ref:429 Too Many Requests error]].

If you get a 429 Too Many Requests error when browsing this site, read on.

You're probably seeing this error because a large number of requests have been made from your IP address over a short period of time. That's probably a lot of requests from you or others who share your IP address (such as your home wi-fi network). Waiting a minute and then retrying should generally work.

If you are an actual human being with a legitimate reason to be browsing the site heavily, first, thank you and sorry about this! We set rate limits to prevent bots, spiders, spammers, and malicious actors from consuming too much of our server's resources so that our server's resources can be devoted to real humans like you. Consider writing to vipulnaik1@gmail.com with your IP address to have the IP address whitelisted. You can get your IP address by [https://www.google.com/search?q=my+ip+address Googling "my IP address"] (scroll down a little bit to where Google includes the IP address in a box). NOTE: If you have both an IPv4 address and an IPv6 address, you should send both; the server supports both IPv4 and IPv6, so either may end up getting used. To check if you have an IPv6 address, try visiting [https://ipv6.google.com/ ipv6.google.com].

If your IP address changes, or you are away from your home network, then you'll get rate-limited again. So if you find yourself getting rate-limited after already having been whitelisted, check if you are on a different IP address than the one for which you requested whitelisting.

Market:Enabling site search autocompletion

2024-08-15T04:56:57Z

Vipul: Created page with "Content copied from Ref:Ref:Enabling site search autocompletion. Images used are specific to this site (Companal). Site search autocompletion is currently broken by default on this site. This page includes details on how to get it to work, and what's going on. ==What's wrong with site search autocompletion and how to fix it== ===What's wrong=== When you start typing something in the site search bar, you'll see it stuck at "Loading search suggestions" as shown in..."

Content copied from [[Ref:Ref:Enabling site search autocompletion]]. Images used are specific to this site (Companal).

Site search autocompletion is currently broken by default on this site. This page includes details on how to get it to work, and what's going on.

==What's wrong with site search autocompletion and how to fix it==

===What's wrong===

When you start typing something in the site search bar, you'll see it stuck at "Loading search suggestions" as shown in the screenshot below:

[[File:Site search autocompletion broken.png]]

Note that the actual search is still working -- you just have to hit Enter after typing the search query and it'll go to the search results page. It's the autocompletion before you hit Enter that is broken.

===How to fix it===

To fix it, you need to follow these steps:

* Write to vipulnaik1@gmail.com asking for a login to the site. Please include the following with your request: preferred username, preferred initial password (you can change it after logging in), real name (if you want it entered), email address to use (if you want an actual email address by which you can be contacted), and whether you want edit access as well. You don't need edit access for enabling site search autocompletion.
* Log in to the site. Then go to [[Special:Preferences]]. Go to the Appearance section and switch the Skin from "Vector (2022)" to "Vector legacy (2010)".
* Make sure to hit "Save" at the bottom.
* Now you can reload the page or load a new page.

Site search autocompletion should now work. Here's an example:

[[File:Site search autocompletion working.png]]

==More background==

We've recently upgraded the MediaWiki version of this wiki from 1.35.13 to 1.41.2 (see [[Special:Version]]). The upgrade allows us to migrate the wiki to a more modern operating system version running PHP 8. With the current setup for MediaWiki 1.41.2, we're in this situation:

* The "Vector legacy (2010)" skin has site search autocompletion working, but it doesn't render well on small screens. Specifically, even on small mobile screens, it still shows the left menu, and doesn't properly use the MobileFrontend extension settings.
* The "Vector (2022)" skin doesn't have site search autocompletion working (see screenshots in preceding section) but it does render fine on mobile devices.

It is possible to set only one default skin (that is applicable to all non-logged-in users and is the default for logged-in users who have not configured a skin for themselves). So, the selection of default skin comes down to whether it's more important for casual users to have the mobile experience working or to have site search autocompletion working. Based on a general understanding of user behavior, we believe that having a usable mobile experience is more important for casual users than having site search autocompletion.

However, for power users who are using the site extensively, site search autocompletion may be important. That's why we've written this page giving guidance on how to set up site search autocompletion.

MediaWiki:Sitenotice

2024-08-15T04:54:43Z

Vipul: Blanked the page

User:Vipul/Sandbox

2024-08-15T04:51:25Z

Vipul:

User:Vipul/Sandbox

2024-08-15T04:48:34Z

Vipul:

User:Vipul/Sandbox

2024-08-15T04:43:49Z

Vipul:

User:Vipul/Sandbox

2024-08-15T04:38:15Z

Vipul:

MediaWiki:Sitenotice

2024-08-15T04:28:59Z

Vipul:

'''This wiki is in the process of being upgraded. The site may go down intermittently. Please try to avoid editing until this notice has been removed.'''

User:Vipul/Sandbox

2024-07-06T01:04:49Z

Vipul:

User:Vipul/Sandbox

2024-07-06T01:00:14Z

Vipul:

User:Vipul/Sandbox

2024-07-06T00:48:26Z

Vipul:

User:Vipul/Sandbox

2024-04-15T03:43:14Z

Vipul:

Test

<math>\frac{\sqrt{e^{2\pi^3}}}{5 + t^{2/313} + 13}</math>

<math>9^{\sqrt{7 + 2}} = 729</math>

<math>2^{8 - 1} = 128</math>

<math>2^7 - 1 = 127</math>

<math>5^{1 + 2} = 125</math>

User:Vipul/Sandbox

2024-04-15T00:25:49Z

Vipul:

Test

<math>\frac{\sqrt{e^{2\pi^3}}}{5 + t^{2/313} + 13}</math>

<math>9^{\sqrt{7 + 2}} = 729</math>

<math>2^{8 - 1} = 128</math>

<math>2^7 - 1 = 127</math>
hello

User:Vipul/Sandbox2

2024-04-15T00:13:45Z

Vipul: Created page with "hello"

hello

User:Vipul/Sandbox

2024-04-15T00:13:34Z

Vipul:

Test

<math>\frac{\sqrt{e^{2\pi^3}}}{5 + t^{2/313} + 13}</math>

<math>9^{\sqrt{7 + 2}} = 729</math>

<math>2^{8 - 1} = 128</math>

hello

User:Vipul/Sandbox

2024-04-15T00:10:45Z

Vipul:

Test

<math>\frac{\sqrt{e^{2\pi^3}}}{5 + t^{2/313} + 13}</math>

<math>9^{\sqrt{7 + 2}} = 729</math>

<math>2^{8 - 1} = 128</math>

User:Vipul/Sandbox

2024-04-15T00:07:16Z

Vipul:

Test

<math>\frac{\sqrt{e^{2\pi^3}}}{5 + t^{2/313} + 13}</math>

<math>9^{\sqrt{7 + 2}} = 729</math>

Market:Privacy policy

2022-09-25T15:38:00Z

Vipul:

This privacy policy is common to subject wikis. For the original privacy policy, refer [[Ref:Ref:Privacy policy]].

==Privacy for readers==

If you are surfing this website, your actions are logged in our usage logs. These usage logs are accessible to:

* The site's administrators and technical support group. For a full list of administrators, contact [[User:Vipul|Vipul Naik]] by email: vipulnaik1@gmail.com.
* The service that hosts the data and servers, which is currently [http://www.linode.com Linode].
* Google Analytics, which has been integrated to collect site statistics. View Google's privacy policy here: https://policies.google.com/privacy?hl=en
* Other third-party JS scripts that collect user activity; none of these should collect any personally identifiable information (PII). For a list of all scripts running at the current time, contact [[User:Vipul|Vipul Naik]] by email: vipulnaik1@gmail.com.

==Privacy for editors==

Editing on subject wikis is generally permitted only for registered users. Registered users must, at the time of registration, provide their real name, and enter basic information about their reason for interest. ''No'' private information such as date of birth, social security or taxation number, or home address is sought.

Regarding personal information:

* The email IDs of registered users are visible to site administrators only. For information about site administrators, contact vipulnaik1@gmail.com with the particular subject wiki and the reason for request.
* All editing activity by registered users is recorded on the site and is visible to all site users. However, this information is not indexed by search engines that follow robots.txt.
* For edits made by registered users when logged in, the originating IP addresses for the edits can be accessed only by the site administrators.
* Passwords chosen by registered users are not humanly accessible, even to site administrators.

Market:Privacy policy

2022-09-25T15:31:39Z

Vipul:

This privacy policy is common to subject wikis. For the original privacy policy, refer [[Ref:Ref:Privacy policy]].

==Privacy for readers==

If you are surfing this website, your actions are logged in our usage logs. These usage logs are accessible to:

* The site's administrators and technical support group. For a full list of administrators, contact [[User:Vipul|Vipul Naik]] by email: vipulnaik1@gmail.com.
* The service that hosts the data and servers, which is currently [http://www.linode.com Linode].
* Google Analytics, which has been integrated to collect site statistics. View Google's privacy policy here: http://www.google.com/intl/en_ALL/privacypolicy.html
* Other third-party JS scripts that collect user activity; none of these should collect any personally identifiable information (PII). For a list of all scripts running at the current time, contact [[User:Vipul|Vipul Naik]] by email: vipulnaik1@gmail.com.

==Privacy for editors==

Editing on subject wikis is generally permitted only for registered users. Registered users must, at the time of registration, provide their real name, and enter basic information about their reason for interest. ''No'' private information such as date of birth, social security or taxation number, or home address is sought.

Regarding personal information:

* The email IDs of registered users are visible to site administrators only. For information about site administrators, contact vipulnaik1@gmail.com with the particular subject wiki and the reason for request.
* All editing activity by registered users is recorded on the site and is visible to all site users. However, this information is not indexed by search engines that follow robots.txt.
* For edits made by registered users when logged in, the originating IP addresses for the edits can be accessed only by the site administrators.
* Passwords chosen by registered users are not humanly accessible, even to site administrators.

Demand curve

2022-04-01T03:44:51Z

Vipul: /* Definition */

{{price-quantity curve}}

==Definition==

The '''demand curve''' for a good is defined with the following in the background:

* The specific good.
* A unit for measuring the quantity of that.
* A unit for measuring price.
* A convention on whether sales taxes are included in the stated price.
* A certain set of economic actors who are the potential buyers of that good.
* A time frame within which the demand is measured.
* An economic backdrop that includes all the [[determinants of demand]] ''other than'' the unit price of that good.

The demand curve has the following characteristics:

* The vertical axis is the ''price'' axis, measuring the price ''per unit'' of the commodity.
* The horizontal axis is the ''quantity'' axis, measuring the quantity of the good demanded in total by all the economic actors chosen above.

Here, ''quantity demanded'' by an economic actor refers to the quantity that that economic actor is ready, willing, and able to buy.

Note that the demand curve makes sense only ''[[ceteris paribus]]'' -- all other determinants of demand being kept constant.

The term '''demand''' is used for the entire price-quantity relationship depicted pictorially by the demand curve.

===Distinction between demand curve, demand function, and demand schedule===

Two terms closely related to the demand curve are the demand function and demand schedule:

* Demand ''function'' is a function that takes as input the unit price and outputs the quantity demanded. The demand curve is a graphical representation of the demand function, but with a heterodox choice of axes: the input variable (price) is plotted on the vertical axis and the output variable (quantity demanded) is plotted on the horizontal axis.
* Demand ''schedule'' is a discrete version of a demand function. It specifies a (finite) list of unit price-quantity demanded pairs. Demand schedules may be created observationally. Graphically, knowing a demand schedule allows us to plot some points on the demand curve, but the behavior of the parts of the demand curve in between those points is not uniquely determined. However, we can infer the approximate nature of the demand function and demand curve from a demand schedule.

==Individual versus market demand curve==

{{further|[[individual demand curve]], [[market demand curve]]}}

===Terminology===

[[Individual demand curve]]s are demand curves for a ''single'' economic actor. This actor could be an individual, a household, or a firm (where the firm may be a for-profit, a non-governmental non-profit, or a governmental agency).

The [[market demand curve]] aggregates (or adds up) the demand curves for a number of economic actors. For instance, the market household demand curve for a good in a town is obtained by adding up the demand curves for all the households in the town. The market demand curve for steel in the automobile industry is obtained by adding up the demand curves for steel for all firms in the automobile industry.

Note that ''market demand'' (which is the aggregate across all economic actors of their demand for a particular good) is distinct from [[aggregate demand]]. Aggregate demand is a controversial macroeconomic notion that is part of [[Keynesian theory]] and roughly describes the total demand in the economy across ''all'' goods. Some schools of economics dispute whether the notion of aggregate demand makes sense even at a theoretical level, because demand for one good is expressed in relation to other goods. None of this discussion of demand curves touches upon aggregate demand.

===Qualitative distinctions===

Here ''individual'' could mean individual, household, or firm -- any single economic actor.

A lot of interesting and quirky phenomena may be obtained at the level of individual demand curves but may become less visible (due to smoothing and averaging out) at the aggregate level because of the canceling out or smoothing out effects. Some examples are discussed below:

* For items where purchase quantities are discrete, individual demand curves are by nature discontinuous, while aggregate demand curves are likely to be continuous given sufficient heterogeneity among individuals. Note that individual demand quantities ''could'' be fractional even with discrete purchase quantities -- for instance, my weekly number of loaves of bread purchased could be <math>3.5</math> if I purchase a loaf of bread every second day.
* Individual demand curves are more likely to exhibit sharp discontinuities for other reasons: Individuals may use threshold prices and [[reference price]]s to determine which item to purchase and how much. For instance, if, for me, <math>A</math> and <math>B</math> are equivalent goods (i.e., they are perfect [[substitute good]]s for each other), then I buy none of <math>A</math> when its price exceeds that of <math>B</math>, but I shift my entire consumption to <math>A</math> when its price drops below that of <math>B</math>. The price of <math>B</math> is thus a point of discontinuity in the demand curve for <math>A</math>. In the aggregate, the heterogeneity of individuals ensures that they do not all perceive the same pairs of goods as perfect substitutes, and hence these jumps are less likely to occur.
* Various violations of the [[law of demand]] (the assertion that demand curves slope downwards), both rational and irrational, are more likely to be seen at the individual level than at the aggregate level: For instance, the [[Giffen good]] phenomenon and the [[Veblen good]] phenomenon may play an important role in the consumption behavior of one individual or household, but because of differing incomes and differing tastes and preferences that lead individuals to value substitutes differently, the phenomena would not apply to all economic actors. Since an aggregate Giffen good phenomenon depends on the phenomenon affecting a large number of individuals, aggregate Giffen good phenomena may be much rarer than individual Giffen good phenomena. The same holds for various forms of mild irrationality and idiosyncratic behavior.

==Examples of demand curves==

This gives some mathematical possibilities for the demand curve. The list is illustrative and not intended to be exhaustive.

===Demand curve for fixed total budget: reciprocal relationship between price and quantity===

[[File:Inverseproportionalitydemandcurve.png|500px]]

Here, the individual or household spends a fixed amount of money on the commodity regardless of its price. Thus, the quantity purchased is inversely proportional to the unit price, i.e., the demand curve equation is given by:

<math>\! q = \frac{b}{p}</math>

where <math>b</math> is the total budget amount that the household spends. Here are some properties of such a demand curve:

* The [[price-elasticity of demand]] for this demand curve is <math>-1</math>.
* As the price falls to <math>0</math>, quantity demanded goes to infinity. An actual demand of <math>\infty</math> (infinity) may be infeasible, hence the above expression may not work for very low prices. However, such a demand curve may well explain what appears to be a [[zero price effect]].
* For the quantity demanded to become zero, the price needs to be raised to infinity. Again, this may not be the case in reality, since with a sufficiently high price, the quantity demanded may be so low that the [[transaction cost]]s dominate the picture.

A slight variant of the above is:

<math>\! q = \frac{b}{p + p_t}</math>

where <math>p_t > 0</math> is the transaction cost (which we assume as a cost per unit quantity purchased). This variant avoids the problem of infinities at one end: as the price falls to <math>0</math>, quantity demanded goes to <math>b/p_t</math>. In particular, for small transaction costs, this quantity demanded is extremely high.

Yet another variant involves two kinds of transaction costs: a transaction cost per unit, and a transaction cost that is constant for all nonzero amounts purchased and <math>0</math> if nothing is purchased. If we denote these two transaction costs as <math>p_t</math> (per unit) and <math>p_f</math> (fixed) then:

<math>\! q = \frac{b - p_f}{p + p_t}</math>

Yet another variant is where there is a minimum quantity that can be demanded if any nonzero quantity is demanded, which we call <math>q_\min</math>. In this case, we first use the formula to determine quantity demanded. If the quantity demanded is less than <math>q_\min</math>, we replace it by <math>0</math>.

===Linear demand curve===

[[File:Lineardemandcurve.png|500px]]

Here, the demand curve is a straight line and is given by an equation of the form:

<math>\! \frac{q}{q_0} + \frac{p}{p_0} = 1 \qquad \operatorname{for} \qquad p \le p_0, \qquad q = 0 \qquad \operatorname{for} \qquad p \ge p_0</math>

Here, <math>q_0</math> is the quantity purchased at zero price and <math>p_0</math> is the minimum price needed for the quantity purchased to drop to <math>0</math>. Some features of this demand curve are:

* The magnitude of price-elasticity of demand is variable. It is less than <math>1</math> for prices greater than <math>p_0/2</math> and greater than <math>1</math> for prices less than <math>p_0/2</math>. The total budget allocated is maximum for a price of <math>p_0/2</math> and a quantity purchased of <math>q_0/2</math>.
* The quantity purchased at a price of <math>0</math> is <math>q_0</math>.
* The minimum price required to push the quantity purchased to <math>0</math> is <math>p_0</math>.

===Demand curve with a region of high price elasticity in between===

[[File:Demandcurvewithinflection.png|500px]]

In the demand curve shown above, at a unit price of about 3, the demand curve is at its ''most'' elastic. For a very small variation in price around this point, demand goes from 2 units to 4 units. For prices greater than or less than 3, the price elasticity is considerably less. The high price elasticity at a price of 3 may arise because that is the price of a close substitute.

===Multiple demand curves===

[[File:Multipledemandcurves.png|500px]]

The picture given above shows two different demand curves for the same good. A change in some [[exogenous parameter]] that is one of the [[determinants of demand]] may lead to an expansion from the inner (blue) demand curve to the outer (purple) demand curve.

For a unit price of 2, the inner demand curve indicates a quantity of 1 unit demanded, while the outer demand curve indicates a quantity of 1 unit demanded.

Similarly, to achieve a quantity demanded of 3 units, a unit price of 2/3 is needed with the inner demand curve, but a unit price of 4/3 is needed with the outer demand curve.

==Curve characteristics==

===Slope or first derivative===

The slope (or rate of change) of the demand curve is inversely related of what is termed the [[price-elasticity of demand]]. The price-elasticity measures the total change in quantity demanded per unit change in price, made dimensionless by dividing by the quantity-price ratio. In other words, at a price <math>p</math> and quantity <math>q</math>, the price-elasticity of demand is:

<math>\! \frac{dq/dp}{q/p}</math>

The slope in mathematical jargon would be:

<math>\! \frac{dp}{dq}</math>

===Sign of slope===

{{further|[[Law of demand]]}}

Typically, the price-elasticity of demand is negative, which is equivalent to saying that the slope of the demand curve is negative, or the demand curve is downward-sloping. In other words, ''[[ceteris paribus]]'':

* A decrease in the price per unit leads to an increase in the total quantity demanded.
* An increase in the price per unit leads to a decrease in the total quantity demanded.

This is termed the [[law of demand]]. There are two broad explanations for the law of demand:

* Concavity of the utility functions of individuals and households: the marginal utility of an individual or household per unit of a good decreases with the amount already purchased. Also, the [[income effect]] and the [[substitution effect]]. {{further|[[Law of demand for individual buyers follows from diminishing marginal utility]]}}
* Heterogeneity in households, i.e., differences in the [[reservation price]]s across households. {{further|[[Law of demand for multiple buyers follows from differences in reservation prices]]}}

A demand curve that violates the law of demand is termed an ''exceptional'' demand curve. One source of exception to the law of demand is [[Veblen good]]s, whose demand is related to [[conspicuous consumption]]. Other goods that appear to violate the law of demand (though they do not directly violate it) are [[Giffen good]]s and certain kinds of goods where there is inadequate information about quality and a higher price may be taken as a signal of higher quality.

===Sign of second derivative===

There is no general principle that uniformly predicts the sign of the second derivative; similarly, there is no overarching rule about whether the price-elasticity of demand rises or falls with price.

In general, there are certain price ranges where the price-elasticity of demand is particularly high. These, in general, tend to be the price ranges where the [[substitution effect]] operates most strongly, i.e., the price ranges where there could be significant changes in the extent to which to substitute towards and away from substitutes. Alternatively, these are the price ranges where the [[reservation price]]s of many households are clustered.

In general below these price ranges, quantity demanded for the good is high, but largely price-inelastic, while above these price ranges, quantity demanded for the good is low, but again largely price-inelastic.

In this model of some critical price ranges, the sign of the second derivative is not constant.

In general, the behavior of the second derivative depends on the following:

* At the level of individual households, it depends on the second derivative of the marginal utility curve, or the ''third'' derivative of the utility curve.
* At the level of an economy, it depends on the distribution of income as well as of tastes and preferences in the economy.

==Empirical estimation==

{{further|[[Demand curve estimation]]}}

The demand curve is difficult to estimate because at any given point in time, we can only get one (quantity, price) pair for the market as a whole. There are, however, ways around this problem that allow us to make a rough sketch of the demand curve.
==Effect of sales tax on demand curve==

{{further|[[effect of sales tax on market price and quantity traded]]}}

For some goods, a [[sales tax]] is levied on the good, usually either a fixed amount per unit of the good sold, or as a fixed proportion of the pre-tax price. In case of a sales tax, there are two possible conventions used when drawing the demand curve:

* In one convention, the unit price refers to the ''pre-tax price''. In this case, an increase in the sales tax leads to a contraction of the demand curve, and a decrease in the sales tax leads to an expansion of the demand curve.
* In the other convention, the unit price refers to the price ''inclusive of taxes''. In this case, a change in the sales tax has no effect on the demand curve; it affects the [[supply curve]] instead.

==Movement along the curve==

{{further|[[convergence towards market price]]}}

Any particular price corresponds to a point on the demand curve: the ''price'' coordinate of the point is that price, while the ''quantity'' coordinate is the quantity demanded at the price. Changes in price, while keeping other factors constant, is termed movement ''along'' the demand curve. Decreasing price with time is termed ''riding down the demand curve'' (also called [[price skimming]]) while increasing price with time is termed ''riding up the demand curve''.

In a free market, suppliers are expected to vary their price until demand equals supply. In other words, demand moves along the demand curve until the price reaches the [[market price]].

==Movement (shifts) of the curve==

{{further|[[comparative statics for demand and supply]]}}

The demand curve changes when one (or more) of the [[determinants of demand]] ''other'' than price changes.

[[File:Multipledemandcurves.png|500px]]

===Outward shift of the demand curve===

An ''outward'' shift of the demand curve (also called an ''expansion'' of the demand curve) indicates an increase in the demand at every price, or equivalently, an increase in the price needed to restrict demand to a particular level.

===Inward shift of the demand curve===

An ''inward'' shift of the demand curve (also called a ''contraction'' of the demand curve) indicates a decrease in the demand at every price, or equivalently, a decrease in the price needed to restrict demand to a particular level.

===Other shape changes of the demand curve===

The demand curve may change in shape in a way that moves it ''inward'' for some price levels and outward for other price levels. This may happen in the case of the [[individual demand curve]] if the degree of substitution with another substitute good increases. It may happen for the [[market demand curve]] due to a change in the income distribution.

Effect of sales tax on market price and quantity traded

2020-06-03T16:27:04Z

Vipul: /* Analysis with pre-tax prices */

This article discusses the effect of a [[sales tax]] on the [[market price]] and equilibrium quantity traded for a good.

==Assumptions==

Prior to beginning the analysis, we note the following:

# A sales tax may be ''revenue-proportional'' (proportional to the price of the trade) or ''quantity-proportional'' (proportional to the quantity being traded). The quantitative analysis differs somewhat in both these cases. However, the qualitative analysis largely does not.
# In this article, we largely focus on the effect of the ''introduction'' of a sales tax, by performing [[comparative statics]] between a world without sales tax and a world with sales tax. Much of this analysis can also be applied to ''increases'' in sales tax. Conversely, a ''decrease'' in, or ''elimination'' of, a sales tax should have the opposite effect.
# For the most part, we focus on short run effects. In particular, this means that we assume the [[law of demand]] and [[law of supply]].
# We assume away the costs of compliance with the tax laws, and do not deal with issues of tax evasion.
# For the most part, we assume competitive markets (though we also discuss other cases). Hence, the [[law of one price]] is assumed to hold, so that we can talk of ''the'' market price.

==What we are interested in tracking==

In the world with no tax, there are two measures of interest:

* The [[market price]]
* The equilibrium quantity traded

In a word with tax, we are interested in tracking three measures:

* The pre-tax market price, i.e., the effective price that the seller gets to keep. This is to be compared to the [[market price]] in a world without sales tax.
* The post-tax market price, i.e., the effective price that the buyer pays. This is obtained by adding the sales tax to the pre-tax market price. This is to be compared to the [[market price]] in a world without sales tax.
* The equilibrium quantity traded. This is to be compared to the equilibrium quantity traded in a world without sales tax.

==Summary of several cases==
{| class="sortable" border="1"
! Case in question !! Conclusion about pre-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about post-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity (or quantities) traded (relative to a world without the tax)
|-
| single good provided in a perfectly competitive market || falls || rises || falls
|-
| single good provided by a monopoly firm || indeterminate || rises || falls
|-
| two partial substitute goods each sold in perfectly competitive markets || falls for at least one good || rises for both goods || falls for at least one good
|-
| two complementary goods each sold in perfectly competitive markets || falls for both goods || rises for at least one good || falls for both goods
|}

==Relationship with other analyses==

===Other effects of sales tax===

* [[Effect of sales tax on economic surplus]] builds on the analysis here to study how sales taxes affect the [[producer surplus]] and [[consumer surplus]] and how they result in a [[deadweight loss due to taxation]].

===Effect of subsidies===

Subsidies are taxes in negative, so their effects on market prices and quantity traded are the exact negatives of the effects of taxes.

However, their effects on economic surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on economic surplus]]
* [[Effect of price floor on economic surplus]]
* [[Effect of quantity ceiling on economic surplus]]

==Effect of sales tax on a single good with a competitive market==

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) for which we are drawing the supply and demand curves.

Note that the same analysis also works for comparative statics where we ''change'' the sales tax on only one class of goods.

===Analytical tools===

There are three kinds of diagrams that we draw to study the situation:

# Consider the world without sales tax. We can draw the usual supply and demand curves and do the usual analysis to find the market price and equilibrium quantity traded.
# Consider the world with sales tax. In this world, consider supply and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply and demand curves with respect to ''post-tax'' prices.

===Analysis with pre-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the pre-tax prices.

'''Supply curve''': The supply curve using pre-tax prices is expected to remain the ''same'' as the supply curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Demand curve''': The demand curve changes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve as follows:

{| class="sortable" border="1"
! Case !! What happens to the demand curve algebraically !! Pictorial depiction
|-
| revenue-propotional sales tax || For a revenue-proportional sales tax with a factor of <math>x</math>, the new demand function at a price of <math>p</math> equals the old demand function at a price of <math>p(1 + x)</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p(1 + x)</math>. The upshot is that the demand curve ''shrinks'' downward by a factor of <math>1 + x</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. [[File:Notaxvspretax.png|700px]]
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new demand function at a price of <math>p</math> is the old demand function at a price of <math>p + b</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p + b</math>. The upshot is that the demand curve shifts downward by a vertical distance of <math>b</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 0.4 price units/unit quanity sales tax (dashed purple). The original curve shrinks downward by 0.4 price units from its original level.[[File:Notaxvspretaxforquantityproportionalsalestax.png|700px]]
|}

The upshot is that the supply curve remains the same and the demand curve moves inward. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price drops. In other words, the new pre-tax market price is lower than the market price in the world without taxes.
* The equilibrium quantity traded falls.

The general picture of what happens, showing the contraction of demand curve and consequent move to a lower equilibrium price and lower quantity traded, is below.

[[File:Demandcontractionandmarketprice.png|700px]]

===Analysis with post-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the post-tax prices.

'''Demand curve''': The demand curve using post-tax prices is expected to remain the ''same'' as the demand curve in a world without taxes, because the price that the buyer sees is the post-tax price.

'''Supply curve''': The supply curve changes. In general, it moves upward. Assuming the law of supply, that is the same as moving inward, i.e., a ''contraction'' of the supply curve. Arithmetically, the new supply curve is related to the old supply curve as follows:

* For a revenue-proportional sales tax with a factor of <math>x</math>, the new supply function at a price of <math>p</math> equals the old supply function at a price of <math>p/(1 + x)</math>. The reason is that, as far as sellers are concerned, the effective price is the pre-tax price <math>p/(1 + x)</math>. The upshot is that the supply curve moves upward by a factor of <math>1 + x</math>.
* For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new supply function at a price of <math>p</math> is the old supply function at a price of <math>p - b</math>. The reason is that, as far as sellers are concerned, the effective price is <math>p - b</math>. The upshot is that the supply curve shifts upward by a vertical distance of <math>b</math>.

The upshot is that the supply curve contracts and the demand curve remains the same. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price rises. In other words, the new post-tax market price is higher than the market price in the world without taxes.
* The equilibrium quantity traded falls.

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price is lower than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the pre-tax curves).
* The post-tax market price is higher than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the post-tax curves).
* The equilibrium quantity traded is less than the equilibrium quantity traded in a world without the tax (this can be seen using ''either'' of the two comparative statics methods employed above).

===Extreme cases of elastic and inelastic supply and demand===

We consider some extreme cases. The first row describes the standard case, and subsequent rows describe extreme cases:

{| class="sortable" border="1"
! Assumption for [[price-elasticity of demand]] !! Assumption for [[price-elasticity of supply]] !! Conclusion about pre-tax market price (relative to market price in a world without the tax) !! Conclusion about post-tax market price (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity traded (relative to a world without the tax)
|-
| negative (satisfies the [[law of demand]]) || positive (satisfies the [[law of supply]]) || falls || rises || falls
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || falls || stays the same || falls
|-
| zero, i.e., a vertical demand curve. We also say that the demand is perfectly price-inelastic || positive (satisfies the [[law of supply]]) || stays the same || rises || stays the same
|-
| negative (satisfies the [[law of demand]]) || infinite, i.e., a horizontal supply curve, e.g., a [[constant cost industry]]. Alternatively, this also applies if the jurisdiction where sales tax is imposed is a small subjurisdiction of the economy and the pre-tax prices of the goods are determined by the world economy. || stays the same || rises || falls
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic. || falls || stays the same || stays the same
|}

===How price-elasticity affects the nature of the effect of sales tax===

The extent to which the sales tax affects the pre-tax price, post-tax price, and equilibrium quantity traded depends upon the [[price-elasticity of demand]] and [[price-elasticity of supply]]. The following are two general principles:

* Between demand and supply, the relatively more price-inelastic side absorbs more of the price burden of the sales tax. In other words, if demand is more inelastic, then the effect of the sales tax is largely seen in terms of an increase in the ''post-tax'' price. If supply is more inelastic, then the effect of the sales tax is largely seen in terms of a decrease in the ''pre-tax'' price. This is in keeping with the general principle attributed to Ricardo that rents are captured by the most inelastic side. Here, the rents are reversed in sign, but the principle stays the same.
* In general, the extent to which the equlibrium quantity traded is affected is negatively related to the price-elasticities of both demand and supply. In other words, if we reduce the price-elasticity of either demand or supply, the sensitivity of the equilibrium quantity traded to the sales tax reduces. In particular, if either demand or supply is perfectly price-inelastic, the equilibrium quantity traded is independent of the sales tax.

==Effect of sales tax on a single good with a monopolist-controlled market==

This section assumes familiarity with the key conclusions of [[determination of price and quantity supplied by monopolistic firm in the short run]].

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) that is supplied by a single seller (the monopolist) that seeks to maximizing profit.

The marginal revenue from the sale of a good equals <math>d(PQ)/dQ</math>, as <math>PQ</math> is revenue and we are interested in the rate of change of revenue as quantity changes. Using the [[calculus:product rule for differentiation|product rule for differentiation]], we find that <math>MR = Q*dP/dQ + P</math>. As explained previously, we expect that dP/dQ is negative in accordance with the law of demand. As such, marginal revenue is less than the price paid, and it may even be zero or negative.

Unlike the perfectly competitive market case discussed previously, we do not perform two separate analyses (pre-tax and post-tax). Rather, we consider various pre-tax and post-tax curves together. The reason is that a "post-tax supply curve" does not make sense in the monopoly case. Also, the analysis is complicated enough as it is, so creating two versions of it isn't worth it!

=== Key curves under consideration ===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''Pre-tax marginal cost curve''': The marginal cost curve using pre-tax prices is expected to remain the ''same'' as the marginal cost curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Pre-tax demand curve''': The pre-tax demand curve changes relative to what it is in a world without taxes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve either through proportional shrinkage toward the quantity axis (for a revenue-proportional sales tax) or through a downward translation toward the quantity by the amount of the tax on unit quantity. For more, see the [[#Analysis of pre-tax prices|analysis of pre-tax prices section]] for the perfectly competitive case.

'''Pre-tax marginal revenue curve''': The pre-tax marginal revenue curve changes relative to what it is in a world without taxes. Qualitatively, the way it changes is the ''same'' as the way the demand curve changes. For a revenue-proportional sales tax, it shrinks proportionally toward the quantity axis. For a quantity-proportional sales tax, it is translated downward. This can be inferred easily from the definition of marginal revenue as <math>d(PQ)/dQ</math>, and the way derivatives interact with addition and scalar multiplication (specifically, [[calculus:differentiation is linear|the fact that differentiation is linear]]).

'''Post-tax demand curve''' (demand curve as experienced by buyers): This remains the same as it would be in a world without taxes.

The upshot: the pre-tax marginal cost curve remains unchanged and the pre-tax marginal revenue curve shrinks downward. We now discuss the implications this has for our conclusions around pre-tax price and quantity traded. ''Prima facie'', this looks a lot like the analysis so far with pre-tax prices for a perfectly competitive market, with marginal revenue curve replacing demand curve and marginal cost curve replacing supply curve. However, there are three subtleties that complicate the picture

# The (price, quantity) pair at which trades actually occur is ''not'' the point of intersection of the marginal cost and marginal revenue curves. Rather, the ''quantity'' is determined by the point of intersection, but the price is determined by looking at the demand curve. '''This distinction alone causes some of our conclusions to break down'''.
# Unlike the demand curve in a perfectly competitive market, the marginal revenue curve is not necessarily downward-sloping. In fact, it need not even always be above the quantity axis! It can have multiple local maxima and local minima. The key distinction is that marginal revenue is affected by a combination of two factors pulling in opposite direction: expansion of the market, and reduction in the price that can be charged to buyers with the highest reservation prices.
# Unlike the supply curve in a perfectly competitive market, the marginal cost curve is not necessarily upward-sloping. It can have multiple local maxima and local minima. The key distinction with the competitive case that the supply curve for a seller in a competitive market is not the entire marginal cost curve but only a ''part of it that slopes upward''. For more, see [[determination of quantity supplied by firm in perfectly competitive market in the short run]].

There are a wide range of cases where we can make assumptions to eliminate problems (2) and (3). However, problem (1) remains.

===The easy case: marginal cost curve increasing everywhere, marginal revenue curve decreasing everywhere===

This is the easy case where, of the three problems mentioned, ''only'' Problem (1) applies.

In the case that the marginal cost curve is increasing throughout the relevant range (outside of which no optima can possibly exist) and the marginal revenue curve is decreasing throughout the relevant range, our pictorial analysis works as in the perfectly competitive case. In particular:

* Since the marginal revenue curve has shrunk downward and leftward, the new point of intersection of the curves has a lower price and lower quantity traded. Thus, the quantity traded is lower than in a world without sales tax. Also, the pre-tax marginal cost experienced by the seller is lower than in a world without sales tax.
* The ''post-tax price charged to buyers'' is higher than what it would be in a world without sales tax. This is because the quantity traded is lower, so referencing the post-tax demand curve (which is the ''same'' as the original demand curve) we get a higher price.
* ''However'', even in this case, the effect on the pre-tax price is ambiguous. This is because there are two competing effects. On the one hand, the quantity traded is lower, causing the maximum price chargeable to increase. On the other hand, the pre-tax demand curve itself has shrunk, causing the price chargeable to decrease.

=== The more general case ===

In the more general case, Problems (2) and (3) can also arise. Specifically, the marginal revenue curve can even go below the quantity axis, and the marginal cost curve can be non-monotonic. In such a situation, we can have multiple locally optimal configurations. When a sales tax is imposed, a monopolist may switch from one optimum to another. An example is in the box.

{{quotation|To illustrate how this latter possibility could happen, imagine that one buyer of the good is willing to pay $3000 for a single unit while all subsequent buyers are willing to pay $2 per unit (up to the 10,000th unit). Imagine also that the marginal cost of producing the first unit is $500, while the marginal cost of producing all units thereafter is $1. The marginal revenue for the first unit is $3000, for the second unit is -$2996 (as the seller would get $2 for each of the two units sold but would effectively lose the ability to charge $3000 for the first unit), and for all units thereafter is $2. With no tax in place, the monopolist would choose to sell 10,000 units for $2 each, making a profit of $9501 ($20,000 - $9,999 - $500) rather than only selling one unit for $3000 (which would only make a profit of $2500). Now suppose a 300% sales tax is imposed. This effectively reduces all marginal revenue figures by 3/4ths. Selling units to customers only willing to pay $2 per unit would no longer be possible, as the pre-tax price could be $0.50 at maximum, and the marginal cost of producing units is $1. However, the buyer willing to pay $3000 could pay a pre-tax price of $750 and the monopolist could make a profit of $250 selling to that buyer alone. So the result of the sales tax in this (unusual) case would be to raise the pre-tax price of the unit from $2 to $750.}}

However, it turns out that any such optimum-switching ''must'' be in the direction of a market shrinkage. In other words, even if we see optimum-switching, where a monopolist switches strategy, it will ''still'' be true that:

* The quantity traded ''decreases'' relative to a world without sales tax.
* The post-tax market price ''increases'' relative to a world without sales tax.

The justification is a little complicated, since we can no longer rely on visual reasoning but must perform careful comparative statics.

==== The explanation for why quantity traded must decrease and post-tax market price must increase under the introduction of a sales tax: setup ====

Denote by <math>(P^*, Q^*)</math> the price and quantity chosen by the monopolist in a world without tax. Suppose <math>(P_1, Q_1)</math> is a (price, quantity) pair on the post-tax demand curve with <math>P_1 < P^*</math> (and therefore <math>Q_1 > Q^*</math>). We will show that the profit from the latter configuration under sales tax is less than the profit under the sales tax from the original optimal configuration <math>(P^*, Q^*)</math>.

First, we note that by the definition of optimality:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

==== Completion of proof for quantity-proportional case ====

In the quantity-proportional case, we have:

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> - Absolute tax burden under <math>(P^*, Q^*)</math>

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> - Absolute tax burden under <math>(P_1, Q_1)</math>

Since <math>Q_1 > Q^*</math>, we obtain that:

Absolute tax burden under <math>(P_1, Q_1)</math> > Absolute tax burden under <math>(P^*, Q^*)</math>

Combining these inequalities, we obtain that:

Profit with sales tax under <math>(P^*, Q^*)</math> > Profit with sales tax under <math>(P_1, Q_1)</math>

This provides the desired conclusion.

==== Completion of proof for revenue-proportional case ====

Denote by <math>x</math> the sales tax rate.

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P_1, Q_1)</math>)

We have that post-tax revenue equals the sum of cost and profit without sales tax. Simplifying a bit, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> = (Profit without sales tax under <math>(P^*, Q^*)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = (Profit without sales tax under <math>(P_1, Q_1)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P_1, Q_1)</math>)

Since <math>Q_1 > Q^*</math>, we have:

Total cost under <math>(P_1, Q_1)</math> <math>\ge</math> Total cost under <math>(P^*, Q^*)</math>

And also, by optimality of <math>(P^*, Q^*)</math>:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

Combining these inequalities with the equations above, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit with sales tax under <math>(P_1, Q_1)</math>

=== Conclusion ===

* The pre-tax price (as received by the monopolist) may increase or decrease. Note that this indeterminacy is present even in the case of an increasing marginal cost curve and decreasing marginal revenue curve. The expected proof breaks down due to the fact that the pre-tax price itself is not obtained by intersecting the two curves.
* The post-tax price (as seen by buyers) must increase. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* The quantity traded must decrease. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* In the special case that we are dealing with an increasing marginal cost curve and a decreasing marginal revenue curve, we can conclude that the marginal cost seen by the seller at the quantity that the seller produces goes ''down'' relative to what it was in a world without sales tax.

==Effect of sales tax that also affects complementary and substitute goods==

The analysis of the preceding section was based on the assumption that the sales tax is levied ''only'' on that particular good for which the analysis is being performed. This assumption is necessary to ensure that the other [[determinants of demand]] and [[determinants of supply]] are unaffected.

However, in real world situations, sales taxes are levied on large classes of goods, and changes to sales taxes are made simultaneously on large classes of goods. In particular, the sales tax may also affect the market prices of [[complementary good]]s and [[substitute good]]s. This means that we either need a more complicated [[partial equilibrium]] analysis (that somehow accounts for the prices of all the complementary and substitute goods) or an even more complicated [[general equilibrium]] analysis. This is extremely tricky. We consider some special cases to illustrate the kinds of effects that may be operational.

===Sales tax on two mutually substitute goods===

Consider two goods <math>A,B</math> that are partial substitutes for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side substitution. We can draw the following conclusions:

# The ''post-tax'' market prices for both <math>A</math> and <math>B</math> are higher than the market price in a world without taxes.
# The ''pre-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' pre-tax market prices are higher than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded. In other words, it cannot happen that the quantity traded for ''both'' goods rises relative to the world without taxes.

==== Justification for conclusion about post-tax market price ====

The conclusion for post-tax price is easiest to justify. We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are substitutes, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''outward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> increases.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the post-tax price on <math>B</math> increases relative to the market price when there was no sales tax on <math>B</math>.

Since both steps increase the post-tax price, the overall effect on the post-tax price is an increase. A similar logic applies to <math>A</math>.

==== Justification for conclusion about pre-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

===Sales tax on two mutually complementary goods===

Consider two goods <math>A,B</math> that are complements for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side complementation or substitution. We can draw the following conclusions:

# The ''pre-tax'' market prices for both <math>A</math> and <math>B</math> are lower than the market price in a world without taxes.
# The ''post-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must rise (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' post-tax market prices are lower than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''both'' <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded.

==== Justification for conclusion about pre-tax market price and quantity traded ====

We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are complements, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''inward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> and the quantity traded decrease.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the pre-tax price on <math>B</math> as well as the quantity traded decrease.

Since both steps decrease pre-tax market price and quantity traded, the overall effect on the pre-tax market price and quantity traded is a decrease. A similar logic applies to <math>A</math>.

==== Justification for conclusion about post-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

Effect of sales tax on market price and quantity traded

2020-05-30T21:37:25Z

Vipul: /* Extreme cases of elastic and inelastic supply and demand */

This article discusses the effect of a [[sales tax]] on the [[market price]] and equilibrium quantity traded for a good.

==Assumptions==

Prior to beginning the analysis, we note the following:

# A sales tax may be ''revenue-proportional'' (proportional to the price of the trade) or ''quantity-proportional'' (proportional to the quantity being traded). The quantitative analysis differs somewhat in both these cases. However, the qualitative analysis largely does not.
# In this article, we largely focus on the effect of the ''introduction'' of a sales tax, by performing [[comparative statics]] between a world without sales tax and a world with sales tax. Much of this analysis can also be applied to ''increases'' in sales tax. Conversely, a ''decrease'' in, or ''elimination'' of, a sales tax should have the opposite effect.
# For the most part, we focus on short run effects. In particular, this means that we assume the [[law of demand]] and [[law of supply]].
# We assume away the costs of compliance with the tax laws, and do not deal with issues of tax evasion.
# For the most part, we assume competitive markets (though we also discuss other cases). Hence, the [[law of one price]] is assumed to hold, so that we can talk of ''the'' market price.

==What we are interested in tracking==

In the world with no tax, there are two measures of interest:

* The [[market price]]
* The equilibrium quantity traded

In a word with tax, we are interested in tracking three measures:

* The pre-tax market price, i.e., the effective price that the seller gets to keep. This is to be compared to the [[market price]] in a world without sales tax.
* The post-tax market price, i.e., the effective price that the buyer pays. This is obtained by adding the sales tax to the pre-tax market price. This is to be compared to the [[market price]] in a world without sales tax.
* The equilibrium quantity traded. This is to be compared to the equilibrium quantity traded in a world without sales tax.

==Summary of several cases==
{| class="sortable" border="1"
! Case in question !! Conclusion about pre-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about post-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity (or quantities) traded (relative to a world without the tax)
|-
| single good provided in a perfectly competitive market || falls || rises || falls
|-
| single good provided by a monopoly firm || indeterminate || rises || falls
|-
| two partial substitute goods each sold in perfectly competitive markets || falls for at least one good || rises for both goods || falls for at least one good
|-
| two complementary goods each sold in perfectly competitive markets || falls for both goods || rises for at least one good || falls for both goods
|}

==Relationship with other analyses==

===Other effects of sales tax===

* [[Effect of sales tax on economic surplus]] builds on the analysis here to study how sales taxes affect the [[producer surplus]] and [[consumer surplus]] and how they result in a [[deadweight loss due to taxation]].

===Effect of subsidies===

Subsidies are taxes in negative, so their effects on market prices and quantity traded are the exact negatives of the effects of taxes.

However, their effects on economic surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on economic surplus]]
* [[Effect of price floor on economic surplus]]
* [[Effect of quantity ceiling on economic surplus]]

==Effect of sales tax on a single good with a competitive market==

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) for which we are drawing the supply and demand curves.

Note that the same analysis also works for comparative statics where we ''change'' the sales tax on only one class of goods.

===Analytical tools===

There are three kinds of diagrams that we draw to study the situation:

# Consider the world without sales tax. We can draw the usual supply and demand curves and do the usual analysis to find the market price and equilibrium quantity traded.
# Consider the world with sales tax. In this world, consider supply and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply and demand curves with respect to ''post-tax'' prices.

===Analysis with pre-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the pre-tax prices.

'''Supply curve''': The supply curve using pre-tax prices is expected to remain the ''same'' as the supply curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Demand curve''': The demand curve changes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve as follows:

{| class="sortable" border="1"
! Case !! What happens to the demand curve algebraically !! Pictorial depiction
|-
| price-propotional sales tax || For a revenue-proportional sales tax with a factor of <math>x</math>, the new demand function at a price of <math>p</math> equals the old demand function at a price of <math>p(1 + x)</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p(1 + x)</math>. The upshot is that the demand curve ''shrinks'' downward by a factor of <math>1 + x</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. [[File:Notaxvspretax.png|700px]]
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new demand function at a price of <math>p</math> is the old demand function at a price of <math>p + b</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p + b</math>. The upshot is that the demand curve shifts downward by a vertical distance of <math>b</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 0.4 price units/unit quanity sales tax (dashed purple). The original curve shrinks downward by 0.4 price units from its original level.[[File:Notaxvspretaxforquantityproportionalsalestax.png|700px]]
|}

The upshot is that the supply curve remains the same and the demand curve moves inward. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price drops. In other words, the new pre-tax market price is lower than the market price in the world without taxes.
* The equilibrium quantity traded falls.

The general picture of what happens, showing the contraction of demand curve and consequent move to a lower equilibrium price and lower quantity traded, is below.

[[File:Demandcontractionandmarketprice.png|700px]]

===Analysis with post-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the post-tax prices.

'''Demand curve''': The demand curve using post-tax prices is expected to remain the ''same'' as the demand curve in a world without taxes, because the price that the buyer sees is the post-tax price.

'''Supply curve''': The supply curve changes. In general, it moves upward. Assuming the law of supply, that is the same as moving inward, i.e., a ''contraction'' of the supply curve. Arithmetically, the new supply curve is related to the old supply curve as follows:

* For a revenue-proportional sales tax with a factor of <math>x</math>, the new supply function at a price of <math>p</math> equals the old supply function at a price of <math>p/(1 + x)</math>. The reason is that, as far as sellers are concerned, the effective price is the pre-tax price <math>p/(1 + x)</math>. The upshot is that the supply curve moves upward by a factor of <math>1 + x</math>.
* For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new supply function at a price of <math>p</math> is the old supply function at a price of <math>p - b</math>. The reason is that, as far as sellers are concerned, the effective price is <math>p - b</math>. The upshot is that the supply curve shifts upward by a vertical distance of <math>b</math>.

The upshot is that the supply curve contracts and the demand curve remains the same. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price rises. In other words, the new post-tax market price is higher than the market price in the world without taxes.
* The equilibrium quantity traded falls.

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price is lower than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the pre-tax curves).
* The post-tax market price is higher than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the post-tax curves).
* The equilibrium quantity traded is less than the equilibrium quantity traded in a world without the tax (this can be seen using ''either'' of the two comparative statics methods employed above).

===Extreme cases of elastic and inelastic supply and demand===

We consider some extreme cases. The first row describes the standard case, and subsequent rows describe extreme cases:

{| class="sortable" border="1"
! Assumption for [[price-elasticity of demand]] !! Assumption for [[price-elasticity of supply]] !! Conclusion about pre-tax market price (relative to market price in a world without the tax) !! Conclusion about post-tax market price (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity traded (relative to a world without the tax)
|-
| negative (satisfies the [[law of demand]]) || positive (satisfies the [[law of supply]]) || falls || rises || falls
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || falls || stays the same || falls
|-
| zero, i.e., a vertical demand curve. We also say that the demand is perfectly price-inelastic || positive (satisfies the [[law of supply]]) || stays the same || rises || stays the same
|-
| negative (satisfies the [[law of demand]]) || infinite, i.e., a horizontal supply curve, e.g., a [[constant cost industry]]. Alternatively, this also applies if the jurisdiction where sales tax is imposed is a small subjurisdiction of the economy and the pre-tax prices of the goods are determined by the world economy. || stays the same || rises || falls
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic. || falls || stays the same || stays the same
|}

===How price-elasticity affects the nature of the effect of sales tax===

The extent to which the sales tax affects the pre-tax price, post-tax price, and equilibrium quantity traded depends upon the [[price-elasticity of demand]] and [[price-elasticity of supply]]. The following are two general principles:

* Between demand and supply, the relatively more price-inelastic side absorbs more of the price burden of the sales tax. In other words, if demand is more inelastic, then the effect of the sales tax is largely seen in terms of an increase in the ''post-tax'' price. If supply is more inelastic, then the effect of the sales tax is largely seen in terms of a decrease in the ''pre-tax'' price. This is in keeping with the general principle attributed to Ricardo that rents are captured by the most inelastic side. Here, the rents are reversed in sign, but the principle stays the same.
* In general, the extent to which the equlibrium quantity traded is affected is negatively related to the price-elasticities of both demand and supply. In other words, if we reduce the price-elasticity of either demand or supply, the sensitivity of the equilibrium quantity traded to the sales tax reduces. In particular, if either demand or supply is perfectly price-inelastic, the equilibrium quantity traded is independent of the sales tax.

==Effect of sales tax on a single good with a monopolist-controlled market==

This section assumes familiarity with the key conclusions of [[determination of price and quantity supplied by monopolistic firm in the short run]].

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) that is supplied by a single seller (the monopolist) that seeks to maximizing profit.

The marginal revenue from the sale of a good equals <math>d(PQ)/dQ</math>, as <math>PQ</math> is revenue and we are interested in the rate of change of revenue as quantity changes. Using the [[calculus:product rule for differentiation|product rule for differentiation]], we find that <math>MR = Q*dP/dQ + P</math>. As explained previously, we expect that dP/dQ is negative in accordance with the law of demand. As such, marginal revenue is less than the price paid, and it may even be zero or negative.

Unlike the perfectly competitive market case discussed previously, we do not perform two separate analyses (pre-tax and post-tax). Rather, we consider various pre-tax and post-tax curves together. The reason is that a "post-tax supply curve" does not make sense in the monopoly case. Also, the analysis is complicated enough as it is, so creating two versions of it isn't worth it!

=== Key curves under consideration ===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''Pre-tax marginal cost curve''': The marginal cost curve using pre-tax prices is expected to remain the ''same'' as the marginal cost curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Pre-tax demand curve''': The pre-tax demand curve changes relative to what it is in a world without taxes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve either through proportional shrinkage toward the quantity axis (for a revenue-proportional sales tax) or through a downward translation toward the quantity by the amount of the tax on unit quantity. For more, see the [[#Analysis of pre-tax prices|analysis of pre-tax prices section]] for the perfectly competitive case.

'''Pre-tax marginal revenue curve''': The pre-tax marginal revenue curve changes relative to what it is in a world without taxes. Qualitatively, the way it changes is the ''same'' as the way the demand curve changes. For a revenue-proportional sales tax, it shrinks proportionally toward the quantity axis. For a quantity-proportional sales tax, it is translated downward. This can be inferred easily from the definition of marginal revenue as <math>d(PQ)/dQ</math>, and the way derivatives interact with addition and scalar multiplication (specifically, [[calculus:differentiation is linear|the fact that differentiation is linear]]).

'''Post-tax demand curve''' (demand curve as experienced by buyers): This remains the same as it would be in a world without taxes.

The upshot: the pre-tax marginal cost curve remains unchanged and the pre-tax marginal revenue curve shrinks downward. We now discuss the implications this has for our conclusions around pre-tax price and quantity traded. ''Prima facie'', this looks a lot like the analysis so far with pre-tax prices for a perfectly competitive market, with marginal revenue curve replacing demand curve and marginal cost curve replacing supply curve. However, there are three subtleties that complicate the picture

# The (price, quantity) pair at which trades actually occur is ''not'' the point of intersection of the marginal cost and marginal revenue curves. Rather, the ''quantity'' is determined by the point of intersection, but the price is determined by looking at the demand curve. '''This distinction alone causes some of our conclusions to break down'''.
# Unlike the demand curve in a perfectly competitive market, the marginal revenue curve is not necessarily downward-sloping. In fact, it need not even always be above the quantity axis! It can have multiple local maxima and local minima. The key distinction is that marginal revenue is affected by a combination of two factors pulling in opposite direction: expansion of the market, and reduction in the price that can be charged to buyers with the highest reservation prices.
# Unlike the supply curve in a perfectly competitive market, the marginal cost curve is not necessarily upward-sloping. It can have multiple local maxima and local minima. The key distinction with the competitive case that the supply curve for a seller in a competitive market is not the entire marginal cost curve but only a ''part of it that slopes upward''. For more, see [[determination of quantity supplied by firm in perfectly competitive market in the short run]].

There are a wide range of cases where we can make assumptions to eliminate problems (2) and (3). However, problem (1) remains.

===The easy case: marginal cost curve increasing everywhere, marginal revenue curve decreasing everywhere===

This is the easy case where, of the three problems mentioned, ''only'' Problem (1) applies.

In the case that the marginal cost curve is increasing throughout the relevant range (outside of which no optima can possibly exist) and the marginal revenue curve is decreasing throughout the relevant range, our pictorial analysis works as in the perfectly competitive case. In particular:

* Since the marginal revenue curve has shrunk downward and leftward, the new point of intersection of the curves has a lower price and lower quantity traded. Thus, the quantity traded is lower than in a world without sales tax. Also, the pre-tax marginal cost experienced by the seller is lower than in a world without sales tax.
* The ''post-tax price charged to buyers'' is higher than what it would be in a world without sales tax. This is because the quantity traded is lower, so referencing the post-tax demand curve (which is the ''same'' as the original demand curve) we get a higher price.
* ''However'', even in this case, the effect on the pre-tax price is ambiguous. This is because there are two competing effects. On the one hand, the quantity traded is lower, causing the maximum price chargeable to increase. On the other hand, the pre-tax demand curve itself has shrunk, causing the price chargeable to decrease.

=== The more general case ===

In the more general case, Problems (2) and (3) can also arise. Specifically, the marginal revenue curve can even go below the quantity axis, and the marginal cost curve can be non-monotonic. In such a situation, we can have multiple locally optimal configurations. When a sales tax is imposed, a monopolist may switch from one optimum to another. An example is in the box.

{{quotation|To illustrate how this latter possibility could happen, imagine that one buyer of the good is willing to pay $3000 for a single unit while all subsequent buyers are willing to pay $2 per unit (up to the 10,000th unit). Imagine also that the marginal cost of producing the first unit is $500, while the marginal cost of producing all units thereafter is $1. The marginal revenue for the first unit is $3000, for the second unit is -$2996 (as the seller would get $2 for each of the two units sold but would effectively lose the ability to charge $3000 for the first unit), and for all units thereafter is $2. With no tax in place, the monopolist would choose to sell 10,000 units for $2 each, making a profit of $9501 ($20,000 - $9,999 - $500) rather than only selling one unit for $3000 (which would only make a profit of $2500). Now suppose a 300% sales tax is imposed. This effectively reduces all marginal revenue figures by 3/4ths. Selling units to customers only willing to pay $2 per unit would no longer be possible, as the pre-tax price could be $0.50 at maximum, and the marginal cost of producing units is $1. However, the buyer willing to pay $3000 could pay a pre-tax price of $750 and the monopolist could make a profit of $250 selling to that buyer alone. So the result of the sales tax in this (unusual) case would be to raise the pre-tax price of the unit from $2 to $750.}}

However, it turns out that any such optimum-switching ''must'' be in the direction of a market shrinkage. In other words, even if we see optimum-switching, where a monopolist switches strategy, it will ''still'' be true that:

* The quantity traded ''decreases'' relative to a world without sales tax.
* The post-tax market price ''increases'' relative to a world without sales tax.

The justification is a little complicated, since we can no longer rely on visual reasoning but must perform careful comparative statics.

==== The explanation for why quantity traded must decrease and post-tax market price must increase under the introduction of a sales tax: setup ====

Denote by <math>(P^*, Q^*)</math> the price and quantity chosen by the monopolist in a world without tax. Suppose <math>(P_1, Q_1)</math> is a (price, quantity) pair on the post-tax demand curve with <math>P_1 < P^*</math> (and therefore <math>Q_1 > Q^*</math>). We will show that the profit from the latter configuration under sales tax is less than the profit under the sales tax from the original optimal configuration <math>(P^*, Q^*)</math>.

First, we note that by the definition of optimality:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

==== Completion of proof for quantity-proportional case ====

In the quantity-proportional case, we have:

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> - Absolute tax burden under <math>(P^*, Q^*)</math>

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> - Absolute tax burden under <math>(P_1, Q_1)</math>

Since <math>Q_1 > Q^*</math>, we obtain that:

Absolute tax burden under <math>(P_1, Q_1)</math> > Absolute tax burden under <math>(P^*, Q^*)</math>

Combining these inequalities, we obtain that:

Profit with sales tax under <math>(P^*, Q^*)</math> > Profit with sales tax under <math>(P_1, Q_1)</math>

This provides the desired conclusion.

==== Completion of proof for revenue-proportional case ====

Denote by <math>x</math> the sales tax rate.

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P_1, Q_1)</math>)

We have that post-tax revenue equals the sum of cost and profit without sales tax. Simplifying a bit, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> = (Profit without sales tax under <math>(P^*, Q^*)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = (Profit without sales tax under <math>(P_1, Q_1)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P_1, Q_1)</math>)

Since <math>Q_1 > Q^*</math>, we have:

Total cost under <math>(P_1, Q_1)</math> <math>\ge</math> Total cost under <math>(P^*, Q^*)</math>

And also, by optimality of <math>(P^*, Q^*)</math>:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

Combining these inequalities with the equations above, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit with sales tax under <math>(P_1, Q_1)</math>

=== Conclusion ===

* The pre-tax price (as received by the monopolist) may increase or decrease. Note that this indeterminacy is present even in the case of an increasing marginal cost curve and decreasing marginal revenue curve. The expected proof breaks down due to the fact that the pre-tax price itself is not obtained by intersecting the two curves.
* The post-tax price (as seen by buyers) must increase. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* The quantity traded must decrease. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* In the special case that we are dealing with an increasing marginal cost curve and a decreasing marginal revenue curve, we can conclude that the marginal cost seen by the seller at the quantity that the seller produces goes ''down'' relative to what it was in a world without sales tax.

==Effect of sales tax that also affects complementary and substitute goods==

The analysis of the preceding section was based on the assumption that the sales tax is levied ''only'' on that particular good for which the analysis is being performed. This assumption is necessary to ensure that the other [[determinants of demand]] and [[determinants of supply]] are unaffected.

However, in real world situations, sales taxes are levied on large classes of goods, and changes to sales taxes are made simultaneously on large classes of goods. In particular, the sales tax may also affect the market prices of [[complementary good]]s and [[substitute good]]s. This means that we either need a more complicated [[partial equilibrium]] analysis (that somehow accounts for the prices of all the complementary and substitute goods) or an even more complicated [[general equilibrium]] analysis. This is extremely tricky. We consider some special cases to illustrate the kinds of effects that may be operational.

===Sales tax on two mutually substitute goods===

Consider two goods <math>A,B</math> that are partial substitutes for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side substitution. We can draw the following conclusions:

# The ''post-tax'' market prices for both <math>A</math> and <math>B</math> are higher than the market price in a world without taxes.
# The ''pre-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' pre-tax market prices are higher than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded. In other words, it cannot happen that the quantity traded for ''both'' goods rises relative to the world without taxes.

==== Justification for conclusion about post-tax market price ====

The conclusion for post-tax price is easiest to justify. We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are substitutes, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''outward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> increases.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the post-tax price on <math>B</math> increases relative to the market price when there was no sales tax on <math>B</math>.

Since both steps increase the post-tax price, the overall effect on the post-tax price is an increase. A similar logic applies to <math>A</math>.

==== Justification for conclusion about pre-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

===Sales tax on two mutually complementary goods===

Consider two goods <math>A,B</math> that are complements for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side complementation or substitution. We can draw the following conclusions:

# The ''pre-tax'' market prices for both <math>A</math> and <math>B</math> are lower than the market price in a world without taxes.
# The ''post-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must rise (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' post-tax market prices are lower than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''both'' <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded.

==== Justification for conclusion about pre-tax market price and quantity traded ====

We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are complements, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''inward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> and the quantity traded decrease.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the pre-tax price on <math>B</math> as well as the quantity traded decrease.

Since both steps decrease pre-tax market price and quantity traded, the overall effect on the pre-tax market price and quantity traded is a decrease. A similar logic applies to <math>A</math>.

==== Justification for conclusion about post-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

Effect of sales tax on market price and quantity traded

2020-05-30T21:36:38Z

Vipul: /* Combined analysis and conclusions */

This article discusses the effect of a [[sales tax]] on the [[market price]] and equilibrium quantity traded for a good.

==Assumptions==

Prior to beginning the analysis, we note the following:

# A sales tax may be ''revenue-proportional'' (proportional to the price of the trade) or ''quantity-proportional'' (proportional to the quantity being traded). The quantitative analysis differs somewhat in both these cases. However, the qualitative analysis largely does not.
# In this article, we largely focus on the effect of the ''introduction'' of a sales tax, by performing [[comparative statics]] between a world without sales tax and a world with sales tax. Much of this analysis can also be applied to ''increases'' in sales tax. Conversely, a ''decrease'' in, or ''elimination'' of, a sales tax should have the opposite effect.
# For the most part, we focus on short run effects. In particular, this means that we assume the [[law of demand]] and [[law of supply]].
# We assume away the costs of compliance with the tax laws, and do not deal with issues of tax evasion.
# For the most part, we assume competitive markets (though we also discuss other cases). Hence, the [[law of one price]] is assumed to hold, so that we can talk of ''the'' market price.

==What we are interested in tracking==

In the world with no tax, there are two measures of interest:

* The [[market price]]
* The equilibrium quantity traded

In a word with tax, we are interested in tracking three measures:

* The pre-tax market price, i.e., the effective price that the seller gets to keep. This is to be compared to the [[market price]] in a world without sales tax.
* The post-tax market price, i.e., the effective price that the buyer pays. This is obtained by adding the sales tax to the pre-tax market price. This is to be compared to the [[market price]] in a world without sales tax.
* The equilibrium quantity traded. This is to be compared to the equilibrium quantity traded in a world without sales tax.

==Summary of several cases==
{| class="sortable" border="1"
! Case in question !! Conclusion about pre-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about post-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity (or quantities) traded (relative to a world without the tax)
|-
| single good provided in a perfectly competitive market || falls || rises || falls
|-
| single good provided by a monopoly firm || indeterminate || rises || falls
|-
| two partial substitute goods each sold in perfectly competitive markets || falls for at least one good || rises for both goods || falls for at least one good
|-
| two complementary goods each sold in perfectly competitive markets || falls for both goods || rises for at least one good || falls for both goods
|}

==Relationship with other analyses==

===Other effects of sales tax===

* [[Effect of sales tax on economic surplus]] builds on the analysis here to study how sales taxes affect the [[producer surplus]] and [[consumer surplus]] and how they result in a [[deadweight loss due to taxation]].

===Effect of subsidies===

Subsidies are taxes in negative, so their effects on market prices and quantity traded are the exact negatives of the effects of taxes.

However, their effects on economic surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on economic surplus]]
* [[Effect of price floor on economic surplus]]
* [[Effect of quantity ceiling on economic surplus]]

==Effect of sales tax on a single good with a competitive market==

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) for which we are drawing the supply and demand curves.

Note that the same analysis also works for comparative statics where we ''change'' the sales tax on only one class of goods.

===Analytical tools===

There are three kinds of diagrams that we draw to study the situation:

# Consider the world without sales tax. We can draw the usual supply and demand curves and do the usual analysis to find the market price and equilibrium quantity traded.
# Consider the world with sales tax. In this world, consider supply and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply and demand curves with respect to ''post-tax'' prices.

===Analysis with pre-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the pre-tax prices.

'''Supply curve''': The supply curve using pre-tax prices is expected to remain the ''same'' as the supply curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Demand curve''': The demand curve changes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve as follows:

{| class="sortable" border="1"
! Case !! What happens to the demand curve algebraically !! Pictorial depiction
|-
| price-propotional sales tax || For a revenue-proportional sales tax with a factor of <math>x</math>, the new demand function at a price of <math>p</math> equals the old demand function at a price of <math>p(1 + x)</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p(1 + x)</math>. The upshot is that the demand curve ''shrinks'' downward by a factor of <math>1 + x</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. [[File:Notaxvspretax.png|700px]]
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new demand function at a price of <math>p</math> is the old demand function at a price of <math>p + b</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p + b</math>. The upshot is that the demand curve shifts downward by a vertical distance of <math>b</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 0.4 price units/unit quanity sales tax (dashed purple). The original curve shrinks downward by 0.4 price units from its original level.[[File:Notaxvspretaxforquantityproportionalsalestax.png|700px]]
|}

The upshot is that the supply curve remains the same and the demand curve moves inward. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price drops. In other words, the new pre-tax market price is lower than the market price in the world without taxes.
* The equilibrium quantity traded falls.

The general picture of what happens, showing the contraction of demand curve and consequent move to a lower equilibrium price and lower quantity traded, is below.

[[File:Demandcontractionandmarketprice.png|700px]]

===Analysis with post-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the post-tax prices.

'''Demand curve''': The demand curve using post-tax prices is expected to remain the ''same'' as the demand curve in a world without taxes, because the price that the buyer sees is the post-tax price.

'''Supply curve''': The supply curve changes. In general, it moves upward. Assuming the law of supply, that is the same as moving inward, i.e., a ''contraction'' of the supply curve. Arithmetically, the new supply curve is related to the old supply curve as follows:

* For a revenue-proportional sales tax with a factor of <math>x</math>, the new supply function at a price of <math>p</math> equals the old supply function at a price of <math>p/(1 + x)</math>. The reason is that, as far as sellers are concerned, the effective price is the pre-tax price <math>p/(1 + x)</math>. The upshot is that the supply curve moves upward by a factor of <math>1 + x</math>.
* For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new supply function at a price of <math>p</math> is the old supply function at a price of <math>p - b</math>. The reason is that, as far as sellers are concerned, the effective price is <math>p - b</math>. The upshot is that the supply curve shifts upward by a vertical distance of <math>b</math>.

The upshot is that the supply curve contracts and the demand curve remains the same. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price rises. In other words, the new post-tax market price is higher than the market price in the world without taxes.
* The equilibrium quantity traded falls.

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price is lower than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the pre-tax curves).
* The post-tax market price is higher than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the post-tax curves).
* The equilibrium quantity traded is less than the equilibrium quantity traded in a world without the tax (this can be seen using ''either'' of the two comparative statics methods employed above).

===Extreme cases of elastic and inelastic supply and demand===

We consider some extreme cases. The first row describes the standard case, and subsequent rows describe extreme cases:

{| class="sortable" border="1"
! Assumption for [[price-elasticity of demand]] !! Assumption for [[price-elasticity of supply]] !! Conclusion about pre-tax market price (relative to market price in a world without the tax) !! Conclusion about post-tax market price (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity traded (relative to a world without the tax)
|-
| negative (satisfies the [[law of demand]]) || positive (satisfies the [[law of supply]]) || falls || rises || falls
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || falls || stays the same || falls
|-
| zero, i.e., a vertical demand curve. We also say that the demand is perfectly price-inelastic || positive (satisfies the [[law of supply]]) || stays the same || rises || stays the same
|-
| negative (satisfies the [[law of demand]]) || infinite, i.e., a horizontal supply curve, e.g., a [[constant cost industry]]. Alternatively, this also applies if the jurisdiction where sales tax is imposed is a small subjurisdiction of the economy and the pre-tax prices of the goods are determined by the world economy. || stays the same || rises || falls
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic || falls || stays the same || stays the same
|}

===How price-elasticity affects the nature of the effect of sales tax===

The extent to which the sales tax affects the pre-tax price, post-tax price, and equilibrium quantity traded depends upon the [[price-elasticity of demand]] and [[price-elasticity of supply]]. The following are two general principles:

* Between demand and supply, the relatively more price-inelastic side absorbs more of the price burden of the sales tax. In other words, if demand is more inelastic, then the effect of the sales tax is largely seen in terms of an increase in the ''post-tax'' price. If supply is more inelastic, then the effect of the sales tax is largely seen in terms of a decrease in the ''pre-tax'' price. This is in keeping with the general principle attributed to Ricardo that rents are captured by the most inelastic side. Here, the rents are reversed in sign, but the principle stays the same.
* In general, the extent to which the equlibrium quantity traded is affected is negatively related to the price-elasticities of both demand and supply. In other words, if we reduce the price-elasticity of either demand or supply, the sensitivity of the equilibrium quantity traded to the sales tax reduces. In particular, if either demand or supply is perfectly price-inelastic, the equilibrium quantity traded is independent of the sales tax.

==Effect of sales tax on a single good with a monopolist-controlled market==

This section assumes familiarity with the key conclusions of [[determination of price and quantity supplied by monopolistic firm in the short run]].

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) that is supplied by a single seller (the monopolist) that seeks to maximizing profit.

The marginal revenue from the sale of a good equals <math>d(PQ)/dQ</math>, as <math>PQ</math> is revenue and we are interested in the rate of change of revenue as quantity changes. Using the [[calculus:product rule for differentiation|product rule for differentiation]], we find that <math>MR = Q*dP/dQ + P</math>. As explained previously, we expect that dP/dQ is negative in accordance with the law of demand. As such, marginal revenue is less than the price paid, and it may even be zero or negative.

Unlike the perfectly competitive market case discussed previously, we do not perform two separate analyses (pre-tax and post-tax). Rather, we consider various pre-tax and post-tax curves together. The reason is that a "post-tax supply curve" does not make sense in the monopoly case. Also, the analysis is complicated enough as it is, so creating two versions of it isn't worth it!

=== Key curves under consideration ===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''Pre-tax marginal cost curve''': The marginal cost curve using pre-tax prices is expected to remain the ''same'' as the marginal cost curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Pre-tax demand curve''': The pre-tax demand curve changes relative to what it is in a world without taxes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve either through proportional shrinkage toward the quantity axis (for a revenue-proportional sales tax) or through a downward translation toward the quantity by the amount of the tax on unit quantity. For more, see the [[#Analysis of pre-tax prices|analysis of pre-tax prices section]] for the perfectly competitive case.

'''Pre-tax marginal revenue curve''': The pre-tax marginal revenue curve changes relative to what it is in a world without taxes. Qualitatively, the way it changes is the ''same'' as the way the demand curve changes. For a revenue-proportional sales tax, it shrinks proportionally toward the quantity axis. For a quantity-proportional sales tax, it is translated downward. This can be inferred easily from the definition of marginal revenue as <math>d(PQ)/dQ</math>, and the way derivatives interact with addition and scalar multiplication (specifically, [[calculus:differentiation is linear|the fact that differentiation is linear]]).

'''Post-tax demand curve''' (demand curve as experienced by buyers): This remains the same as it would be in a world without taxes.

The upshot: the pre-tax marginal cost curve remains unchanged and the pre-tax marginal revenue curve shrinks downward. We now discuss the implications this has for our conclusions around pre-tax price and quantity traded. ''Prima facie'', this looks a lot like the analysis so far with pre-tax prices for a perfectly competitive market, with marginal revenue curve replacing demand curve and marginal cost curve replacing supply curve. However, there are three subtleties that complicate the picture

# The (price, quantity) pair at which trades actually occur is ''not'' the point of intersection of the marginal cost and marginal revenue curves. Rather, the ''quantity'' is determined by the point of intersection, but the price is determined by looking at the demand curve. '''This distinction alone causes some of our conclusions to break down'''.
# Unlike the demand curve in a perfectly competitive market, the marginal revenue curve is not necessarily downward-sloping. In fact, it need not even always be above the quantity axis! It can have multiple local maxima and local minima. The key distinction is that marginal revenue is affected by a combination of two factors pulling in opposite direction: expansion of the market, and reduction in the price that can be charged to buyers with the highest reservation prices.
# Unlike the supply curve in a perfectly competitive market, the marginal cost curve is not necessarily upward-sloping. It can have multiple local maxima and local minima. The key distinction with the competitive case that the supply curve for a seller in a competitive market is not the entire marginal cost curve but only a ''part of it that slopes upward''. For more, see [[determination of quantity supplied by firm in perfectly competitive market in the short run]].

There are a wide range of cases where we can make assumptions to eliminate problems (2) and (3). However, problem (1) remains.

===The easy case: marginal cost curve increasing everywhere, marginal revenue curve decreasing everywhere===

This is the easy case where, of the three problems mentioned, ''only'' Problem (1) applies.

In the case that the marginal cost curve is increasing throughout the relevant range (outside of which no optima can possibly exist) and the marginal revenue curve is decreasing throughout the relevant range, our pictorial analysis works as in the perfectly competitive case. In particular:

* Since the marginal revenue curve has shrunk downward and leftward, the new point of intersection of the curves has a lower price and lower quantity traded. Thus, the quantity traded is lower than in a world without sales tax. Also, the pre-tax marginal cost experienced by the seller is lower than in a world without sales tax.
* The ''post-tax price charged to buyers'' is higher than what it would be in a world without sales tax. This is because the quantity traded is lower, so referencing the post-tax demand curve (which is the ''same'' as the original demand curve) we get a higher price.
* ''However'', even in this case, the effect on the pre-tax price is ambiguous. This is because there are two competing effects. On the one hand, the quantity traded is lower, causing the maximum price chargeable to increase. On the other hand, the pre-tax demand curve itself has shrunk, causing the price chargeable to decrease.

=== The more general case ===

In the more general case, Problems (2) and (3) can also arise. Specifically, the marginal revenue curve can even go below the quantity axis, and the marginal cost curve can be non-monotonic. In such a situation, we can have multiple locally optimal configurations. When a sales tax is imposed, a monopolist may switch from one optimum to another. An example is in the box.

{{quotation|To illustrate how this latter possibility could happen, imagine that one buyer of the good is willing to pay $3000 for a single unit while all subsequent buyers are willing to pay $2 per unit (up to the 10,000th unit). Imagine also that the marginal cost of producing the first unit is $500, while the marginal cost of producing all units thereafter is $1. The marginal revenue for the first unit is $3000, for the second unit is -$2996 (as the seller would get $2 for each of the two units sold but would effectively lose the ability to charge $3000 for the first unit), and for all units thereafter is $2. With no tax in place, the monopolist would choose to sell 10,000 units for $2 each, making a profit of $9501 ($20,000 - $9,999 - $500) rather than only selling one unit for $3000 (which would only make a profit of $2500). Now suppose a 300% sales tax is imposed. This effectively reduces all marginal revenue figures by 3/4ths. Selling units to customers only willing to pay $2 per unit would no longer be possible, as the pre-tax price could be $0.50 at maximum, and the marginal cost of producing units is $1. However, the buyer willing to pay $3000 could pay a pre-tax price of $750 and the monopolist could make a profit of $250 selling to that buyer alone. So the result of the sales tax in this (unusual) case would be to raise the pre-tax price of the unit from $2 to $750.}}

However, it turns out that any such optimum-switching ''must'' be in the direction of a market shrinkage. In other words, even if we see optimum-switching, where a monopolist switches strategy, it will ''still'' be true that:

* The quantity traded ''decreases'' relative to a world without sales tax.
* The post-tax market price ''increases'' relative to a world without sales tax.

The justification is a little complicated, since we can no longer rely on visual reasoning but must perform careful comparative statics.

==== The explanation for why quantity traded must decrease and post-tax market price must increase under the introduction of a sales tax: setup ====

Denote by <math>(P^*, Q^*)</math> the price and quantity chosen by the monopolist in a world without tax. Suppose <math>(P_1, Q_1)</math> is a (price, quantity) pair on the post-tax demand curve with <math>P_1 < P^*</math> (and therefore <math>Q_1 > Q^*</math>). We will show that the profit from the latter configuration under sales tax is less than the profit under the sales tax from the original optimal configuration <math>(P^*, Q^*)</math>.

First, we note that by the definition of optimality:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

==== Completion of proof for quantity-proportional case ====

In the quantity-proportional case, we have:

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> - Absolute tax burden under <math>(P^*, Q^*)</math>

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> - Absolute tax burden under <math>(P_1, Q_1)</math>

Since <math>Q_1 > Q^*</math>, we obtain that:

Absolute tax burden under <math>(P_1, Q_1)</math> > Absolute tax burden under <math>(P^*, Q^*)</math>

Combining these inequalities, we obtain that:

Profit with sales tax under <math>(P^*, Q^*)</math> > Profit with sales tax under <math>(P_1, Q_1)</math>

This provides the desired conclusion.

==== Completion of proof for revenue-proportional case ====

Denote by <math>x</math> the sales tax rate.

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P_1, Q_1)</math>)

We have that post-tax revenue equals the sum of cost and profit without sales tax. Simplifying a bit, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> = (Profit without sales tax under <math>(P^*, Q^*)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = (Profit without sales tax under <math>(P_1, Q_1)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P_1, Q_1)</math>)

Since <math>Q_1 > Q^*</math>, we have:

Total cost under <math>(P_1, Q_1)</math> <math>\ge</math> Total cost under <math>(P^*, Q^*)</math>

And also, by optimality of <math>(P^*, Q^*)</math>:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

Combining these inequalities with the equations above, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit with sales tax under <math>(P_1, Q_1)</math>

=== Conclusion ===

* The pre-tax price (as received by the monopolist) may increase or decrease. Note that this indeterminacy is present even in the case of an increasing marginal cost curve and decreasing marginal revenue curve. The expected proof breaks down due to the fact that the pre-tax price itself is not obtained by intersecting the two curves.
* The post-tax price (as seen by buyers) must increase. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* The quantity traded must decrease. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* In the special case that we are dealing with an increasing marginal cost curve and a decreasing marginal revenue curve, we can conclude that the marginal cost seen by the seller at the quantity that the seller produces goes ''down'' relative to what it was in a world without sales tax.

==Effect of sales tax that also affects complementary and substitute goods==

The analysis of the preceding section was based on the assumption that the sales tax is levied ''only'' on that particular good for which the analysis is being performed. This assumption is necessary to ensure that the other [[determinants of demand]] and [[determinants of supply]] are unaffected.

However, in real world situations, sales taxes are levied on large classes of goods, and changes to sales taxes are made simultaneously on large classes of goods. In particular, the sales tax may also affect the market prices of [[complementary good]]s and [[substitute good]]s. This means that we either need a more complicated [[partial equilibrium]] analysis (that somehow accounts for the prices of all the complementary and substitute goods) or an even more complicated [[general equilibrium]] analysis. This is extremely tricky. We consider some special cases to illustrate the kinds of effects that may be operational.

===Sales tax on two mutually substitute goods===

Consider two goods <math>A,B</math> that are partial substitutes for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side substitution. We can draw the following conclusions:

# The ''post-tax'' market prices for both <math>A</math> and <math>B</math> are higher than the market price in a world without taxes.
# The ''pre-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' pre-tax market prices are higher than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded. In other words, it cannot happen that the quantity traded for ''both'' goods rises relative to the world without taxes.

==== Justification for conclusion about post-tax market price ====

The conclusion for post-tax price is easiest to justify. We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are substitutes, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''outward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> increases.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the post-tax price on <math>B</math> increases relative to the market price when there was no sales tax on <math>B</math>.

Since both steps increase the post-tax price, the overall effect on the post-tax price is an increase. A similar logic applies to <math>A</math>.

==== Justification for conclusion about pre-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

===Sales tax on two mutually complementary goods===

Consider two goods <math>A,B</math> that are complements for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side complementation or substitution. We can draw the following conclusions:

# The ''pre-tax'' market prices for both <math>A</math> and <math>B</math> are lower than the market price in a world without taxes.
# The ''post-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must rise (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' post-tax market prices are lower than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''both'' <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded.

==== Justification for conclusion about pre-tax market price and quantity traded ====

We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are complements, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''inward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> and the quantity traded decrease.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the pre-tax price on <math>B</math> as well as the quantity traded decrease.

Since both steps decrease pre-tax market price and quantity traded, the overall effect on the pre-tax market price and quantity traded is a decrease. A similar logic applies to <math>A</math>.

==== Justification for conclusion about post-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

Effect of sales tax on market price and quantity traded

2020-05-30T21:33:42Z

Vipul: /* Summary of several cases */

This article discusses the effect of a [[sales tax]] on the [[market price]] and equilibrium quantity traded for a good.

==Assumptions==

Prior to beginning the analysis, we note the following:

# A sales tax may be ''revenue-proportional'' (proportional to the price of the trade) or ''quantity-proportional'' (proportional to the quantity being traded). The quantitative analysis differs somewhat in both these cases. However, the qualitative analysis largely does not.
# In this article, we largely focus on the effect of the ''introduction'' of a sales tax, by performing [[comparative statics]] between a world without sales tax and a world with sales tax. Much of this analysis can also be applied to ''increases'' in sales tax. Conversely, a ''decrease'' in, or ''elimination'' of, a sales tax should have the opposite effect.
# For the most part, we focus on short run effects. In particular, this means that we assume the [[law of demand]] and [[law of supply]].
# We assume away the costs of compliance with the tax laws, and do not deal with issues of tax evasion.
# For the most part, we assume competitive markets (though we also discuss other cases). Hence, the [[law of one price]] is assumed to hold, so that we can talk of ''the'' market price.

==What we are interested in tracking==

In the world with no tax, there are two measures of interest:

* The [[market price]]
* The equilibrium quantity traded

In a word with tax, we are interested in tracking three measures:

* The pre-tax market price, i.e., the effective price that the seller gets to keep. This is to be compared to the [[market price]] in a world without sales tax.
* The post-tax market price, i.e., the effective price that the buyer pays. This is obtained by adding the sales tax to the pre-tax market price. This is to be compared to the [[market price]] in a world without sales tax.
* The equilibrium quantity traded. This is to be compared to the equilibrium quantity traded in a world without sales tax.

==Summary of several cases==
{| class="sortable" border="1"
! Case in question !! Conclusion about pre-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about post-tax market price(s) (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity (or quantities) traded (relative to a world without the tax)
|-
| single good provided in a perfectly competitive market || falls || rises || falls
|-
| single good provided by a monopoly firm || indeterminate || rises || falls
|-
| two partial substitute goods each sold in perfectly competitive markets || falls for at least one good || rises for both goods || falls for at least one good
|-
| two complementary goods each sold in perfectly competitive markets || falls for both goods || rises for at least one good || falls for both goods
|}

==Relationship with other analyses==

===Other effects of sales tax===

* [[Effect of sales tax on economic surplus]] builds on the analysis here to study how sales taxes affect the [[producer surplus]] and [[consumer surplus]] and how they result in a [[deadweight loss due to taxation]].

===Effect of subsidies===

Subsidies are taxes in negative, so their effects on market prices and quantity traded are the exact negatives of the effects of taxes.

However, their effects on economic surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on economic surplus]]
* [[Effect of price floor on economic surplus]]
* [[Effect of quantity ceiling on economic surplus]]

==Effect of sales tax on a single good with a competitive market==

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) for which we are drawing the supply and demand curves.

Note that the same analysis also works for comparative statics where we ''change'' the sales tax on only one class of goods.

===Analytical tools===

There are three kinds of diagrams that we draw to study the situation:

# Consider the world without sales tax. We can draw the usual supply and demand curves and do the usual analysis to find the market price and equilibrium quantity traded.
# Consider the world with sales tax. In this world, consider supply and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply and demand curves with respect to ''post-tax'' prices.

===Analysis with pre-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the pre-tax prices.

'''Supply curve''': The supply curve using pre-tax prices is expected to remain the ''same'' as the supply curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Demand curve''': The demand curve changes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve as follows:

{| class="sortable" border="1"
! Case !! What happens to the demand curve algebraically !! Pictorial depiction
|-
| price-propotional sales tax || For a revenue-proportional sales tax with a factor of <math>x</math>, the new demand function at a price of <math>p</math> equals the old demand function at a price of <math>p(1 + x)</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p(1 + x)</math>. The upshot is that the demand curve ''shrinks'' downward by a factor of <math>1 + x</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. [[File:Notaxvspretax.png|700px]]
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new demand function at a price of <math>p</math> is the old demand function at a price of <math>p + b</math>. The reason is that, as far as buyers are concerned, the effective price is <math>p + b</math>. The upshot is that the demand curve shifts downward by a vertical distance of <math>b</math>. || An example picture is below, comparing the no-tax demand curve (solid blue) with the pre-tax demand curve for a 0.4 price units/unit quanity sales tax (dashed purple). The original curve shrinks downward by 0.4 price units from its original level.[[File:Notaxvspretaxforquantityproportionalsalestax.png|700px]]
|}

The upshot is that the supply curve remains the same and the demand curve moves inward. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price drops. In other words, the new pre-tax market price is lower than the market price in the world without taxes.
* The equilibrium quantity traded falls.

The general picture of what happens, showing the contraction of demand curve and consequent move to a lower equilibrium price and lower quantity traded, is below.

[[File:Demandcontractionandmarketprice.png|700px]]

===Analysis with post-tax prices===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the supply and demand curves for the latter in terms of the post-tax prices.

'''Demand curve''': The demand curve using post-tax prices is expected to remain the ''same'' as the demand curve in a world without taxes, because the price that the buyer sees is the post-tax price.

'''Supply curve''': The supply curve changes. In general, it moves upward. Assuming the law of supply, that is the same as moving inward, i.e., a ''contraction'' of the supply curve. Arithmetically, the new supply curve is related to the old supply curve as follows:

* For a revenue-proportional sales tax with a factor of <math>x</math>, the new supply function at a price of <math>p</math> equals the old supply function at a price of <math>p/(1 + x)</math>. The reason is that, as far as sellers are concerned, the effective price is the pre-tax price <math>p/(1 + x)</math>. The upshot is that the supply curve moves upward by a factor of <math>1 + x</math>.
* For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new supply function at a price of <math>p</math> is the old supply function at a price of <math>p - b</math>. The reason is that, as far as sellers are concerned, the effective price is <math>p - b</math>. The upshot is that the supply curve shifts upward by a vertical distance of <math>b</math>.

The upshot is that the supply curve contracts and the demand curve remains the same. Thus, as with the general analysis of [[comparative statics for demand and supply]], we obtain that:

* The market price rises. In other words, the new post-tax market price is higher than the market price in the world without taxes.
* The equilibrium quantity traded falls.

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price is lower than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the pre-tax curves)
* The post-tax market price is higher than the market price in a world without the tax (this can be seen via the comparative statics between the no-tax and the post-tax curves)
* The equilibrium quantity traded is less than the equilibrium quantity traded in a world without the tax (this can be seen using ''either'' of the two comparative statics methods employed above)

===Extreme cases of elastic and inelastic supply and demand===

We consider some extreme cases. The first row describes the standard case, and subsequent rows describe extreme cases:

{| class="sortable" border="1"
! Assumption for [[price-elasticity of demand]] !! Assumption for [[price-elasticity of supply]] !! Conclusion about pre-tax market price (relative to market price in a world without the tax) !! Conclusion about post-tax market price (relative to market price in a world without the tax) !! Conclusion about equilibrium quantity traded (relative to a world without the tax)
|-
| negative (satisfies the [[law of demand]]) || positive (satisfies the [[law of supply]]) || falls || rises || falls
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || falls || stays the same || falls
|-
| zero, i.e., a vertical demand curve. We also say that the demand is perfectly price-inelastic || positive (satisfies the [[law of supply]]) || stays the same || rises || stays the same
|-
| negative (satisfies the [[law of demand]]) || infinite, i.e., a horizontal supply curve, e.g., a [[constant cost industry]]. Alternatively, this also applies if the jurisdiction where sales tax is imposed is a small subjurisdiction of the economy and the pre-tax prices of the goods are determined by the world economy. || stays the same || rises || falls
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic || falls || stays the same || stays the same
|}

===How price-elasticity affects the nature of the effect of sales tax===

The extent to which the sales tax affects the pre-tax price, post-tax price, and equilibrium quantity traded depends upon the [[price-elasticity of demand]] and [[price-elasticity of supply]]. The following are two general principles:

* Between demand and supply, the relatively more price-inelastic side absorbs more of the price burden of the sales tax. In other words, if demand is more inelastic, then the effect of the sales tax is largely seen in terms of an increase in the ''post-tax'' price. If supply is more inelastic, then the effect of the sales tax is largely seen in terms of a decrease in the ''pre-tax'' price. This is in keeping with the general principle attributed to Ricardo that rents are captured by the most inelastic side. Here, the rents are reversed in sign, but the principle stays the same.
* In general, the extent to which the equlibrium quantity traded is affected is negatively related to the price-elasticities of both demand and supply. In other words, if we reduce the price-elasticity of either demand or supply, the sensitivity of the equilibrium quantity traded to the sales tax reduces. In particular, if either demand or supply is perfectly price-inelastic, the equilibrium quantity traded is independent of the sales tax.

==Effect of sales tax on a single good with a monopolist-controlled market==

This section assumes familiarity with the key conclusions of [[determination of price and quantity supplied by monopolistic firm in the short run]].

We consider comparative statics between two situations:

* A world where there are no sales taxes
* A world where sales taxes are introduced on a ''single'' good (or class of goods) that is supplied by a single seller (the monopolist) that seeks to maximizing profit.

The marginal revenue from the sale of a good equals <math>d(PQ)/dQ</math>, as <math>PQ</math> is revenue and we are interested in the rate of change of revenue as quantity changes. Using the [[calculus:product rule for differentiation|product rule for differentiation]], we find that <math>MR = Q*dP/dQ + P</math>. As explained previously, we expect that dP/dQ is negative in accordance with the law of demand. As such, marginal revenue is less than the price paid, and it may even be zero or negative.

Unlike the perfectly competitive market case discussed previously, we do not perform two separate analyses (pre-tax and post-tax). Rather, we consider various pre-tax and post-tax curves together. The reason is that a "post-tax supply curve" does not make sense in the monopoly case. Also, the analysis is complicated enough as it is, so creating two versions of it isn't worth it!

=== Key curves under consideration ===

We want to perform comparative statics between the world without sales tax and the world with sales tax. We consider the marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''Pre-tax marginal cost curve''': The marginal cost curve using pre-tax prices is expected to remain the ''same'' as the marginal cost curve in a world without taxes, because the price that the seller sees is the pre-tax price.

'''Pre-tax demand curve''': The pre-tax demand curve changes relative to what it is in a world without taxes. In general, it moves downward. Assuming the law of demand, that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new demand curve is related to the old demand curve either through proportional shrinkage toward the quantity axis (for a revenue-proportional sales tax) or through a downward translation toward the quantity by the amount of the tax on unit quantity. For more, see the [[#Analysis of pre-tax prices|analysis of pre-tax prices section]] for the perfectly competitive case.

'''Pre-tax marginal revenue curve''': The pre-tax marginal revenue curve changes relative to what it is in a world without taxes. Qualitatively, the way it changes is the ''same'' as the way the demand curve changes. For a revenue-proportional sales tax, it shrinks proportionally toward the quantity axis. For a quantity-proportional sales tax, it is translated downward. This can be inferred easily from the definition of marginal revenue as <math>d(PQ)/dQ</math>, and the way derivatives interact with addition and scalar multiplication (specifically, [[calculus:differentiation is linear|the fact that differentiation is linear]]).

'''Post-tax demand curve''' (demand curve as experienced by buyers): This remains the same as it would be in a world without taxes.

The upshot: the pre-tax marginal cost curve remains unchanged and the pre-tax marginal revenue curve shrinks downward. We now discuss the implications this has for our conclusions around pre-tax price and quantity traded. ''Prima facie'', this looks a lot like the analysis so far with pre-tax prices for a perfectly competitive market, with marginal revenue curve replacing demand curve and marginal cost curve replacing supply curve. However, there are three subtleties that complicate the picture

# The (price, quantity) pair at which trades actually occur is ''not'' the point of intersection of the marginal cost and marginal revenue curves. Rather, the ''quantity'' is determined by the point of intersection, but the price is determined by looking at the demand curve. '''This distinction alone causes some of our conclusions to break down'''.
# Unlike the demand curve in a perfectly competitive market, the marginal revenue curve is not necessarily downward-sloping. In fact, it need not even always be above the quantity axis! It can have multiple local maxima and local minima. The key distinction is that marginal revenue is affected by a combination of two factors pulling in opposite direction: expansion of the market, and reduction in the price that can be charged to buyers with the highest reservation prices.
# Unlike the supply curve in a perfectly competitive market, the marginal cost curve is not necessarily upward-sloping. It can have multiple local maxima and local minima. The key distinction with the competitive case that the supply curve for a seller in a competitive market is not the entire marginal cost curve but only a ''part of it that slopes upward''. For more, see [[determination of quantity supplied by firm in perfectly competitive market in the short run]].

There are a wide range of cases where we can make assumptions to eliminate problems (2) and (3). However, problem (1) remains.

===The easy case: marginal cost curve increasing everywhere, marginal revenue curve decreasing everywhere===

This is the easy case where, of the three problems mentioned, ''only'' Problem (1) applies.

In the case that the marginal cost curve is increasing throughout the relevant range (outside of which no optima can possibly exist) and the marginal revenue curve is decreasing throughout the relevant range, our pictorial analysis works as in the perfectly competitive case. In particular:

* Since the marginal revenue curve has shrunk downward and leftward, the new point of intersection of the curves has a lower price and lower quantity traded. Thus, the quantity traded is lower than in a world without sales tax. Also, the pre-tax marginal cost experienced by the seller is lower than in a world without sales tax.
* The ''post-tax price charged to buyers'' is higher than what it would be in a world without sales tax. This is because the quantity traded is lower, so referencing the post-tax demand curve (which is the ''same'' as the original demand curve) we get a higher price.
* ''However'', even in this case, the effect on the pre-tax price is ambiguous. This is because there are two competing effects. On the one hand, the quantity traded is lower, causing the maximum price chargeable to increase. On the other hand, the pre-tax demand curve itself has shrunk, causing the price chargeable to decrease.

=== The more general case ===

In the more general case, Problems (2) and (3) can also arise. Specifically, the marginal revenue curve can even go below the quantity axis, and the marginal cost curve can be non-monotonic. In such a situation, we can have multiple locally optimal configurations. When a sales tax is imposed, a monopolist may switch from one optimum to another. An example is in the box.

{{quotation|To illustrate how this latter possibility could happen, imagine that one buyer of the good is willing to pay $3000 for a single unit while all subsequent buyers are willing to pay $2 per unit (up to the 10,000th unit). Imagine also that the marginal cost of producing the first unit is $500, while the marginal cost of producing all units thereafter is $1. The marginal revenue for the first unit is $3000, for the second unit is -$2996 (as the seller would get $2 for each of the two units sold but would effectively lose the ability to charge $3000 for the first unit), and for all units thereafter is $2. With no tax in place, the monopolist would choose to sell 10,000 units for $2 each, making a profit of $9501 ($20,000 - $9,999 - $500) rather than only selling one unit for $3000 (which would only make a profit of $2500). Now suppose a 300% sales tax is imposed. This effectively reduces all marginal revenue figures by 3/4ths. Selling units to customers only willing to pay $2 per unit would no longer be possible, as the pre-tax price could be $0.50 at maximum, and the marginal cost of producing units is $1. However, the buyer willing to pay $3000 could pay a pre-tax price of $750 and the monopolist could make a profit of $250 selling to that buyer alone. So the result of the sales tax in this (unusual) case would be to raise the pre-tax price of the unit from $2 to $750.}}

However, it turns out that any such optimum-switching ''must'' be in the direction of a market shrinkage. In other words, even if we see optimum-switching, where a monopolist switches strategy, it will ''still'' be true that:

* The quantity traded ''decreases'' relative to a world without sales tax.
* The post-tax market price ''increases'' relative to a world without sales tax.

The justification is a little complicated, since we can no longer rely on visual reasoning but must perform careful comparative statics.

==== The explanation for why quantity traded must decrease and post-tax market price must increase under the introduction of a sales tax: setup ====

Denote by <math>(P^*, Q^*)</math> the price and quantity chosen by the monopolist in a world without tax. Suppose <math>(P_1, Q_1)</math> is a (price, quantity) pair on the post-tax demand curve with <math>P_1 < P^*</math> (and therefore <math>Q_1 > Q^*</math>). We will show that the profit from the latter configuration under sales tax is less than the profit under the sales tax from the original optimal configuration <math>(P^*, Q^*)</math>.

First, we note that by the definition of optimality:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

==== Completion of proof for quantity-proportional case ====

In the quantity-proportional case, we have:

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> - Absolute tax burden under <math>(P^*, Q^*)</math>

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> - Absolute tax burden under <math>(P_1, Q_1)</math>

Since <math>Q_1 > Q^*</math>, we obtain that:

Absolute tax burden under <math>(P_1, Q_1)</math> > Absolute tax burden under <math>(P^*, Q^*)</math>

Combining these inequalities, we obtain that:

Profit with sales tax under <math>(P^*, Q^*)</math> > Profit with sales tax under <math>(P_1, Q_1)</math>

This provides the desired conclusion.

==== Completion of proof for revenue-proportional case ====

Denote by <math>x</math> the sales tax rate.

Profit with sales tax under <math>(P^*, Q^*)</math> = Profit without sales tax under <math>(P^*, Q^*)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = Profit without sales tax under <math>(P_1, Q_1)</math> <math> - x/(1 + x)</math> times (post-tax revenue under <math>(P_1, Q_1)</math>)

We have that post-tax revenue equals the sum of cost and profit without sales tax. Simplifying a bit, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> = (Profit without sales tax under <math>(P^*, Q^*)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P^*, Q^*)</math>)

Profit with sales tax under <math>(P_1, Q_1)</math> = (Profit without sales tax under <math>(P_1, Q_1)</math>)/(<math>1 + x</math>) <math> - x/(1 + x)</math> times (total cost under <math>(P_1, Q_1)</math>)

Since <math>Q_1 > Q^*</math>, we have:

Total cost under <math>(P_1, Q_1)</math> <math>\ge</math> Total cost under <math>(P^*, Q^*)</math>

And also, by optimality of <math>(P^*, Q^*)</math>:

Profit without sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit without sales tax under <math>(P_1, Q_1)</math>

Combining these inequalities with the equations above, we get:

Profit with sales tax under <math>(P^*, Q^*)</math> <math>\ge</math> Profit with sales tax under <math>(P_1, Q_1)</math>

=== Conclusion ===

* The pre-tax price (as received by the monopolist) may increase or decrease. Note that this indeterminacy is present even in the case of an increasing marginal cost curve and decreasing marginal revenue curve. The expected proof breaks down due to the fact that the pre-tax price itself is not obtained by intersecting the two curves.
* The post-tax price (as seen by buyers) must increase. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* The quantity traded must decrease. This observation depends on the law of demand, but does not make any additional assumptions about the marginal cost and marginal revenue curve.
* In the special case that we are dealing with an increasing marginal cost curve and a decreasing marginal revenue curve, we can conclude that the marginal cost seen by the seller at the quantity that the seller produces goes ''down'' relative to what it was in a world without sales tax.

==Effect of sales tax that also affects complementary and substitute goods==

The analysis of the preceding section was based on the assumption that the sales tax is levied ''only'' on that particular good for which the analysis is being performed. This assumption is necessary to ensure that the other [[determinants of demand]] and [[determinants of supply]] are unaffected.

However, in real world situations, sales taxes are levied on large classes of goods, and changes to sales taxes are made simultaneously on large classes of goods. In particular, the sales tax may also affect the market prices of [[complementary good]]s and [[substitute good]]s. This means that we either need a more complicated [[partial equilibrium]] analysis (that somehow accounts for the prices of all the complementary and substitute goods) or an even more complicated [[general equilibrium]] analysis. This is extremely tricky. We consider some special cases to illustrate the kinds of effects that may be operational.

===Sales tax on two mutually substitute goods===

Consider two goods <math>A,B</math> that are partial substitutes for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side substitution. We can draw the following conclusions:

# The ''post-tax'' market prices for both <math>A</math> and <math>B</math> are higher than the market price in a world without taxes.
# The ''pre-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' pre-tax market prices are higher than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''at least'' one of <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded. In other words, it cannot happen that the quantity traded for ''both'' goods rises relative to the world without taxes.

==== Justification for conclusion about post-tax market price ====

The conclusion for post-tax price is easiest to justify. We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are substitutes, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''outward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> increases.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the post-tax price on <math>B</math> increases relative to the market price when there was no sales tax on <math>B</math>.

Since both steps increase the post-tax price, the overall effect on the post-tax price is an increase. A similar logic applies to <math>A</math>.

==== Justification for conclusion about pre-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

===Sales tax on two mutually complementary goods===

Consider two goods <math>A,B</math> that are complements for each other as far as buyers are concerned. Starting with a world with no sales tax, a sales tax is then levied on ''both'' <math>A</math> and <math>B</math>. Also assume that the suppliers of <math>A</math> and <math>B</math> are disjoint, so there is no supply-side complementation or substitution. We can draw the following conclusions:

# The ''pre-tax'' market prices for both <math>A</math> and <math>B</math> are lower than the market price in a world without taxes.
# The ''post-tax'' market price for ''at least'' one of <math>A</math> and <math>B</math> must rise (or stay the same) relative to its market price. In other words, it cannot happen that ''both'' post-tax market prices are lower than the respective market prices in a world without taxes.
# The equilibrium quantity traded for ''both'' <math>A</math> and <math>B</math> must fall (or stay the same) relative to the original equilibrium quantity traded.

==== Justification for conclusion about pre-tax market price and quantity traded ====

We proceed in two steps:

* First, let us introduce sales tax only on <math>A</math>. Using the analysis for a single good, we obtain that the post-tax price on <math>A</math> increases relative to a world without sales tax, and the quantity traded decreases. Since the goods are complements, the increase in price of <math>A</math> pushes the demand curve for <math>B</math> ''inward'' (i.e., demand for <math>B</math> expands). Therefore, the market price for <math>B</math> and the quantity traded decrease.
* Now, apply the sales tax on <math>B</math>. Using the analysis for a single god, we obtain that the pre-tax price on <math>B</math> as well as the quantity traded decrease.

Since both steps decrease pre-tax market price and quantity traded, the overall effect on the pre-tax market price and quantity traded is a decrease. A similar logic applies to <math>A</math>.

==== Justification for conclusion about post-tax market price and quantity traded ====

The conclusion about pre-tax market price and quantity traded is harder to justify since it involves an ''either/or'' of two possibilities. The explanation hinges on the [[law of joint demand for two goods]].

Sales tax

2020-05-30T21:32:25Z

Vipul: /* Effect of increasing and decreasing the tax rate on the economic surplus */

==Definition==

A '''sales tax''' is a tax imposed by a government on final sales or purchases.

A sales tax is a kind of [[consumption tax]], and it differs from a [[value-added tax]] in that the tax is collected only at the point of final purchase rather than at intermediate steps on the ''value added'' at each step.

A sales tax may be of either of these two forms:

* A '''revenue-proportional sales tax''': Here, the sales tax is specified as a fraction of the total pre-tax revenue and added to it. The buyer pays a ''post-tax price'' per unit of the quantity which is the sum of the pre-tax price and the sales tax (applied as a percentage of the pre-tax price). In particular, the difference between pre-tax and post-tax revenue ''grows'' as the unit price increases.
* A '''quantity-proportional sales tax''': Here, the sales tax is specified per unit of the quantity being sold. For instance, a sales tax on wheat flour might specify a tax in money units per unit mass of wheat flour. In particular, the difference between the pre-tax and post-tax price is a constant and is independent of the seller's choice of price.

==Mechanics==

===Burden of remitting the tax===

In most jurisdictions that impose sales taxes, the responsibility for computing and collecting the sales tax, as well as remitting the amount to the taxing authority, falls on the seller. Failure to do so may lead to trouble for the seller, not for the buyer.

There is a corresponding notion to sales tax that applies to ''buyers'', and this typically applies to items purchased from outside the jurisdiction for use within the jurisdiction. This is termed [[use tax]], and is typically set at the same rate as sales tax.

===Interpretation of percentages for revenue-proportional sales tax===

{{further|[[inclusive versus exclusive tax rates]]}}

Note that unlike the [[income tax]], the sales tax is computed as a percentage of the pre-tax revenue and ''added'' to the pre-tax revenue to determine how much the buyer will pay. Taxes computed this way are called "exclusive taxes", i.e.., the taxable quantity does not itself include the tax amount.

For instance, for a sales tax of 25%, the post-tax price is <math>1.25</math> times the pre-tax price. The taxing authority collects <math>0.25</math> times the pre-tax price, which is <math>0.20</math> times, or <math>20\%</math> of, the post-tax price. Note that the percentage 20% is different from the sales tax percentage. In general, ''the percentage of post-tax price (which would be called the inclusive tax rate) collected by the taxing authority is lower than the quoted sales tax percentage (which is the exclusive tax rate)''. However, for small values of revenue-proportional sales tax, these two percentages are almost the same.

The explicit formula is this. In fractional term, if the sales tax fraction of pre-tax price is <math>x</math>, the fraction of post-tax price is:

<math>\! \frac{x}{1 + x}</math>

===Inclusion or exclusion of sales tax from marked price===

Conventions on whether the marked prices for items are quoted inclusively or exclusively of sales tax vary from place to place. As a general rule, vending machines and other fixed-price self-serve sales machines typically quote prices inclusive of sales tax, regardless of whether the sales tax is computed inclusively or exclusively. This is largely to make payment simpler. Similarly, shops, markets, and restaurants that are selling a few specific items in bulk may quote the prices inclusive of sales tax to avoid the overhead of sales tax computation associated with each item and make the process easier and faster for buyers and sellers.

However, many shops and markets quote a list price that does not include sales tax, and they generally compute the sales tax at the end, as a percentage of the overall bill, at the time of checkout or bill payment. This may be for a number of reasons:

* It makes the price appear smaller than it is, playing on the behavioral economics biases of consumers.
* It means that buyers and sellers alike can see for themselves how much of the money is being taken away in the form of sales taxes, which may make them more resistant to sales tax increases and more likely to push for reductions in sales taxes. Inclusive quotation of prices may mean that buyers are more likely to blame sellers for the higher prices that result from increases in sales tax rates (and conversely, congratulate sellers for price reductions due to decreases in sales tax rates).
* The explicit itemization of sales tax gives buyers a signal (perhaps a false one) that the sellers are complying with sales tax laws. Of course, it's easy for a seller to itemize a sales tax and then pocket it rather than remitting it to the government, but that might feel a lot more like fraud than simply quoting an inclusive price and not remitting the part devoted to sales tax.
* In cases where the [[price-elasticity of supply]] is high, sellers are unlikely to change their pre-tax price by much in the face of small changes in sales tax rates. By quoting prices exclusive of sales taxes, the sellers can avoid the [[menu cost]]s of relabeling items and simply change the percentage computed for sales tax, which is often a one-time step for the computer program used at checkout.

== Applicability ==

=== Finality ===

Sales taxes are ''only'' levied on sales to final end users (consumers). They are ''not'' levied on sales of raw materials or pre-final products.

For instance, consider this example:

* An electricity supplier sells electricity to a computer chip manufacturer.
* The computer chip manufacturer sells the chips to a laptop manufacturer.
* The laptop manufacturer sells the laptop to a laptop retailer.
* The laptop retailer sells the laptop to the consumer.

In this case, the first three sales are not subject to sales tax, but the fourth sale is.

If, instead, each of the sales had been subject to a sales tax, then we could encounter a situation of [[double taxation]]: the earlier sales would end up getting taxed ''repeatedly'', both directly and indirectly through the later sales.

There is a taxation setup where each stage gets taxed separately, called the [[value added tax]] (VAT). VAT avoids the double taxation problem by only taxing the value ''added'' at each stage, and therefore not double-taxing the original value that has already been taxed.

Generally, the decision on whether to levy sales tax is made by the business rather than the consumer, In case the business is not levying sales tax, a proof may be needed from the consumer that the good or service being purchased will be resold or used as an input to another production process.

=== Sales taxes on sales of used goods ===

Sales of used goods (such as used books or clothes) may or may not be subject to sales tax. The details depend on the laws of the taxing jurisdiction. An example of a jurisdiction where sales tax applies to used goods is the state of California in the United States. Jurisdictions where sales tax needs to be applied for sales of used goods require this tax to apply even if the resale is at a lower price than the original sale price.

This sales tax is in ''addition'' to any taxes that the seller would need to pay if the items were sold at a profit (a higher price than the purchase price); taxes on such profits would be paid as [[income tax]].

Sales taxes on used goods can result in double taxation.

==Additive nature of sales tax and relation with market size==

Sales tax is by nature additive: the total sales tax on a set of transactions is the sum of the sales taxes on each of the transactions individually. In particular, this means that adding a new set of transactions to the market simply increases the absolute amount of the sales tax. In particular:

* For a revenue-proportional sales tax, the larger the total post-tax revenue, the larger the government revenue from the tax.
* For a quantity-proportional sales tax, the larger the total quantity traded, the larger the government revenue from the tax.

=== Quantity-proportional sales tax ===

For a quantity-proportional sales tax, the effects of market structure changes are simple: any market structure change that increases the quantity traded increases the absolute amount of the sales tax (i.e., the government revenue from the tax). In particular, in a competitive market:

* An expansion of demand (i.e. the demand curve moving rightward) increases quantity traded and therefore increases government revenue.
* An expansion of supply (e.g., through the introduction of more sellers, or an improvement in sellers' production technology) increases quantity traded and therefore increases government revenue.

Similar conclusions hold for non-competitive markets, with various caveats.

=== Revenue-proportional sales tax ===

For a revenue-proportional sales tax, the relation between market structure and tax revenue is more complicated. In particular, in a competitive market:

* An expansion of demand (i.e. the demand curve moving rightward) increases quantity traded as well as the market price in the short run, and therefore increases revenue (in the short run).
* An expansion of supply (e.g., through the introduction of more sellers, or an improvement in sellers' production technology) increases quantity traded but decreases price. The net effect on government revenue is ambiguous, since the net effect on total seller revenue is ambiguous.

==Effects of sales tax==

The ''effect'' of a sales tax is understood to mean the effect of introducing the sales tax on a good where there was none before. The analysis of such effects is an example of [[comparative statics]].

===Effect on market price and quantity traded===

{{further|[[effect of sales tax on market price and quantity traded]]}}

Consider the simplifying assumptions of a competitive market, and assume that the sales tax is levied ''only'' on a particular good and not on the various [[substitute good]]s and [[complementary good]]s. Also, we assume that the [[law of demand]] and [[law of supply]] hold (these assumptions are usually valid in the short run). Under these assumptions, the following are the effects of introducing or increasing a sales tax:

{| class="sortable" border="1"
! Item of interest !! Direction of effect (non-edge case) relative to a world without sales tax!! Would the same effect be observed if an existing sales tax percentage is ''increased''? !! Edge case !! Conditions for edge case
|-
| pre-tax price (i.e., the effective price for the seller) || goes down || yes || pre-tax price stays the same|| One of these: The [[demand curve]] is vertical, i.e., the [[price-elasticity of demand]] is zero. Intuitively, what this means is that the quantity demanded is unaffected by price, so the entire burden of the sales tax is passed on to buyers (consumers). The supply curve is horizontal, i.e., the [[price-elasticity of supply]] is infinite.
|-
| post-tax price (i.e., the effective price for the buyer) || goes up || yes || post-tax price stays the same || One of these: The [[supply curve]] is vertical, i.e., the [[price-elasticity of supply]] is zero. Intuitively, what this means is that the quantity supplied is unaffected by price, so the entire burden of the sales tax is absorbed by sellers. The [[demand curve]] is horizontal, i.e., the [[price-elasticity of demand]] is infinite.
|-
| quantity traded || goes down || yes || quantity traded stays the same || Either the demand or the supply curve is vertical, i.e., either the [[price-elasticity of demand]] or the [[price-elasticity of supply]] is zero.
|}

===Effect on economic surplus and its distribution===

{{further|[[effect of sales tax on economic surplus]]}}

In the absence of a sales tax, the [[economic surplus]] arising from the sale of a good is captured by two types of parties -- sellers/producers (in the form of [[producer surplus]]) and buyers/consumers (in the form of [[consumer surplus]]).

Once a sales tax is introduced, there are generally two important effects:

# Now, the economic surplus is captured by three types of parties -- producers ([[producer surplus]]), consumers ([[consumer surplus]]), and the taxing authority ([[government surplus]]).
# The total economic surplus goes down: The new total economic surplus, even ''including'' the portion captured by the taxing authority, is less than the original economic surplus. ''Both'' the producer surplus ''and'' the consumer surplus go down. While part of the reduction in their surpluses is captured by the taxing authority, part of it is lost. The loss can be attributed to the trades that do ''not'' occur because of the decline in quantity traded, and is an example of a [[deadweight loss due to taxation]]. Geometrically, it can be measured as the area of a [[Harberger triangle]].

[[File:Harbergertriangle.png|700px]]

Here are some of the relationships:

Producer surplus in a world without sales tax [corresponds to C + D + F] = (Producer surplus in a world with sales tax [corresponds to D]) + (Part of government surplus whose incidence falls on the producers [corresponds to C]) + (Part of deadweight loss whose incidence falls on the producers [corresponds to F])

and:

Consumer surplus in a world without sales tax [corresponds to A + B + E] = (Consumer surplus in a world with sales tax [corresponds to A]) + (Part of government surplus whose incidence falls on the consumers [corresponds to B]) + (Part of deadweight loss whose incidence falls on the consumers [corresponds to E])

Overall:

economic surplus in a world without sales tax [corresponds to A + B + C + D + E + F]= (economic surplus in a world with sales tax [corresponds to A + B + C + D]) + (Deadweight loss due to taxation [corresponds to E + F])

Note that this analysis ''includes'' government surplus in the economic surplus. The bad effect of taxation, as per this analysis, is the deadweight loss represented by the Harberger triangle.

The [[tax incidence]] question is: how is the burden of taxation (both in terms of the part captured through government surplus and the deadweight loss) distributed between producers and consumers? The answer depends on the relative price-elasticities of the demand and supply curves.

{| class="sortable" border="1"
! Assumption for [[price-elasticity of demand]] !! Assumption for [[price-elasticity of supply]] !! Conclusion about consumer surplus relative to a world without sales tax !! Conclusion about producer surplus relative to a world without sales tax !! Conclusion about deadweight loss
|-
| negative (satisfies the [[law of demand]]) || positive (satisfies the [[law of supply]]) || falls, captured by both government surplus and deadweight loss || falls, captured by both government surplus and deadweight loss || positive
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || it was zero to begin with, and stays zero || falls, captured by both government surplus and deadweight loss || positive
|-
| zero, i.e., a vertical demand curve. We also say that the demand is perfectly price-inelastic || positive (satisfies the [[law of supply]]) ||falls, but it was infinite to begin with, remains infinite || stays the same || zero, because there is no decline in quantity traded
|-
| negative (satisfies the [[law of demand]]) || infinite, i.e., a horizontal supply curve, e.g., a [[constant cost industry]] || falls, captured by both government surplus and deadweight loss || it was zero to begin with, and stays zero || positive
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic ||stays the same || falls || zero, because there is no decline in quantity traded
|}

====Effect of increasing and decreasing the tax rate on the economic surplus====

Most of the qualitative directions regarding what happens when we ''introduce'' a sales tax are similar to what happens when we ''increase'' an existing sales tax. The exception is government surplus, where the effect of increasing an existing nonzero tax rate is ambiguous:

{| class="sortable" border="1"
! Measure !! What happens to it? !! Conceptual explanation !! Pictorial explanation
|-
| [[producer surplus]] || falls || Both the equilibrium quantity traded and the pre-tax price fall, so producers are squeezed from both sides. || The triangle whose area measures producer surplus becomes strictly smaller.
|-
| [[consumer surplus]] || falls || The equilibrium quantity traded falls and the post-tax price rises, so consumers are squeezed from both sides (they make fewer trades, and the surplus per trade falls). || The triangle whose area measures consumer surplus becomes strictly smaller.
|-
| [[government surplus]] || ambiguous || There are two opposite effects: on the one hand, a higher sales tax means a larger difference between post-tax and pre-tax price (so a larger revenue per unit quantity traded). On the other hand, the quantity traded is lower. This is a sales tax analogue of the [[Laffer curve]] effect. || The vertical thickness (height) of the rectangle representing government surplus increases, while the horizontal length (the equilibrium quantity traded) falls. It is unclear which effect dominates.
|-
| [[deadweight loss due to taxation]] || rises || The equilibrium quantity traded falls. || The triangle whose area measures deadweight loss becomes strictly larger.
|-
| [[economic surplus]] (includes producer surplus, consumer surplus, government surplus) || falls || This follows from deadweight loss becoming larger. || The area we are trying to measure becomes strictly smaller.
|}

In other words, raising taxes has clear negative effects on ''everything'' except the government surplus (the tax revenue collected), where the effect is ambiguous.

Sales tax

2020-05-30T21:29:54Z

Vipul: /* Effect of increasing and decreasing the tax rate on the economic surplus */

==Definition==

A '''sales tax''' is a tax imposed by a government on final sales or purchases.

A sales tax is a kind of [[consumption tax]], and it differs from a [[value-added tax]] in that the tax is collected only at the point of final purchase rather than at intermediate steps on the ''value added'' at each step.

A sales tax may be of either of these two forms:

* A '''revenue-proportional sales tax''': Here, the sales tax is specified as a fraction of the total pre-tax revenue and added to it. The buyer pays a ''post-tax price'' per unit of the quantity which is the sum of the pre-tax price and the sales tax (applied as a percentage of the pre-tax price). In particular, the difference between pre-tax and post-tax revenue ''grows'' as the unit price increases.
* A '''quantity-proportional sales tax''': Here, the sales tax is specified per unit of the quantity being sold. For instance, a sales tax on wheat flour might specify a tax in money units per unit mass of wheat flour. In particular, the difference between the pre-tax and post-tax price is a constant and is independent of the seller's choice of price.

==Mechanics==

===Burden of remitting the tax===

In most jurisdictions that impose sales taxes, the responsibility for computing and collecting the sales tax, as well as remitting the amount to the taxing authority, falls on the seller. Failure to do so may lead to trouble for the seller, not for the buyer.

There is a corresponding notion to sales tax that applies to ''buyers'', and this typically applies to items purchased from outside the jurisdiction for use within the jurisdiction. This is termed [[use tax]], and is typically set at the same rate as sales tax.

===Interpretation of percentages for revenue-proportional sales tax===

{{further|[[inclusive versus exclusive tax rates]]}}

Note that unlike the [[income tax]], the sales tax is computed as a percentage of the pre-tax revenue and ''added'' to the pre-tax revenue to determine how much the buyer will pay. Taxes computed this way are called "exclusive taxes", i.e.., the taxable quantity does not itself include the tax amount.

For instance, for a sales tax of 25%, the post-tax price is <math>1.25</math> times the pre-tax price. The taxing authority collects <math>0.25</math> times the pre-tax price, which is <math>0.20</math> times, or <math>20\%</math> of, the post-tax price. Note that the percentage 20% is different from the sales tax percentage. In general, ''the percentage of post-tax price (which would be called the inclusive tax rate) collected by the taxing authority is lower than the quoted sales tax percentage (which is the exclusive tax rate)''. However, for small values of revenue-proportional sales tax, these two percentages are almost the same.

The explicit formula is this. In fractional term, if the sales tax fraction of pre-tax price is <math>x</math>, the fraction of post-tax price is:

<math>\! \frac{x}{1 + x}</math>

===Inclusion or exclusion of sales tax from marked price===

Conventions on whether the marked prices for items are quoted inclusively or exclusively of sales tax vary from place to place. As a general rule, vending machines and other fixed-price self-serve sales machines typically quote prices inclusive of sales tax, regardless of whether the sales tax is computed inclusively or exclusively. This is largely to make payment simpler. Similarly, shops, markets, and restaurants that are selling a few specific items in bulk may quote the prices inclusive of sales tax to avoid the overhead of sales tax computation associated with each item and make the process easier and faster for buyers and sellers.

However, many shops and markets quote a list price that does not include sales tax, and they generally compute the sales tax at the end, as a percentage of the overall bill, at the time of checkout or bill payment. This may be for a number of reasons:

* It makes the price appear smaller than it is, playing on the behavioral economics biases of consumers.
* It means that buyers and sellers alike can see for themselves how much of the money is being taken away in the form of sales taxes, which may make them more resistant to sales tax increases and more likely to push for reductions in sales taxes. Inclusive quotation of prices may mean that buyers are more likely to blame sellers for the higher prices that result from increases in sales tax rates (and conversely, congratulate sellers for price reductions due to decreases in sales tax rates).
* The explicit itemization of sales tax gives buyers a signal (perhaps a false one) that the sellers are complying with sales tax laws. Of course, it's easy for a seller to itemize a sales tax and then pocket it rather than remitting it to the government, but that might feel a lot more like fraud than simply quoting an inclusive price and not remitting the part devoted to sales tax.
* In cases where the [[price-elasticity of supply]] is high, sellers are unlikely to change their pre-tax price by much in the face of small changes in sales tax rates. By quoting prices exclusive of sales taxes, the sellers can avoid the [[menu cost]]s of relabeling items and simply change the percentage computed for sales tax, which is often a one-time step for the computer program used at checkout.

== Applicability ==

=== Finality ===

Sales taxes are ''only'' levied on sales to final end users (consumers). They are ''not'' levied on sales of raw materials or pre-final products.

For instance, consider this example:

* An electricity supplier sells electricity to a computer chip manufacturer.
* The computer chip manufacturer sells the chips to a laptop manufacturer.
* The laptop manufacturer sells the laptop to a laptop retailer.
* The laptop retailer sells the laptop to the consumer.

In this case, the first three sales are not subject to sales tax, but the fourth sale is.

If, instead, each of the sales had been subject to a sales tax, then we could encounter a situation of [[double taxation]]: the earlier sales would end up getting taxed ''repeatedly'', both directly and indirectly through the later sales.

There is a taxation setup where each stage gets taxed separately, called the [[value added tax]] (VAT). VAT avoids the double taxation problem by only taxing the value ''added'' at each stage, and therefore not double-taxing the original value that has already been taxed.

Generally, the decision on whether to levy sales tax is made by the business rather than the consumer, In case the business is not levying sales tax, a proof may be needed from the consumer that the good or service being purchased will be resold or used as an input to another production process.

=== Sales taxes on sales of used goods ===

Sales of used goods (such as used books or clothes) may or may not be subject to sales tax. The details depend on the laws of the taxing jurisdiction. An example of a jurisdiction where sales tax applies to used goods is the state of California in the United States. Jurisdictions where sales tax needs to be applied for sales of used goods require this tax to apply even if the resale is at a lower price than the original sale price.

This sales tax is in ''addition'' to any taxes that the seller would need to pay if the items were sold at a profit (a higher price than the purchase price); taxes on such profits would be paid as [[income tax]].

Sales taxes on used goods can result in double taxation.

==Additive nature of sales tax and relation with market size==

Sales tax is by nature additive: the total sales tax on a set of transactions is the sum of the sales taxes on each of the transactions individually. In particular, this means that adding a new set of transactions to the market simply increases the absolute amount of the sales tax. In particular:

* For a revenue-proportional sales tax, the larger the total post-tax revenue, the larger the government revenue from the tax.
* For a quantity-proportional sales tax, the larger the total quantity traded, the larger the government revenue from the tax.

=== Quantity-proportional sales tax ===

For a quantity-proportional sales tax, the effects of market structure changes are simple: any market structure change that increases the quantity traded increases the absolute amount of the sales tax (i.e., the government revenue from the tax). In particular, in a competitive market:

* An expansion of demand (i.e. the demand curve moving rightward) increases quantity traded and therefore increases government revenue.
* An expansion of supply (e.g., through the introduction of more sellers, or an improvement in sellers' production technology) increases quantity traded and therefore increases government revenue.

Similar conclusions hold for non-competitive markets, with various caveats.

=== Revenue-proportional sales tax ===

For a revenue-proportional sales tax, the relation between market structure and tax revenue is more complicated. In particular, in a competitive market:

* An expansion of demand (i.e. the demand curve moving rightward) increases quantity traded as well as the market price in the short run, and therefore increases revenue (in the short run).
* An expansion of supply (e.g., through the introduction of more sellers, or an improvement in sellers' production technology) increases quantity traded but decreases price. The net effect on government revenue is ambiguous, since the net effect on total seller revenue is ambiguous.

==Effects of sales tax==

The ''effect'' of a sales tax is understood to mean the effect of introducing the sales tax on a good where there was none before. The analysis of such effects is an example of [[comparative statics]].

===Effect on market price and quantity traded===

{{further|[[effect of sales tax on market price and quantity traded]]}}

Consider the simplifying assumptions of a competitive market, and assume that the sales tax is levied ''only'' on a particular good and not on the various [[substitute good]]s and [[complementary good]]s. Also, we assume that the [[law of demand]] and [[law of supply]] hold (these assumptions are usually valid in the short run). Under these assumptions, the following are the effects of introducing or increasing a sales tax:

{| class="sortable" border="1"
! Item of interest !! Direction of effect (non-edge case) relative to a world without sales tax!! Would the same effect be observed if an existing sales tax percentage is ''increased''? !! Edge case !! Conditions for edge case
|-
| pre-tax price (i.e., the effective price for the seller) || goes down || yes || pre-tax price stays the same|| One of these: The [[demand curve]] is vertical, i.e., the [[price-elasticity of demand]] is zero. Intuitively, what this means is that the quantity demanded is unaffected by price, so the entire burden of the sales tax is passed on to buyers (consumers). The supply curve is horizontal, i.e., the [[price-elasticity of supply]] is infinite.
|-
| post-tax price (i.e., the effective price for the buyer) || goes up || yes || post-tax price stays the same || One of these: The [[supply curve]] is vertical, i.e., the [[price-elasticity of supply]] is zero. Intuitively, what this means is that the quantity supplied is unaffected by price, so the entire burden of the sales tax is absorbed by sellers. The [[demand curve]] is horizontal, i.e., the [[price-elasticity of demand]] is infinite.
|-
| quantity traded || goes down || yes || quantity traded stays the same || Either the demand or the supply curve is vertical, i.e., either the [[price-elasticity of demand]] or the [[price-elasticity of supply]] is zero.
|}

===Effect on economic surplus and its distribution===

{{further|[[effect of sales tax on economic surplus]]}}

In the absence of a sales tax, the [[economic surplus]] arising from the sale of a good is captured by two types of parties -- sellers/producers (in the form of [[producer surplus]]) and buyers/consumers (in the form of [[consumer surplus]]).

Once a sales tax is introduced, there are generally two important effects:

# Now, the economic surplus is captured by three types of parties -- producers ([[producer surplus]]), consumers ([[consumer surplus]]), and the taxing authority ([[government surplus]]).
# The total economic surplus goes down: The new total economic surplus, even ''including'' the portion captured by the taxing authority, is less than the original economic surplus. ''Both'' the producer surplus ''and'' the consumer surplus go down. While part of the reduction in their surpluses is captured by the taxing authority, part of it is lost. The loss can be attributed to the trades that do ''not'' occur because of the decline in quantity traded, and is an example of a [[deadweight loss due to taxation]]. Geometrically, it can be measured as the area of a [[Harberger triangle]].

[[File:Harbergertriangle.png|700px]]

Here are some of the relationships:

Producer surplus in a world without sales tax [corresponds to C + D + F] = (Producer surplus in a world with sales tax [corresponds to D]) + (Part of government surplus whose incidence falls on the producers [corresponds to C]) + (Part of deadweight loss whose incidence falls on the producers [corresponds to F])

and:

Consumer surplus in a world without sales tax [corresponds to A + B + E] = (Consumer surplus in a world with sales tax [corresponds to A]) + (Part of government surplus whose incidence falls on the consumers [corresponds to B]) + (Part of deadweight loss whose incidence falls on the consumers [corresponds to E])

Overall:

economic surplus in a world without sales tax [corresponds to A + B + C + D + E + F]= (economic surplus in a world with sales tax [corresponds to A + B + C + D]) + (Deadweight loss due to taxation [corresponds to E + F])

Note that this analysis ''includes'' government surplus in the economic surplus. The bad effect of taxation, as per this analysis, is the deadweight loss represented by the Harberger triangle.

The [[tax incidence]] question is: how is the burden of taxation (both in terms of the part captured through government surplus and the deadweight loss) distributed between producers and consumers? The answer depends on the relative price-elasticities of the demand and supply curves.

{| class="sortable" border="1"
! Assumption for [[price-elasticity of demand]] !! Assumption for [[price-elasticity of supply]] !! Conclusion about consumer surplus relative to a world without sales tax !! Conclusion about producer surplus relative to a world without sales tax !! Conclusion about deadweight loss
|-
| negative (satisfies the [[law of demand]]) || positive (satisfies the [[law of supply]]) || falls, captured by both government surplus and deadweight loss || falls, captured by both government surplus and deadweight loss || positive
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || it was zero to begin with, and stays zero || falls, captured by both government surplus and deadweight loss || positive
|-
| zero, i.e., a vertical demand curve. We also say that the demand is perfectly price-inelastic || positive (satisfies the [[law of supply]]) ||falls, but it was infinite to begin with, remains infinite || stays the same || zero, because there is no decline in quantity traded
|-
| negative (satisfies the [[law of demand]]) || infinite, i.e., a horizontal supply curve, e.g., a [[constant cost industry]] || falls, captured by both government surplus and deadweight loss || it was zero to begin with, and stays zero || positive
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic ||stays the same || falls || zero, because there is no decline in quantity traded
|}

====Effect of increasing and decreasing the tax rate on the economic surplus====

Most of the qualitative directions regarding what happens when we ''introduce'' a sales tax are similar to what happens when we ''increase'' an existing sales tax. The exception is government surplus, where the effect of increasing an existing nonzero tax rate is ambiguous:

{| class="sortable" border="1"
! Measure !! What happens to it? !! Conceptual explanation !! Pictorial explanation
|-
| [[Producer surplus]] || falls || Both the equilibrium quantity traded and the pre-tax price fall, so producers are squeezed from both sides. || The triangle whose area measures producer surplus becomes strictly smaller.
|-
| [[Consumer surplus]] || falls || The equilibrium quantity traded falls and the post-tax price rises, so consumers are squeezed from both sides (they make fewer trades, and the surplus per trade falls). || The triangle whose area measures consumer surplus becomes strictly smaller.
|-
| [[Government surplus]] || ambiguous || There are two opposite effects: on the one hand, a higher sales tax means a larger difference between post-tax and pre-tax price (so a larger revenue per unit quantity traded). On the other hand, the quantity traded is lower. This is a sales tax analogue of the [[Laffer curve]] effect. || The vertical thickness (height) of the rectangle representing government surplus increases, while the horizontal length (the equilibrium quantity traded) falls. It is unclear which effect dominates.
|-
| [[Deadweight loss due to taxation]] || rises || The equilibrium quantity traded falls. || The triangle whose area measures deadweight loss becomes strictly larger.
|-
| [[Economic surplus]] (includes producer surplus, consumer surplus, government surplus) || falls || This follows from deadweight loss becoming larger. || The area we are trying to measure becomes strictly smaller.
|}

In other words, raising taxes has clear negative effects on ''everything'' except the government surplus (the tax revenue collected), where the effect is ambiguous.

Sales tax

2020-05-30T21:26:34Z

Vipul: /* Effect of increasing and decreasing the tax rate on the economic surplus */

==Definition==

A '''sales tax''' is a tax imposed by a government on final sales or purchases.

A sales tax is a kind of [[consumption tax]], and it differs from a [[value-added tax]] in that the tax is collected only at the point of final purchase rather than at intermediate steps on the ''value added'' at each step.

A sales tax may be of either of these two forms:

* A '''revenue-proportional sales tax''': Here, the sales tax is specified as a fraction of the total pre-tax revenue and added to it. The buyer pays a ''post-tax price'' per unit of the quantity which is the sum of the pre-tax price and the sales tax (applied as a percentage of the pre-tax price). In particular, the difference between pre-tax and post-tax revenue ''grows'' as the unit price increases.
* A '''quantity-proportional sales tax''': Here, the sales tax is specified per unit of the quantity being sold. For instance, a sales tax on wheat flour might specify a tax in money units per unit mass of wheat flour. In particular, the difference between the pre-tax and post-tax price is a constant and is independent of the seller's choice of price.

==Mechanics==

===Burden of remitting the tax===

In most jurisdictions that impose sales taxes, the responsibility for computing and collecting the sales tax, as well as remitting the amount to the taxing authority, falls on the seller. Failure to do so may lead to trouble for the seller, not for the buyer.

There is a corresponding notion to sales tax that applies to ''buyers'', and this typically applies to items purchased from outside the jurisdiction for use within the jurisdiction. This is termed [[use tax]], and is typically set at the same rate as sales tax.

===Interpretation of percentages for revenue-proportional sales tax===

{{further|[[inclusive versus exclusive tax rates]]}}

Note that unlike the [[income tax]], the sales tax is computed as a percentage of the pre-tax revenue and ''added'' to the pre-tax revenue to determine how much the buyer will pay. Taxes computed this way are called "exclusive taxes", i.e.., the taxable quantity does not itself include the tax amount.

For instance, for a sales tax of 25%, the post-tax price is <math>1.25</math> times the pre-tax price. The taxing authority collects <math>0.25</math> times the pre-tax price, which is <math>0.20</math> times, or <math>20\%</math> of, the post-tax price. Note that the percentage 20% is different from the sales tax percentage. In general, ''the percentage of post-tax price (which would be called the inclusive tax rate) collected by the taxing authority is lower than the quoted sales tax percentage (which is the exclusive tax rate)''. However, for small values of revenue-proportional sales tax, these two percentages are almost the same.

The explicit formula is this. In fractional term, if the sales tax fraction of pre-tax price is <math>x</math>, the fraction of post-tax price is:

<math>\! \frac{x}{1 + x}</math>

===Inclusion or exclusion of sales tax from marked price===

Conventions on whether the marked prices for items are quoted inclusively or exclusively of sales tax vary from place to place. As a general rule, vending machines and other fixed-price self-serve sales machines typically quote prices inclusive of sales tax, regardless of whether the sales tax is computed inclusively or exclusively. This is largely to make payment simpler. Similarly, shops, markets, and restaurants that are selling a few specific items in bulk may quote the prices inclusive of sales tax to avoid the overhead of sales tax computation associated with each item and make the process easier and faster for buyers and sellers.

However, many shops and markets quote a list price that does not include sales tax, and they generally compute the sales tax at the end, as a percentage of the overall bill, at the time of checkout or bill payment. This may be for a number of reasons:

* It makes the price appear smaller than it is, playing on the behavioral economics biases of consumers.
* It means that buyers and sellers alike can see for themselves how much of the money is being taken away in the form of sales taxes, which may make them more resistant to sales tax increases and more likely to push for reductions in sales taxes. Inclusive quotation of prices may mean that buyers are more likely to blame sellers for the higher prices that result from increases in sales tax rates (and conversely, congratulate sellers for price reductions due to decreases in sales tax rates).
* The explicit itemization of sales tax gives buyers a signal (perhaps a false one) that the sellers are complying with sales tax laws. Of course, it's easy for a seller to itemize a sales tax and then pocket it rather than remitting it to the government, but that might feel a lot more like fraud than simply quoting an inclusive price and not remitting the part devoted to sales tax.
* In cases where the [[price-elasticity of supply]] is high, sellers are unlikely to change their pre-tax price by much in the face of small changes in sales tax rates. By quoting prices exclusive of sales taxes, the sellers can avoid the [[menu cost]]s of relabeling items and simply change the percentage computed for sales tax, which is often a one-time step for the computer program used at checkout.

== Applicability ==

=== Finality ===

Sales taxes are ''only'' levied on sales to final end users (consumers). They are ''not'' levied on sales of raw materials or pre-final products.

For instance, consider this example:

* An electricity supplier sells electricity to a computer chip manufacturer.
* The computer chip manufacturer sells the chips to a laptop manufacturer.
* The laptop manufacturer sells the laptop to a laptop retailer.
* The laptop retailer sells the laptop to the consumer.

In this case, the first three sales are not subject to sales tax, but the fourth sale is.

If, instead, each of the sales had been subject to a sales tax, then we could encounter a situation of [[double taxation]]: the earlier sales would end up getting taxed ''repeatedly'', both directly and indirectly through the later sales.

There is a taxation setup where each stage gets taxed separately, called the [[value added tax]] (VAT). VAT avoids the double taxation problem by only taxing the value ''added'' at each stage, and therefore not double-taxing the original value that has already been taxed.

Generally, the decision on whether to levy sales tax is made by the business rather than the consumer, In case the business is not levying sales tax, a proof may be needed from the consumer that the good or service being purchased will be resold or used as an input to another production process.

=== Sales taxes on sales of used goods ===

Sales of used goods (such as used books or clothes) may or may not be subject to sales tax. The details depend on the laws of the taxing jurisdiction. An example of a jurisdiction where sales tax applies to used goods is the state of California in the United States. Jurisdictions where sales tax needs to be applied for sales of used goods require this tax to apply even if the resale is at a lower price than the original sale price.

This sales tax is in ''addition'' to any taxes that the seller would need to pay if the items were sold at a profit (a higher price than the purchase price); taxes on such profits would be paid as [[income tax]].

Sales taxes on used goods can result in double taxation.

==Additive nature of sales tax and relation with market size==

Sales tax is by nature additive: the total sales tax on a set of transactions is the sum of the sales taxes on each of the transactions individually. In particular, this means that adding a new set of transactions to the market simply increases the absolute amount of the sales tax. In particular:

* For a revenue-proportional sales tax, the larger the total post-tax revenue, the larger the government revenue from the tax.
* For a quantity-proportional sales tax, the larger the total quantity traded, the larger the government revenue from the tax.

=== Quantity-proportional sales tax ===

For a quantity-proportional sales tax, the effects of market structure changes are simple: any market structure change that increases the quantity traded increases the absolute amount of the sales tax (i.e., the government revenue from the tax). In particular, in a competitive market:

* An expansion of demand (i.e. the demand curve moving rightward) increases quantity traded and therefore increases government revenue.
* An expansion of supply (e.g., through the introduction of more sellers, or an improvement in sellers' production technology) increases quantity traded and therefore increases government revenue.

Similar conclusions hold for non-competitive markets, with various caveats.

=== Revenue-proportional sales tax ===

For a revenue-proportional sales tax, the relation between market structure and tax revenue is more complicated. In particular, in a competitive market:

* An expansion of demand (i.e. the demand curve moving rightward) increases quantity traded as well as the market price in the short run, and therefore increases revenue (in the short run).
* An expansion of supply (e.g., through the introduction of more sellers, or an improvement in sellers' production technology) increases quantity traded but decreases price. The net effect on government revenue is ambiguous, since the net effect on total seller revenue is ambiguous.

==Effects of sales tax==

The ''effect'' of a sales tax is understood to mean the effect of introducing the sales tax on a good where there was none before. The analysis of such effects is an example of [[comparative statics]].

===Effect on market price and quantity traded===

{{further|[[effect of sales tax on market price and quantity traded]]}}

Consider the simplifying assumptions of a competitive market, and assume that the sales tax is levied ''only'' on a particular good and not on the various [[substitute good]]s and [[complementary good]]s. Also, we assume that the [[law of demand]] and [[law of supply]] hold (these assumptions are usually valid in the short run). Under these assumptions, the following are the effects of introducing or increasing a sales tax:

{| class="sortable" border="1"
! Item of interest !! Direction of effect (non-edge case) relative to a world without sales tax!! Would the same effect be observed if an existing sales tax percentage is ''increased''? !! Edge case !! Conditions for edge case
|-
| pre-tax price (i.e., the effective price for the seller) || goes down || yes || pre-tax price stays the same|| One of these: The [[demand curve]] is vertical, i.e., the [[price-elasticity of demand]] is zero. Intuitively, what this means is that the quantity demanded is unaffected by price, so the entire burden of the sales tax is passed on to buyers (consumers). The supply curve is horizontal, i.e., the [[price-elasticity of supply]] is infinite.
|-
| post-tax price (i.e., the effective price for the buyer) || goes up || yes || post-tax price stays the same || One of these: The [[supply curve]] is vertical, i.e., the [[price-elasticity of supply]] is zero. Intuitively, what this means is that the quantity supplied is unaffected by price, so the entire burden of the sales tax is absorbed by sellers. The [[demand curve]] is horizontal, i.e., the [[price-elasticity of demand]] is infinite.
|-
| quantity traded || goes down || yes || quantity traded stays the same || Either the demand or the supply curve is vertical, i.e., either the [[price-elasticity of demand]] or the [[price-elasticity of supply]] is zero.
|}

===Effect on economic surplus and its distribution===

{{further|[[effect of sales tax on economic surplus]]}}

In the absence of a sales tax, the [[economic surplus]] arising from the sale of a good is captured by two types of parties -- sellers/producers (in the form of [[producer surplus]]) and buyers/consumers (in the form of [[consumer surplus]]).

Once a sales tax is introduced, there are generally two important effects:

# Now, the economic surplus is captured by three types of parties -- producers ([[producer surplus]]), consumers ([[consumer surplus]]), and the taxing authority ([[government surplus]]).
# The total economic surplus goes down: The new total economic surplus, even ''including'' the portion captured by the taxing authority, is less than the original economic surplus. ''Both'' the producer surplus ''and'' the consumer surplus go down. While part of the reduction in their surpluses is captured by the taxing authority, part of it is lost. The loss can be attributed to the trades that do ''not'' occur because of the decline in quantity traded, and is an example of a [[deadweight loss due to taxation]]. Geometrically, it can be measured as the area of a [[Harberger triangle]].

[[File:Harbergertriangle.png|700px]]

Here are some of the relationships:

Producer surplus in a world without sales tax [corresponds to C + D + F] = (Producer surplus in a world with sales tax [corresponds to D]) + (Part of government surplus whose incidence falls on the producers [corresponds to C]) + (Part of deadweight loss whose incidence falls on the producers [corresponds to F])

and:

Consumer surplus in a world without sales tax [corresponds to A + B + E] = (Consumer surplus in a world with sales tax [corresponds to A]) + (Part of government surplus whose incidence falls on the consumers [corresponds to B]) + (Part of deadweight loss whose incidence falls on the consumers [corresponds to E])

Overall:

economic surplus in a world without sales tax [corresponds to A + B + C + D + E + F]= (economic surplus in a world with sales tax [corresponds to A + B + C + D]) + (Deadweight loss due to taxation [corresponds to E + F])

Note that this analysis ''includes'' government surplus in the economic surplus. The bad effect of taxation, as per this analysis, is the deadweight loss represented by the Harberger triangle.

The [[tax incidence]] question is: how is the burden of taxation (both in terms of the part captured through government surplus and the deadweight loss) distributed between producers and consumers? The answer depends on the relative price-elasticities of the demand and supply curves.

{| class="sortable" border="1"
! Assumption for [[price-elasticity of demand]] !! Assumption for [[price-elasticity of supply]] !! Conclusion about consumer surplus relative to a world without sales tax !! Conclusion about producer surplus relative to a world without sales tax !! Conclusion about deadweight loss
|-
| negative (satisfies the [[law of demand]]) || positive (satisfies the [[law of supply]]) || falls, captured by both government surplus and deadweight loss || falls, captured by both government surplus and deadweight loss || positive
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || it was zero to begin with, and stays zero || falls, captured by both government surplus and deadweight loss || positive
|-
| zero, i.e., a vertical demand curve. We also say that the demand is perfectly price-inelastic || positive (satisfies the [[law of supply]]) ||falls, but it was infinite to begin with, remains infinite || stays the same || zero, because there is no decline in quantity traded
|-
| negative (satisfies the [[law of demand]]) || infinite, i.e., a horizontal supply curve, e.g., a [[constant cost industry]] || falls, captured by both government surplus and deadweight loss || it was zero to begin with, and stays zero || positive
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic ||stays the same || falls || zero, because there is no decline in quantity traded
|}

====Effect of increasing and decreasing the tax rate on the economic surplus====

Most of the qualitative directions regarding what happens when we ''introduce'' a sales tax are similar to what happens when we ''increase'' an existing sales tax. The exception is government surplus, where the effect of increasing an existing nonzero tax rate is ambiguous:

{| class="sortable" border="1"
! Measure !! What happens to it? !! Conceptual explanation !! Pictorial explanation
|-
| [[Producer surplus]] || falls || Both the equilibrium quantity traded and the pre-tax price fall, so producers are squeezed from both sides. || The triangle whose area measures producer surplus becomes strictly smaller.
|-
| [[Consumer surplus]] || falls || The equilibrium quantity traded falls and the post-tax price rises, so consumers are squeezed from both sides (they make fewer trades, and the surplus per trade falls). || The triangle whose area measures consumer surplus becomes strictly smaller.
|-
| [[Government surplus]] || ambiguous || There are two opposite effects: on the one hand, a higher sales tax means a larger difference between post-tax and pre-tax price (so a larger revenue per unit quantity traded). On the other hand, the quantity traded is lower. This is a sales tax analogue of the [[Laffer curve]] effect. || The vertical thickness (height) of the rectangle representing government surplus increases, while the horizontal length (the equilibrium quantity traded) falls. It is unclear which effect dominates.
|-
| [[Deadweight loss due to taxation]] || rises || The equilibrium quantity traded falls. || The triangle whose area measures deadweight loss becomes strictly larger.
|-
| [[economic surplus]] (includes producer surplus, consumer surplus, government surplus) || falls || This follows from deadweight loss becoming larger. || The area we are trying to measure becomes strictly smaller.
|}

In other words, raising taxes has clear negative effects on ''everything'' except the government surplus (the tax revenue collected), where the effect is ambiguous.

Price change ceiling

2020-03-31T04:57:34Z

Vipul:

== Definition ==

A '''price change ceiling''' is an upper limit placed by a government or regulatory body with government sanction on the rate at which a price can be increased. It is a variant on the concept of a [[price ceiling]].

== Examples ==

* The most common and widely used example of a price change ceiling is the vacancy decontrol form of rent control, where a cap is placed on the year-over-year growth in rent for a given rental agreement between a buyer and a seller, although there is usually no absolute cap on the amount of the rent. When the tenant leaves, a new rent may be set for the new tenant.
* Some stock markets have ceilings on how much the price of a stock can change in a given day, in order to reduce rapid variation in prices.
* Price change ceilings may be imposed to prevent [[price gouging]] during emergencies.

== Justification ==

The following are typical reasons for price change ceilings:

* Reduce the incidence of sellers exploiting buyers through lock-in.
* Reduce volatility and increase predictability in the market.
* Address potential problems of [[price gouging]].

== Types of price change ceiling ==

=== Classification based on what "price" means ===

* Price change ceiling applied to the market as a whole: Here, no seller is allowed to sell at a price more than some percentage higher than the market price at some point in the recent past (e.g., no seller is allowed to sell at more than 10% of the average price in the market last week).
* Price change ceiling specific to a seller: Here, the price a seller is currently selling at is compared to the price the seller sold at in the past.
* Price change ceiling specific to a pair of buyer and seller: This makes sense in the context of a repeat transaction. Rent regulations of the "vacancy decontrol" form are like that -- the rent of a given housing unit is allowed to increase at some maximum annual rate for a given pair of landlord and tenant, but once the tenant moves out, the landlord may give the apartment out for rent at any price.

=== Classification based on how "change" is bounded ===

* An ''additive price change ceiling'' is a ceiling based on the (additive) difference between the price and the previous price. For instance, an additive price change ceiling of 3 currency units per unit of the good means that if the previous price is 10, the new price can be at most 13, and if the previous price is 100, the new price can be at most 103.
* A ''multiplicative price change ceiling'' is a ceiling based on the ratio of the price and the previous price. For instance, a multiplicative price change ceiling of 20% means that if the previous price is 10, the new price can be at most 12, and if the previous price is 100, the new price can be at most 120.

=== Classification based on the time periods between price changes ===

The reference "previous price" may be calculated as the price as of the previous day, or previous week, or previous year. If price varies continuously, a convention may be used, such as taking the end-of-day price, or average price across the day.

== Short-run impact of price change ceilings: they can lead to binding price ceilings in the face of demand and supply shocks ===

A sudden [[demand shock]] or [[supply shock]] can cause the equilbrium, market-clearing price of a good to increase a lot, more than the price change ceiling allows. At this point, the price change ceiling functions as a uniform fixed [[price ceiling]] in the short run, and has the same short-run static analysis.

== Long-run impact of price change ceilings ==

A price change ceiling is non-binding in the long run if the rate of change of the market price is expected to always be less than the price change ceiling.

A price change ceiling is binding in the long run if the rate of change of the market price is expected to, at least sometimes, be more than the price change ceiling.

In this section, we discuss binding price change ceilings; non-binding price change ceilings should have very little impact on buyers or sellers.

=== Binding price change ceilings, when specific to pairs of buyer and seller, create a lasting contractual relationship between them, which can lead to smoothing of price increases over the years ===

When a binding price change ceiling is specific to a pair of buyer and seller, such as in the case of vacancy decontrol, it effectively gives the buyer a long-term ownership stake in the relationship (in the form of price guarantees over the coming year). Exiting the relationship costs the buyer as the buyer now needs to search for another relationship, at a possibly higher price than the sheltered, ceilinged price.

The seller may therefore factor this into the initial price for the buyer. Knowing that the seller will be locked into restricted price increases for possibly a long period of time, the seller may therefore charge a larger initial price than they otherwise would.

Price ceiling

2020-03-31T04:19:24Z

Vipul: /* Generally, price ceilings reduce seller incentives to prepare for demand and supply shocks, but the story is a little more complicated */

==Definition==

A '''price ceiling''' is an upper limit placed by a regulatory authority (such as a government, or regulatory authority with government sanction, or private party controlling a marketplace) on the price (per unit) of a good.

A price ceiling is a form of [[price control]]. Other forms of price control include [[minimum price]]s, [[price change ceiling]]s, and [[profit ceiling]]s.

At any given time, a price ceiling is one of these:

* '''Non-binding price ceiling''': This is a [[price ceiling]] that is greater than the current [[market price]].
* '''Binding price ceiling''': This is a [[price ceiling]] that is less than the current [[market price]]. Binding price ceilings cause a reduction in the price, and may increase or decrease the quantity traded depending on the market structure.

A particularly extreme form of price ceiling, which is not usually thought of that way, is a price ceiling of zero. This refers to situations where it is legal to give a good or service for free but it is illegal to offer the good or service in exchange for money. Price ceilings of zero are usually justified on aesthetic and ethical grounds as it is believed that the exchange of money sullies certain types of transaction. Since the market price for most forms of exchange is positive, price ceilings of zero are typically binding price ceilings. Examples include:

* [[Prostitution]] (the sale of sexual services), which is illegal, though not often rigorously prosecuted, in many countries
* [[Organ trade]], i.e., there are often jurisdictions where it is legal to donate an organ such as a kidney but illegal to buy or sell it.
* Adoption: In many places, it is not legal for a pregnant mother to sell her baby for adoption to a couple willing to adopt the kid, though it is legal to put the baby up for adoption.

== Type of price ceilings based on how they apply ==

=== Uniform fixed price ceiling ===

The simplest kind of price ceiling is a price ceiling that is fixed (i.e., a fixed price per unit) and imposed uniformly across all transactions, i.e., for all buyers and sellers. The value of this fixed price ceiling may change over time but generally does so through discrete policy changes. Therefore, in the short run, and possibly even the medium-to-long run, the price ceiling can be considered fixed.

There are two other kinds of variants of price ceilings.

=== Price change ceiling ===

{{further|[[Price change ceiling]]}}

This is a ceiling on how rapidly a price is allowed to increase. Price change ceilings may be any of these:
* Price change ceiling applied to the market as a whole: Here, no seller is allowed to sell at a price more than some percentage higher than the market price at some point in the recent past (e.g., no seller is allowed to sell at more than 10% of the average price in the market last week).
* Price change ceiling specific to a seller: Here, the price a seller is currently selling at is compared to the price the seller sold at in the past.
* Price change ceiling specific to a pair of buyer and seller: This makes sense in the context of a repeat transaction. Rent regulations of the "vacancy decontrol" form are like that -- the rent of a given housing unit is allowed to increase at some maximum annual rate for a given pair of landlord and tenant, but once the tenant moves out, the landlord may give the apartment out for rent at any price.

For static analysis at a single point in time, price change ceilings may seem to function effectively as price ceilings; however, the long-run analysis (across multiple time periods where price changes can be made) is quite different. In particular, the "expectation regarding future prices" by both buyers and sellers, that shapes both the demand and supply curves, is affected by the structure of the price change ceiling. Despite these differences, in the cases where unexpected demand or supply shocks cause price change ceilings to create binding price ceilings, they behave qualitatively like uniform fixed price ceilings.

=== Profit ceiling ===

{{further|[[Profit ceiling]]}}

Here, sellers are forbidden from selling a good at a price greater than some multiple of the cost of production, to prevent excessive profiteering, while taking into account the cost of production.

Profit ceilings are effectively fixed price ceilings in cases where the marginal cost of production is constant across quantities and between sellers. However, in most real-world cases, profit ceilings are reasonably different from fixed price ceilings. Please see the [[profit ceiling]] page for more detailed models of how profit ceilings work.

=== A note on "voluntary" price ceilings ===

In general, only sellers with [[market power]] (i.e., sellers who can influence the market price, either as monopoly sellers or part of a small oligopoly) can adhere to voluntary price ceilings. Small sellers in a competitive market who choose to adhere to voluntary price ceilings, not raising prices to the market equilibrium, will not be able to meet the huge amount of market demand directed at them.

In the face of huge demand shocks and supply shocks, it is possible for ''de facto'' price ceilings to take effect, not through a single regulatory authority or marketplace controller, but though all sellers deciding to not risk increasing prices, even if that means shortfalls and forgone profits. The two typical reasons are:

* Potential regulation and litigation: Sellers may fear that if they raise prices, they will attract the ire of regulators, even if no current regulations forbid them raising prices.
* Public opinion: Sellers may fear that negative public sentiment against [[price gouging]] may hurt their reputation more than any additional profits they will make by selling at a higher price, or any additional goodwill they will generate among actual customers who appreciate not having a shortfall. The idea here is that it's not just the actual buyers, but also others who are unable to buy, or even general spectators, who could create trouble for the seller. The more diversified the seller, the bigger this public opinion concern (so a seller who ''only'' sells the good affected by the price ceiling may be less concerned, but a seller who sells many other goods may be concerned about reputational impact on sales of those other goods).

It is worth keeping in mind that this sort of "voluntary" price ceiling can really be effective only if some sellers have market power, or if there is widespread agreement between sellers about the wisdom of adhering to the "voluntary" price ceilings.

== The distinction between price ceiling-like policies and other similar market controls ==

=== Price ceilings versus sales taxes ===

As we'll discuss later on this page, price ceilings and [[sales tax]]es have similar effects -- they generally reduce quantity traded relative to an unrestricted market, and they cause a deadweight loss (which, in simple cases, is given by the Harberger triangle). Moreover, each approach has many real-world variants, so we should really think of a cluster of "price ceiling-like" policies versus a cluster of "sales tax-like" policies.

Conceptually, the main difference between the clusters is that sales tax-like policies aim to mimic the behavior of an unrestricted market -- just one where buyers and sellers see different prices (with the difference pocketed by the taxing authority). They therefore retain many of the dynamics of an unregulated market as far as the buyers and sellers individually are concerned. In contrast, price ceiling-like policies are qualitatively different from unrestricted markets to the point that buyers and sellers can see and feel the differences directly.

Price ceilings and sales taxes also work quite differently in non-competitive markets. In a monopoly market, it is possible for a price ceiling to increase the quantity traded. In contrast, a sales tax will reduce quantity traded, even in a monopoly market.

=== Price ceilings versus quantity ceilings ===

Both price ceilings and [[quantity ceiling]]s effectively create a situation where the quantity traded is less than it would be without a ceiling. However, quantity ceilings favor sellers over buyers, and also shift the burden of non-price competition to sellers: sellers compete with each other for permission to produce a larger share of the quantity ceiling.

==Basic theory: the effects of price ceilings in competitive markets==

The simple analysis in this section assumes a fixed price ceiling and ignores some of the indirect effects of price ceilings:

* Expectations regarding future prices: Price ceilings affect not just current prices but also expectations regarding future prices, on both the demand and supply side. This is particularly important for goods where buying now and buying later can substitute for each other, or where producing now and producing later are substitutes. In particular, the existence of the price ceiling affects the shape of the demand and supply curve. Moreover, the nature of the ceiling (whether it's a fixed price ceiling or a price change ceiling, and how people expect the price ceiling itself to evolve) plays a part in how this effect plays out. We will ignore these considerations.
* Interaction with price ceilings on substitute goods and complementary goods

===Non-binding price ceiling: price ceilings have no effect when they are above the market-clearing price===

A price ceiling that is set above the [[market price]] of the good has no direct short-run effect.

===Binding price ceiling: price ceilings create excess demand when they are below the market-clearing price===

If the price ceiling is below the [[market price]], the quantity demand for the good exceeds the quantity supplied for the good, resulting in a situation of scarcity or [[excess demand]]. This results in a loss of economic surplus compared to the situation of a market-clearing price.

For instance, in the figure below, if the price ceiling is set at the price level of the horizontal line AB, then there is a shortfall equal to the length of the segment AB.

Since a price ceiling creates a shortfall, it is not immediately clear which of the buyers willing to buy the good at the lower price will succeed in buying it (i.e., there is [[non-price competition]] among buyers, as discussed later in this page). Under the '''efficient allocation assumption''' (i.e., perfect sorting among buyers, ''and'' no costs imposed by non-price competition), the deadweight loss equals that arising from the case when the same quantity traded is accomplished by means of a [[sales tax]], and is described by the area of the [[Harberger triangle]], bounded by a vertical line through A and the demand and supply curves (so that two of its vertices are A and C). For more discussion, see [[Effect of price ceiling on economic surplus]].

[[File:Shortfallbelowmarketprice.png|500px]]

==Basic theory: the effects of price ceilings in monopolistic markets==

{{NeedsGraph}}

As was the case with the competitive markets analysis, the simple analysis in this section assumes a fixed price ceiling and ignores:

* Expectations regarding future prices
* Interaction with price ceilings on substitute goods and complementary goods

=== The basic case of increasing marginal costs ===

We restrict attention to cases where the monopolist's marginal cost curve is increasing, to avoid issues related to multiple optima. Many of the conclusions we draw are not dependent on this assumption.

There are three key price points relative to which price ceilings can be compared. For more context, see [[determination of price and quantity supplied by monopolistic firm in the short run]].

* The '''free market price''' (without any price ceiling), chosen by the monopolist for profit maximization.
* The '''optimal price''', which is the price point for the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market price would be if the market were competitive. This is based on the [[determination of quantity supplied by firm in perfectly competitive market in the short run]], where we find that the supply curve coincides with the short-run marginal cost curve if the latter is increasing.
* The '''free market marginal cost''', which is the marginal cost at the quantity being traded without any price ceiling. This is equal to the marginal revenue, since a monopolist optimizes at marginal cost equals marginal revenue.

There are two interesting values of quantity traded:

* The '''market quantity traded''', which is the quantity traded in the market without any price ceiling.
* The '''optimal quantity traded''', which is the maximum possible quantity traded, and is the quantity at the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market quantity traded would be if a competitive market were simulated with the same demand and supply structure.

We can now make cases based on the value of the price ceiling. We move the price ceiling ''down'', so the earlier rows discuss larger price ceilings and the later rows discuss lower price ceilings.

For any given price ceiling, there are two possibilities:

* It is a non-binding price ceiling, i.e., it is greater than or equal to the free market price. In this case, the market behavior remains the same as it would in a free market.
* It is a binding price ceiling in the sense of price, i.e., it is less than the free market price. In this case, the market price equals the binding price (note that this is no longer true with more complicated market structures, such as the case when the marginal cost curve is not increasing).

{| class="sortable" border="1"
! Price ceiling !! Binding or non-binding (binding means that the market price equals the ceiling, non-binding means it continues to equal the free market price) !! Quantity traded (compared to free market) !! Directional change in quantity traded as price decreases !! Location of the (price, quantity) pair !! Is there a shortfall?
|-
| Greater than or equal to than the free market price || Non-binding || Same || No change || On the market demand curve, same as without any price ceiling || No
|-
| Less than the free market price, but more than the optimal price || Binding || More || Increasing || On the market demand curve, moving down and right along the curve. The price being charged is the ''maximum'' possible price for the given quantity traded || No
|-
| Equal to the optimal price || Binding || More || Maximized || At the intersection of the market demand curve and short-run marginal cost curve || No
|-
| Less than the optimal price, but more than the free market marginal cost || Binding || More || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Equal to the free market marginal cost || Binding || Same || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Less than the free market marginal cost || Binding || Less || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|}

==Short-run impact of binding price ceilings in perfectly competitive markets==

===Non-price competition mechanisms===

The key problem that needs to be solved in case of a binding price ceiling is the problem: given that the quantity supplied is less than the quantity demanded, who among the different potential buyers of the good gets how much of it? There are two broad categories of approaches:

* Queueing, rationing, and queue-rationing
* Black markets

====Queueing, rationing, and queue-rationing====

{{further|[[Queueing, rationing, and queue-rationing]]}}

* Queueing is an approach where buyers are served in some form of a queue. The simplest is a time-based queue (first-come-first-serve) though other forms of priority queue are also possible.
* Rationing is an approach that limits the amount that each buyer can buy.
* Queue-rationing refers to a mix of queueing and rationing. For instance, each buyer can buy only a fixed amount in each iteration of purchase, and a buyer can take only one other position in the queue at a time (or even within a time period, for instance, per day). For instance, if the ration is 5 units per purchase, and the buyer wants to buy 48 units, the buyer will have to stand in the queue 10 times.

A key idea to keep in mind when thinking about these policies (queueing, rationing, and queue-rationing) is that the policies are determined mainly by sellers, but sellers do not internalize most of the gains from selecting policies that improve the efficiency of allocation between buyers. Sellers may, however, gain indirectly through reputational benefits, or spillover benefits to other goods the seller is selling.

====Black markets====

A [[black market]], or an illegal market in the good, is one way around the problem of a price ceiling. In this scenario, a small quantity of the good is sold in the legal market at a price equal to the price ceiling, whereas the rest of the good is sold in the black market at the true equilibrium price. In fact, the black market price may well be ''higher'' than the market price would be in the absence of a price ceiling, because of the added costs incurred by sellers to evade the law.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Under most sets of assumptions (in particular, assuming that there are no [[external cost]]s or [[external benefit]]s), price ceilings have a negative effect on economic surplus in competitive markets. In general, the following are true:

* Non-binding price ceilings have no effect on economic surplus.
* Binding price ceilings have negative effects on economic surplus as well as producer surplus, with the magnitude of the effect increasing as the ceiling price goes lower. The effect on consumer surplus is ambiguous. This is a [[deadweight loss]].

Note that there are three components to the deadweight loss arising due to a binding price ceiling:

* The ''inevitable'' deadweight loss, that is given by the area of the [[Harberger triangle]].
* The deadweight loss that arises due to imperfect sorting among buyers (i.e., buyers who value a good less get it). In other words, this occurs because non-price competition did not do its job well.
* The deadweight loss arising from the transaction costs associated with non-price competition.

==Short-run impact of binding price ceilings in monopolistic markets==

===Non-price competition mechanisms===

Similar to the case of a competitive market, binding price ceilings can create shortfalls, leading to non-price competition among buyers. However, unlike the case of competitive markets, not every binding price ceiling leads to a shortfall and to non-price competition. More specifically, a binding price ceiling leads to shortfalls only if it is set to below the optimal price as defined in [[#Basic theory: the effects of price ceilings in monopolistic markets]], i.e., the price at which the marginal cost curve and market demand curve intersect.

When the price ceiling is set to below the optimal price, the non-price competition mechanisms are similar to those in a competitive market, namely:

* Queueing, rationing, and queue-rationing
* Black markets

One difference is that since the monopolist has complete control over the supply of the market, it may be easier for the monopolist to choose the non-price competition strategy more freely.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Here we assume that the good being sold has no [[external cost|external costs]] or [[external benefit|external benefits]].

The discussion here builds on that in [[#Basic theory: the effects of price ceilings in monopolistic markets]]. You may need to reference that for more context around some of the terminology used.

For some of the rows, we can draw definite conclusions only under the '''efficient allocation assumption''': perfect sorting among buyers (the buyers who acquire the good are those who value it most highly), ''and'' the non-price competition imposes no extra costs on buyers and sellers. The caveats are noted in the corresponding cells where they apply.

The "optimal price" in the table below is obtained as the price point at the intersection of the marginal cost curve and the market demand curve. This is essentially what the price would be if the seller could be made to behave as if operating in perfect competition.
{| class="sortable" border="1"
! Price ceiling range !! economic surplus compared to no price ceiling !! Producer surplus compared to no price ceiling !! Consumer surplus compared to no price ceiling !! Direction of change of economic surplus with decreasing price ceiling !! Direction of change of producer surplus with decreasing price ceiling !! Direction of change of consumer surplus with decreasing price ceiling !! Qualitative comments
|-
| Greater than or equal to the free market price || Same || Same || Same || None || None || None || Deadweight loss is intact as the price ceiling has no effect
|-
| Less than the free market price and greater than the optimal price || More || Less || More || Increasing || Decreasing || Increasing || Deadweight loss due to monopoly is ameliorated by the price ceiling
|-
| Equal to the optimal price || More || Less || More || Maximized || Decreasing || Ambiguous || Deadweight loss is eliminated as perfect competition is emulated
|-
| Less than the optimal price and greater than the free market marginal cost || More (assuming efficient allocation), indeterminate otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || Deadweight loss is now no longer due to monopolistic pricing but rather due to price ceilings cutting off beneficial transactions
|-
| Equal to the free market marginal cost || Same (assuming efficient allocation), less otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || The quantity traded mimics that in the no-ceiling case, but the price at which the trades occur is lower. Assuming efficient allocation (i.e., the goods go to the buyers valuing them most highly), the economic surplus is the same but it is distributed more to consumers. Without the efficient allocation assumption, total economic surplus is down, with producer surplus down and the effect on consumer surplus indeterminate.
|-
| Less than the free market marginal cost || Less || Less || Starts out as more (assuming efficient allocation), may later becomes less. Without the efficient allocation assumption, indeterminate. || Decreasing || Decreasing || Ambiguous || Deadweight loss now exceeds that of monopoly, even under the efficient allocation assumption.
|}

==Long-run impact of price ceilings==

The long-run impact of a price ceiling is a much more complicated matter than the short-run impact. There are, roughly speaking, three sources of complication:

* Expectations regarding future demand and supply patterns: A price ceiling that is binding today may become non-binding in the future, and a price ceiling that is non-binding today may become binding in the future. Both the normal course of supply-and-demand changes as well as low-probability demand and supply shocks need to be examined in connection with the price ceiling.
* Intertemporal substitution with the future: Buyers and sellers who can substitute buying or selling now against buying or selling in the future, have to consider the effect of the price ceiling on how they distribute their buying or selling behavior over time. Note that this long-run consideration can also change the present-day shape of the supply and demand curves, thereby causing a short-run effect.
* The distinction between short-run and long-run supply, through reconfiguration: In the short run, sellers are generally constrained to a increasing short-run marginal cost curve. In the long run, the seller can change the mix of inputs, for instance, by acquiring more land and capital or hiring more people.

The type of impact a price ceiling has also depends on its structure. The analysis can differ quite a bit between uniform fixed price ceilings, price change ceilings, and profit ceilings. However, we can say a few broad things.

=== Price ceilings are more likely to cause firms to exit the market in the long run than in the short run, and have qualitatively different effects in increasing cost industries versus decreasing cost industries ===

In the short run, even in the face of a price ceiling, a firm may continue to produce as long as the minimum AVC value (at [[minimum efficient scale]]) is less than the price ceiling. That's because the firm has sunk its fixed costs. If the price ceiling is even lower than the firm's AVC, the firm may simply stay idle in the short run.

In the long run, however, firms are looking at their average total cost and comparing it with the minimum between what they expect the price to be (taking the minimum across the price ceiling and market price). There are two competing considerations here -- the ability to optimize better in the long run, and the ability to exit altogether in the long run. Here is how they interact for a firm in a large, competitive market:

* On the one hand, the long-run knowledge of the price ceiling allows the firm to choose a configuration of fixed and variable costs that is optimized for that price ceiling, rather than its prediction for the unrestricted price.
** For an [[increasing cost industry]], the firm will do so by reducing its fixed costs and reducing overall production. This can make the shortfall even worse than in the short run.
** For a [[constant cost industry]] or [[decreasing cost industry]], the firm (since it is small relative to the market) will still keep producing at maximum capacity. So there is no change.
* On the other hand, solving this problem might also show the firm that it does not have a configuration that allows for long-run profitability. Specifically, if the price ceiling is less than the minimum possible average total cost (ATC) for the firm, it will exit the market.
** For a constant cost industry or decreasing cost industry, the minimum ATC is attained at the maximum level of production. In other words, in such cases, if even at the maximum level of production, the firm is unable to make its ATC drop to below the price ceiling, it will exit the market. Over time, this might reduce the number of firms in the market, causing larger shortfalls.

The situation is a little different in a monopolistic firm, but the underlying trade-off remains the same: the firm can optimize better in the long run, but it can also choose to exit altogether.

=== Generally, price ceilings reduce seller incentives to prepare for demand and supply shocks, but the story is a little more complicated ===

A price ceiling that is non-binding now could become binding in the face of a demand shock or supply shock that increases market prices, especially in the short run when firms cannot reconfigure their factors of production.

If the price mechanism is allowed to operate freely, the firm may have stronger incentives to prepare for such situations, because the better prepared it is, the more it can sell and the more it can profit from the increased prices. Specifically, the firm may do one or more of these:

* Stockpile extra production that can be released into the market in the face of a demand or supply shock that raises price.
* Develop better forecasting so that shocks can be anticipated, and prepared for a little bit in advance (this can be combined with the previous point to give the idea of "speculative production" -- if the forecast shows increased demand, then start stockpiling).
* Configure their production process so that it is easier to reconfigure quickly (i.e., make the long run less long).

For instance, let's say a firm is one firm among many in a competitive market and an increasing cost industry (we'll assume an increasing cost industry because with a decreasing cost industry, firms are anyway maxed out on production capacity). The market price of a good under normal conditions is 1. The firm correctly forecasts a soon-to-happen demand shock that would cause the market price to go up to 3,. There is a price ceiling of 2.

* If there were no price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a market price of 3.
* Due to the price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a price of 2.

Comparing these two, we see that the price ceiling prevents the firm from capturing all the gains in market price. Therefore, even if the firm does increase its production, it will increase it to a lower level (enough for the price ceiling of 2) rather than to the higher level (enough for the market price of 3). Thus, although the firm's long-run planning will alleviate the shortfall a little bit compared to not being prepared at all, the shortfall is still not going to be eliminated.

The above assumes that the firm has definite knowledge of the demand shock. However, the situation gets more complicated when the demand shock is more probabilistic. For instance, suppose the firm believes that there is some probability that a demand shock will cause the market price to rise to 3. The firm has to choose to reconfigure its fixed costs to gear toward producing enough for the market price of 3, or stay with its current setup, or anything in between. Whatever choice the firm makes, it will have to compare the expected gain from that choice of both the options.

Even in this more complicated situation, the presence of the price ceiling reduces, overall, the extent to which the firm will increase its production, by reducing the upside. However, the specifics will depend on other questions such as whether the firm's production cycle, as well as its buyers, can engage in intertemporal substitution.

Note that this analysis is contingent on some assumptions:

* The price ceiling is a uniform fixed price ceiling: More complicated price ceiling formulas, like [[price change ceiling]]s and [[profit ceiling]]s, share some qualitative characteristics but are also different in other ways.
* The price ceiling is known in advance to the firm: A price ceiling imposed suddenly without warning after a demand shock will have a less detrimental effect on quantity; the firm that had ramped up production has now already invested the fixed costs (thinking it could profit more), and is therefore able to produce more.

=== Price ceilings can change the way buyers substitute intertemporally ===

For goods where present purchases can substitute for future purchases, buyers respond to expectations of future price increases by buying more now. In markets with price ceilings that may become binding, buyers have to factor in not just the future market prices but also future availability. This can change the buyers' decision of how much to buy now, but it's ambiguous in what direction the buyers' behavior will change. Specifically, the way the buyers' behavior changes depends partly on how much each buyer perceives as the costs of non-price competition and how much the buyer's individual reservation price compared with the market price.

For instance, let's say buyers expect a demand shock or supply shock in the future that would, in a free market, cause the price of toilet paper to rise. This might incentivize buyers to stock up on toilet paper right now. Now, if a price ceiling is implemented that prevents the price of toilet paper from rising, buyers' expectations will shift from an expectation of increased price to an expectation of reduced availability, and the possibility that the buyer may have to engage in non-price competition to get the good. This, too, might incentivize buyers to stock up on toilet paper right now. However, the relative strength of the incentive to stock up on toilet paper, between the free market and price ceiling case, is ambiguous.

This ambiguity is related to the idea that the effect of price ceilings on consumer surplus is ambiguous (though it's definitely negative for producer surplus and overall economic surplus).

Note that the possibility of [[black market]]s does increase the incentive to buy and hoard.

==Related notions==

* [[Maximum retail price]] is an upper limit that the producer or wholesale distributor puts on the price at which retailers can sell the commodity to customers. Maximum retail prices do not usually have the inefficiencies associated with price ceilings, because producers of the goods can vary maximum retail prices according to demand trends over the somewhat longer term.

Price ceiling

2020-03-31T04:18:13Z

Vipul: /* Generally, price ceilings reduce seller incentives to prepare for demand and supply shocks, but the story is a little more complicated */

==Definition==

A '''price ceiling''' is an upper limit placed by a regulatory authority (such as a government, or regulatory authority with government sanction, or private party controlling a marketplace) on the price (per unit) of a good.

A price ceiling is a form of [[price control]]. Other forms of price control include [[minimum price]]s, [[price change ceiling]]s, and [[profit ceiling]]s.

At any given time, a price ceiling is one of these:

* '''Non-binding price ceiling''': This is a [[price ceiling]] that is greater than the current [[market price]].
* '''Binding price ceiling''': This is a [[price ceiling]] that is less than the current [[market price]]. Binding price ceilings cause a reduction in the price, and may increase or decrease the quantity traded depending on the market structure.

A particularly extreme form of price ceiling, which is not usually thought of that way, is a price ceiling of zero. This refers to situations where it is legal to give a good or service for free but it is illegal to offer the good or service in exchange for money. Price ceilings of zero are usually justified on aesthetic and ethical grounds as it is believed that the exchange of money sullies certain types of transaction. Since the market price for most forms of exchange is positive, price ceilings of zero are typically binding price ceilings. Examples include:

* [[Prostitution]] (the sale of sexual services), which is illegal, though not often rigorously prosecuted, in many countries
* [[Organ trade]], i.e., there are often jurisdictions where it is legal to donate an organ such as a kidney but illegal to buy or sell it.
* Adoption: In many places, it is not legal for a pregnant mother to sell her baby for adoption to a couple willing to adopt the kid, though it is legal to put the baby up for adoption.

== Type of price ceilings based on how they apply ==

=== Uniform fixed price ceiling ===

The simplest kind of price ceiling is a price ceiling that is fixed (i.e., a fixed price per unit) and imposed uniformly across all transactions, i.e., for all buyers and sellers. The value of this fixed price ceiling may change over time but generally does so through discrete policy changes. Therefore, in the short run, and possibly even the medium-to-long run, the price ceiling can be considered fixed.

There are two other kinds of variants of price ceilings.

=== Price change ceiling ===

{{further|[[Price change ceiling]]}}

This is a ceiling on how rapidly a price is allowed to increase. Price change ceilings may be any of these:
* Price change ceiling applied to the market as a whole: Here, no seller is allowed to sell at a price more than some percentage higher than the market price at some point in the recent past (e.g., no seller is allowed to sell at more than 10% of the average price in the market last week).
* Price change ceiling specific to a seller: Here, the price a seller is currently selling at is compared to the price the seller sold at in the past.
* Price change ceiling specific to a pair of buyer and seller: This makes sense in the context of a repeat transaction. Rent regulations of the "vacancy decontrol" form are like that -- the rent of a given housing unit is allowed to increase at some maximum annual rate for a given pair of landlord and tenant, but once the tenant moves out, the landlord may give the apartment out for rent at any price.

For static analysis at a single point in time, price change ceilings may seem to function effectively as price ceilings; however, the long-run analysis (across multiple time periods where price changes can be made) is quite different. In particular, the "expectation regarding future prices" by both buyers and sellers, that shapes both the demand and supply curves, is affected by the structure of the price change ceiling. Despite these differences, in the cases where unexpected demand or supply shocks cause price change ceilings to create binding price ceilings, they behave qualitatively like uniform fixed price ceilings.

=== Profit ceiling ===

{{further|[[Profit ceiling]]}}

Here, sellers are forbidden from selling a good at a price greater than some multiple of the cost of production, to prevent excessive profiteering, while taking into account the cost of production.

Profit ceilings are effectively fixed price ceilings in cases where the marginal cost of production is constant across quantities and between sellers. However, in most real-world cases, profit ceilings are reasonably different from fixed price ceilings. Please see the [[profit ceiling]] page for more detailed models of how profit ceilings work.

=== A note on "voluntary" price ceilings ===

In general, only sellers with [[market power]] (i.e., sellers who can influence the market price, either as monopoly sellers or part of a small oligopoly) can adhere to voluntary price ceilings. Small sellers in a competitive market who choose to adhere to voluntary price ceilings, not raising prices to the market equilibrium, will not be able to meet the huge amount of market demand directed at them.

In the face of huge demand shocks and supply shocks, it is possible for ''de facto'' price ceilings to take effect, not through a single regulatory authority or marketplace controller, but though all sellers deciding to not risk increasing prices, even if that means shortfalls and forgone profits. The two typical reasons are:

* Potential regulation and litigation: Sellers may fear that if they raise prices, they will attract the ire of regulators, even if no current regulations forbid them raising prices.
* Public opinion: Sellers may fear that negative public sentiment against [[price gouging]] may hurt their reputation more than any additional profits they will make by selling at a higher price, or any additional goodwill they will generate among actual customers who appreciate not having a shortfall. The idea here is that it's not just the actual buyers, but also others who are unable to buy, or even general spectators, who could create trouble for the seller. The more diversified the seller, the bigger this public opinion concern (so a seller who ''only'' sells the good affected by the price ceiling may be less concerned, but a seller who sells many other goods may be concerned about reputational impact on sales of those other goods).

It is worth keeping in mind that this sort of "voluntary" price ceiling can really be effective only if some sellers have market power, or if there is widespread agreement between sellers about the wisdom of adhering to the "voluntary" price ceilings.

== The distinction between price ceiling-like policies and other similar market controls ==

=== Price ceilings versus sales taxes ===

As we'll discuss later on this page, price ceilings and [[sales tax]]es have similar effects -- they generally reduce quantity traded relative to an unrestricted market, and they cause a deadweight loss (which, in simple cases, is given by the Harberger triangle). Moreover, each approach has many real-world variants, so we should really think of a cluster of "price ceiling-like" policies versus a cluster of "sales tax-like" policies.

Conceptually, the main difference between the clusters is that sales tax-like policies aim to mimic the behavior of an unrestricted market -- just one where buyers and sellers see different prices (with the difference pocketed by the taxing authority). They therefore retain many of the dynamics of an unregulated market as far as the buyers and sellers individually are concerned. In contrast, price ceiling-like policies are qualitatively different from unrestricted markets to the point that buyers and sellers can see and feel the differences directly.

Price ceilings and sales taxes also work quite differently in non-competitive markets. In a monopoly market, it is possible for a price ceiling to increase the quantity traded. In contrast, a sales tax will reduce quantity traded, even in a monopoly market.

=== Price ceilings versus quantity ceilings ===

Both price ceilings and [[quantity ceiling]]s effectively create a situation where the quantity traded is less than it would be without a ceiling. However, quantity ceilings favor sellers over buyers, and also shift the burden of non-price competition to sellers: sellers compete with each other for permission to produce a larger share of the quantity ceiling.

==Basic theory: the effects of price ceilings in competitive markets==

The simple analysis in this section assumes a fixed price ceiling and ignores some of the indirect effects of price ceilings:

* Expectations regarding future prices: Price ceilings affect not just current prices but also expectations regarding future prices, on both the demand and supply side. This is particularly important for goods where buying now and buying later can substitute for each other, or where producing now and producing later are substitutes. In particular, the existence of the price ceiling affects the shape of the demand and supply curve. Moreover, the nature of the ceiling (whether it's a fixed price ceiling or a price change ceiling, and how people expect the price ceiling itself to evolve) plays a part in how this effect plays out. We will ignore these considerations.
* Interaction with price ceilings on substitute goods and complementary goods

===Non-binding price ceiling: price ceilings have no effect when they are above the market-clearing price===

A price ceiling that is set above the [[market price]] of the good has no direct short-run effect.

===Binding price ceiling: price ceilings create excess demand when they are below the market-clearing price===

If the price ceiling is below the [[market price]], the quantity demand for the good exceeds the quantity supplied for the good, resulting in a situation of scarcity or [[excess demand]]. This results in a loss of economic surplus compared to the situation of a market-clearing price.

For instance, in the figure below, if the price ceiling is set at the price level of the horizontal line AB, then there is a shortfall equal to the length of the segment AB.

Since a price ceiling creates a shortfall, it is not immediately clear which of the buyers willing to buy the good at the lower price will succeed in buying it (i.e., there is [[non-price competition]] among buyers, as discussed later in this page). Under the '''efficient allocation assumption''' (i.e., perfect sorting among buyers, ''and'' no costs imposed by non-price competition), the deadweight loss equals that arising from the case when the same quantity traded is accomplished by means of a [[sales tax]], and is described by the area of the [[Harberger triangle]], bounded by a vertical line through A and the demand and supply curves (so that two of its vertices are A and C). For more discussion, see [[Effect of price ceiling on economic surplus]].

[[File:Shortfallbelowmarketprice.png|500px]]

==Basic theory: the effects of price ceilings in monopolistic markets==

{{NeedsGraph}}

As was the case with the competitive markets analysis, the simple analysis in this section assumes a fixed price ceiling and ignores:

* Expectations regarding future prices
* Interaction with price ceilings on substitute goods and complementary goods

=== The basic case of increasing marginal costs ===

We restrict attention to cases where the monopolist's marginal cost curve is increasing, to avoid issues related to multiple optima. Many of the conclusions we draw are not dependent on this assumption.

There are three key price points relative to which price ceilings can be compared. For more context, see [[determination of price and quantity supplied by monopolistic firm in the short run]].

* The '''free market price''' (without any price ceiling), chosen by the monopolist for profit maximization.
* The '''optimal price''', which is the price point for the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market price would be if the market were competitive. This is based on the [[determination of quantity supplied by firm in perfectly competitive market in the short run]], where we find that the supply curve coincides with the short-run marginal cost curve if the latter is increasing.
* The '''free market marginal cost''', which is the marginal cost at the quantity being traded without any price ceiling. This is equal to the marginal revenue, since a monopolist optimizes at marginal cost equals marginal revenue.

There are two interesting values of quantity traded:

* The '''market quantity traded''', which is the quantity traded in the market without any price ceiling.
* The '''optimal quantity traded''', which is the maximum possible quantity traded, and is the quantity at the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market quantity traded would be if a competitive market were simulated with the same demand and supply structure.

We can now make cases based on the value of the price ceiling. We move the price ceiling ''down'', so the earlier rows discuss larger price ceilings and the later rows discuss lower price ceilings.

For any given price ceiling, there are two possibilities:

* It is a non-binding price ceiling, i.e., it is greater than or equal to the free market price. In this case, the market behavior remains the same as it would in a free market.
* It is a binding price ceiling in the sense of price, i.e., it is less than the free market price. In this case, the market price equals the binding price (note that this is no longer true with more complicated market structures, such as the case when the marginal cost curve is not increasing).

{| class="sortable" border="1"
! Price ceiling !! Binding or non-binding (binding means that the market price equals the ceiling, non-binding means it continues to equal the free market price) !! Quantity traded (compared to free market) !! Directional change in quantity traded as price decreases !! Location of the (price, quantity) pair !! Is there a shortfall?
|-
| Greater than or equal to than the free market price || Non-binding || Same || No change || On the market demand curve, same as without any price ceiling || No
|-
| Less than the free market price, but more than the optimal price || Binding || More || Increasing || On the market demand curve, moving down and right along the curve. The price being charged is the ''maximum'' possible price for the given quantity traded || No
|-
| Equal to the optimal price || Binding || More || Maximized || At the intersection of the market demand curve and short-run marginal cost curve || No
|-
| Less than the optimal price, but more than the free market marginal cost || Binding || More || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Equal to the free market marginal cost || Binding || Same || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Less than the free market marginal cost || Binding || Less || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|}

==Short-run impact of binding price ceilings in perfectly competitive markets==

===Non-price competition mechanisms===

The key problem that needs to be solved in case of a binding price ceiling is the problem: given that the quantity supplied is less than the quantity demanded, who among the different potential buyers of the good gets how much of it? There are two broad categories of approaches:

* Queueing, rationing, and queue-rationing
* Black markets

====Queueing, rationing, and queue-rationing====

{{further|[[Queueing, rationing, and queue-rationing]]}}

* Queueing is an approach where buyers are served in some form of a queue. The simplest is a time-based queue (first-come-first-serve) though other forms of priority queue are also possible.
* Rationing is an approach that limits the amount that each buyer can buy.
* Queue-rationing refers to a mix of queueing and rationing. For instance, each buyer can buy only a fixed amount in each iteration of purchase, and a buyer can take only one other position in the queue at a time (or even within a time period, for instance, per day). For instance, if the ration is 5 units per purchase, and the buyer wants to buy 48 units, the buyer will have to stand in the queue 10 times.

A key idea to keep in mind when thinking about these policies (queueing, rationing, and queue-rationing) is that the policies are determined mainly by sellers, but sellers do not internalize most of the gains from selecting policies that improve the efficiency of allocation between buyers. Sellers may, however, gain indirectly through reputational benefits, or spillover benefits to other goods the seller is selling.

====Black markets====

A [[black market]], or an illegal market in the good, is one way around the problem of a price ceiling. In this scenario, a small quantity of the good is sold in the legal market at a price equal to the price ceiling, whereas the rest of the good is sold in the black market at the true equilibrium price. In fact, the black market price may well be ''higher'' than the market price would be in the absence of a price ceiling, because of the added costs incurred by sellers to evade the law.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Under most sets of assumptions (in particular, assuming that there are no [[external cost]]s or [[external benefit]]s), price ceilings have a negative effect on economic surplus in competitive markets. In general, the following are true:

* Non-binding price ceilings have no effect on economic surplus.
* Binding price ceilings have negative effects on economic surplus as well as producer surplus, with the magnitude of the effect increasing as the ceiling price goes lower. The effect on consumer surplus is ambiguous. This is a [[deadweight loss]].

Note that there are three components to the deadweight loss arising due to a binding price ceiling:

* The ''inevitable'' deadweight loss, that is given by the area of the [[Harberger triangle]].
* The deadweight loss that arises due to imperfect sorting among buyers (i.e., buyers who value a good less get it). In other words, this occurs because non-price competition did not do its job well.
* The deadweight loss arising from the transaction costs associated with non-price competition.

==Short-run impact of binding price ceilings in monopolistic markets==

===Non-price competition mechanisms===

Similar to the case of a competitive market, binding price ceilings can create shortfalls, leading to non-price competition among buyers. However, unlike the case of competitive markets, not every binding price ceiling leads to a shortfall and to non-price competition. More specifically, a binding price ceiling leads to shortfalls only if it is set to below the optimal price as defined in [[#Basic theory: the effects of price ceilings in monopolistic markets]], i.e., the price at which the marginal cost curve and market demand curve intersect.

When the price ceiling is set to below the optimal price, the non-price competition mechanisms are similar to those in a competitive market, namely:

* Queueing, rationing, and queue-rationing
* Black markets

One difference is that since the monopolist has complete control over the supply of the market, it may be easier for the monopolist to choose the non-price competition strategy more freely.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Here we assume that the good being sold has no [[external cost|external costs]] or [[external benefit|external benefits]].

The discussion here builds on that in [[#Basic theory: the effects of price ceilings in monopolistic markets]]. You may need to reference that for more context around some of the terminology used.

For some of the rows, we can draw definite conclusions only under the '''efficient allocation assumption''': perfect sorting among buyers (the buyers who acquire the good are those who value it most highly), ''and'' the non-price competition imposes no extra costs on buyers and sellers. The caveats are noted in the corresponding cells where they apply.

The "optimal price" in the table below is obtained as the price point at the intersection of the marginal cost curve and the market demand curve. This is essentially what the price would be if the seller could be made to behave as if operating in perfect competition.
{| class="sortable" border="1"
! Price ceiling range !! economic surplus compared to no price ceiling !! Producer surplus compared to no price ceiling !! Consumer surplus compared to no price ceiling !! Direction of change of economic surplus with decreasing price ceiling !! Direction of change of producer surplus with decreasing price ceiling !! Direction of change of consumer surplus with decreasing price ceiling !! Qualitative comments
|-
| Greater than or equal to the free market price || Same || Same || Same || None || None || None || Deadweight loss is intact as the price ceiling has no effect
|-
| Less than the free market price and greater than the optimal price || More || Less || More || Increasing || Decreasing || Increasing || Deadweight loss due to monopoly is ameliorated by the price ceiling
|-
| Equal to the optimal price || More || Less || More || Maximized || Decreasing || Ambiguous || Deadweight loss is eliminated as perfect competition is emulated
|-
| Less than the optimal price and greater than the free market marginal cost || More (assuming efficient allocation), indeterminate otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || Deadweight loss is now no longer due to monopolistic pricing but rather due to price ceilings cutting off beneficial transactions
|-
| Equal to the free market marginal cost || Same (assuming efficient allocation), less otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || The quantity traded mimics that in the no-ceiling case, but the price at which the trades occur is lower. Assuming efficient allocation (i.e., the goods go to the buyers valuing them most highly), the economic surplus is the same but it is distributed more to consumers. Without the efficient allocation assumption, total economic surplus is down, with producer surplus down and the effect on consumer surplus indeterminate.
|-
| Less than the free market marginal cost || Less || Less || Starts out as more (assuming efficient allocation), may later becomes less. Without the efficient allocation assumption, indeterminate. || Decreasing || Decreasing || Ambiguous || Deadweight loss now exceeds that of monopoly, even under the efficient allocation assumption.
|}

==Long-run impact of price ceilings==

The long-run impact of a price ceiling is a much more complicated matter than the short-run impact. There are, roughly speaking, three sources of complication:

* Expectations regarding future demand and supply patterns: A price ceiling that is binding today may become non-binding in the future, and a price ceiling that is non-binding today may become binding in the future. Both the normal course of supply-and-demand changes as well as low-probability demand and supply shocks need to be examined in connection with the price ceiling.
* Intertemporal substitution with the future: Buyers and sellers who can substitute buying or selling now against buying or selling in the future, have to consider the effect of the price ceiling on how they distribute their buying or selling behavior over time. Note that this long-run consideration can also change the present-day shape of the supply and demand curves, thereby causing a short-run effect.
* The distinction between short-run and long-run supply, through reconfiguration: In the short run, sellers are generally constrained to a increasing short-run marginal cost curve. In the long run, the seller can change the mix of inputs, for instance, by acquiring more land and capital or hiring more people.

The type of impact a price ceiling has also depends on its structure. The analysis can differ quite a bit between uniform fixed price ceilings, price change ceilings, and profit ceilings. However, we can say a few broad things.

=== Price ceilings are more likely to cause firms to exit the market in the long run than in the short run, and have qualitatively different effects in increasing cost industries versus decreasing cost industries ===

In the short run, even in the face of a price ceiling, a firm may continue to produce as long as the minimum AVC value (at [[minimum efficient scale]]) is less than the price ceiling. That's because the firm has sunk its fixed costs. If the price ceiling is even lower than the firm's AVC, the firm may simply stay idle in the short run.

In the long run, however, firms are looking at their average total cost and comparing it with the minimum between what they expect the price to be (taking the minimum across the price ceiling and market price). There are two competing considerations here -- the ability to optimize better in the long run, and the ability to exit altogether in the long run. Here is how they interact for a firm in a large, competitive market:

* On the one hand, the long-run knowledge of the price ceiling allows the firm to choose a configuration of fixed and variable costs that is optimized for that price ceiling, rather than its prediction for the unrestricted price.
** For an [[increasing cost industry]], the firm will do so by reducing its fixed costs and reducing overall production. This can make the shortfall even worse than in the short run.
** For a [[constant cost industry]] or [[decreasing cost industry]], the firm (since it is small relative to the market) will still keep producing at maximum capacity. So there is no change.
* On the other hand, solving this problem might also show the firm that it does not have a configuration that allows for long-run profitability. Specifically, if the price ceiling is less than the minimum possible average total cost (ATC) for the firm, it will exit the market.
** For a constant cost industry or decreasing cost industry, the minimum ATC is attained at the maximum level of production. In other words, in such cases, if even at the maximum level of production, the firm is unable to make its ATC drop to below the price ceiling, it will exit the market. Over time, this might reduce the number of firms in the market, causing larger shortfalls.

The situation is a little different in a monopolistic firm, but the underlying trade-off remains the same: the firm can optimize better in the long run, but it can also choose to exit altogether.

=== Generally, price ceilings reduce seller incentives to prepare for demand and supply shocks, but the story is a little more complicated ===

A price ceiling that is non-binding now could become binding in the face of a demand shock or supply shock that increases market prices, especially in the short run when firms cannot reconfigure their factors of production.

If the price mechanism is allowed to operate freely, the firm may have stronger incentives to prepare for such situations, because the better prepared it is, the more it can sell and the more it can profit from the increased prices. Specifically, the firm may do one or more of these:

* Stockpile extra production that can be released into the market in the face of a demand or supply shock that raises price.
* Develop better forecasting so that shocks can be anticipated, and prepared for a little bit in advance (this can be combined with the previous point to give the idea of "speculative production" -- if the forecast shows increased demand, then start stockpiling).
* Configure their production process so that it is easier to reconfigure quickly (i.e., make the long run less long).

For instance, let's say a firm is one firm among many in a competitive market and an increasing cost industry (we'll assume an increasing cost industry because with a decreasing cost industry, firms are anyway maxed out on production capacity). The market price of a good under normal conditions is 1. The firm correctly forecasts a soon-to-happen demand shock that would cause the market price to go up to 3,. There is a price ceiling of 2.

* If there were no price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a market price of 3.
* Due to the price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a price of 2.

Comparing these two, we see that the price ceiling prevents the firm from capturing all the gains in market price. Therefore, even if the firm does increase its production, it will increase it to a lower level (enough for the price ceiling of 2) rather than to the higher level (enough for the market price of 3). Thus, although the firm's long-run planning will alleviate the shortfall a little bit compared to not being prepared at all, the shortfall is still not going to be eliminated.

The above assumes that the firm has definite knowledge of the demand shock. However, the situation gets more complicated when the demand shock is more probabilistic. For instance, if the firm believes that there is some probability that a demand shock will cause the market price to rise to 3. The firm has to choose to reconfigure its fixed costs to gear toward producing enough for the market price of 3, or stay with its current setup, or anything in between. Whatever choice the firm makes, it will have to compare the expected gain from that choice of both the options.

Even in this more complicated situation, the presence of the price ceiling reduces, overall, the extent to which the firm will increase its production, by reducing the upside. However, the specifics will depend on other questions such as whether the firm's production cycle, as well as its buyers, can engage in intertemporal substitution.

Note that this analysis is contingent on some assumptions:

* The price ceiling is a uniform fixed price ceiling: More complicated price ceiling formulas, like [[price change ceiling]]s and [[profit ceiling]]s, share some qualitative characteristics but are also different in other ways.
* The price ceiling is known in advance to the firm: A price ceiling imposed suddenly without warning after a demand shock will have a less detrimental effect on quantity; the firm that had ramped up production has now already invested the fixed costs (thinking it could profit more), and is therefore able to produce more.

=== Price ceilings can change the way buyers substitute intertemporally ===

For goods where present purchases can substitute for future purchases, buyers respond to expectations of future price increases by buying more now. In markets with price ceilings that may become binding, buyers have to factor in not just the future market prices but also future availability. This can change the buyers' decision of how much to buy now, but it's ambiguous in what direction the buyers' behavior will change. Specifically, the way the buyers' behavior changes depends partly on how much each buyer perceives as the costs of non-price competition and how much the buyer's individual reservation price compared with the market price.

For instance, let's say buyers expect a demand shock or supply shock in the future that would, in a free market, cause the price of toilet paper to rise. This might incentivize buyers to stock up on toilet paper right now. Now, if a price ceiling is implemented that prevents the price of toilet paper from rising, buyers' expectations will shift from an expectation of increased price to an expectation of reduced availability, and the possibility that the buyer may have to engage in non-price competition to get the good. This, too, might incentivize buyers to stock up on toilet paper right now. However, the relative strength of the incentive to stock up on toilet paper, between the free market and price ceiling case, is ambiguous.

This ambiguity is related to the idea that the effect of price ceilings on consumer surplus is ambiguous (though it's definitely negative for producer surplus and overall economic surplus).

Note that the possibility of [[black market]]s does increase the incentive to buy and hoard.

==Related notions==

* [[Maximum retail price]] is an upper limit that the producer or wholesale distributor puts on the price at which retailers can sell the commodity to customers. Maximum retail prices do not usually have the inefficiencies associated with price ceilings, because producers of the goods can vary maximum retail prices according to demand trends over the somewhat longer term.

Price ceiling

2020-03-31T04:15:46Z

Vipul: /* Long-run impact of price ceilings */

==Definition==

A '''price ceiling''' is an upper limit placed by a regulatory authority (such as a government, or regulatory authority with government sanction, or private party controlling a marketplace) on the price (per unit) of a good.

A price ceiling is a form of [[price control]]. Other forms of price control include [[minimum price]]s, [[price change ceiling]]s, and [[profit ceiling]]s.

At any given time, a price ceiling is one of these:

* '''Non-binding price ceiling''': This is a [[price ceiling]] that is greater than the current [[market price]].
* '''Binding price ceiling''': This is a [[price ceiling]] that is less than the current [[market price]]. Binding price ceilings cause a reduction in the price, and may increase or decrease the quantity traded depending on the market structure.

A particularly extreme form of price ceiling, which is not usually thought of that way, is a price ceiling of zero. This refers to situations where it is legal to give a good or service for free but it is illegal to offer the good or service in exchange for money. Price ceilings of zero are usually justified on aesthetic and ethical grounds as it is believed that the exchange of money sullies certain types of transaction. Since the market price for most forms of exchange is positive, price ceilings of zero are typically binding price ceilings. Examples include:

* [[Prostitution]] (the sale of sexual services), which is illegal, though not often rigorously prosecuted, in many countries
* [[Organ trade]], i.e., there are often jurisdictions where it is legal to donate an organ such as a kidney but illegal to buy or sell it.
* Adoption: In many places, it is not legal for a pregnant mother to sell her baby for adoption to a couple willing to adopt the kid, though it is legal to put the baby up for adoption.

== Type of price ceilings based on how they apply ==

=== Uniform fixed price ceiling ===

The simplest kind of price ceiling is a price ceiling that is fixed (i.e., a fixed price per unit) and imposed uniformly across all transactions, i.e., for all buyers and sellers. The value of this fixed price ceiling may change over time but generally does so through discrete policy changes. Therefore, in the short run, and possibly even the medium-to-long run, the price ceiling can be considered fixed.

There are two other kinds of variants of price ceilings.

=== Price change ceiling ===

{{further|[[Price change ceiling]]}}

This is a ceiling on how rapidly a price is allowed to increase. Price change ceilings may be any of these:
* Price change ceiling applied to the market as a whole: Here, no seller is allowed to sell at a price more than some percentage higher than the market price at some point in the recent past (e.g., no seller is allowed to sell at more than 10% of the average price in the market last week).
* Price change ceiling specific to a seller: Here, the price a seller is currently selling at is compared to the price the seller sold at in the past.
* Price change ceiling specific to a pair of buyer and seller: This makes sense in the context of a repeat transaction. Rent regulations of the "vacancy decontrol" form are like that -- the rent of a given housing unit is allowed to increase at some maximum annual rate for a given pair of landlord and tenant, but once the tenant moves out, the landlord may give the apartment out for rent at any price.

For static analysis at a single point in time, price change ceilings may seem to function effectively as price ceilings; however, the long-run analysis (across multiple time periods where price changes can be made) is quite different. In particular, the "expectation regarding future prices" by both buyers and sellers, that shapes both the demand and supply curves, is affected by the structure of the price change ceiling. Despite these differences, in the cases where unexpected demand or supply shocks cause price change ceilings to create binding price ceilings, they behave qualitatively like uniform fixed price ceilings.

=== Profit ceiling ===

{{further|[[Profit ceiling]]}}

Here, sellers are forbidden from selling a good at a price greater than some multiple of the cost of production, to prevent excessive profiteering, while taking into account the cost of production.

Profit ceilings are effectively fixed price ceilings in cases where the marginal cost of production is constant across quantities and between sellers. However, in most real-world cases, profit ceilings are reasonably different from fixed price ceilings. Please see the [[profit ceiling]] page for more detailed models of how profit ceilings work.

=== A note on "voluntary" price ceilings ===

In general, only sellers with [[market power]] (i.e., sellers who can influence the market price, either as monopoly sellers or part of a small oligopoly) can adhere to voluntary price ceilings. Small sellers in a competitive market who choose to adhere to voluntary price ceilings, not raising prices to the market equilibrium, will not be able to meet the huge amount of market demand directed at them.

In the face of huge demand shocks and supply shocks, it is possible for ''de facto'' price ceilings to take effect, not through a single regulatory authority or marketplace controller, but though all sellers deciding to not risk increasing prices, even if that means shortfalls and forgone profits. The two typical reasons are:

* Potential regulation and litigation: Sellers may fear that if they raise prices, they will attract the ire of regulators, even if no current regulations forbid them raising prices.
* Public opinion: Sellers may fear that negative public sentiment against [[price gouging]] may hurt their reputation more than any additional profits they will make by selling at a higher price, or any additional goodwill they will generate among actual customers who appreciate not having a shortfall. The idea here is that it's not just the actual buyers, but also others who are unable to buy, or even general spectators, who could create trouble for the seller. The more diversified the seller, the bigger this public opinion concern (so a seller who ''only'' sells the good affected by the price ceiling may be less concerned, but a seller who sells many other goods may be concerned about reputational impact on sales of those other goods).

It is worth keeping in mind that this sort of "voluntary" price ceiling can really be effective only if some sellers have market power, or if there is widespread agreement between sellers about the wisdom of adhering to the "voluntary" price ceilings.

== The distinction between price ceiling-like policies and other similar market controls ==

=== Price ceilings versus sales taxes ===

As we'll discuss later on this page, price ceilings and [[sales tax]]es have similar effects -- they generally reduce quantity traded relative to an unrestricted market, and they cause a deadweight loss (which, in simple cases, is given by the Harberger triangle). Moreover, each approach has many real-world variants, so we should really think of a cluster of "price ceiling-like" policies versus a cluster of "sales tax-like" policies.

Conceptually, the main difference between the clusters is that sales tax-like policies aim to mimic the behavior of an unrestricted market -- just one where buyers and sellers see different prices (with the difference pocketed by the taxing authority). They therefore retain many of the dynamics of an unregulated market as far as the buyers and sellers individually are concerned. In contrast, price ceiling-like policies are qualitatively different from unrestricted markets to the point that buyers and sellers can see and feel the differences directly.

Price ceilings and sales taxes also work quite differently in non-competitive markets. In a monopoly market, it is possible for a price ceiling to increase the quantity traded. In contrast, a sales tax will reduce quantity traded, even in a monopoly market.

=== Price ceilings versus quantity ceilings ===

Both price ceilings and [[quantity ceiling]]s effectively create a situation where the quantity traded is less than it would be without a ceiling. However, quantity ceilings favor sellers over buyers, and also shift the burden of non-price competition to sellers: sellers compete with each other for permission to produce a larger share of the quantity ceiling.

==Basic theory: the effects of price ceilings in competitive markets==

The simple analysis in this section assumes a fixed price ceiling and ignores some of the indirect effects of price ceilings:

* Expectations regarding future prices: Price ceilings affect not just current prices but also expectations regarding future prices, on both the demand and supply side. This is particularly important for goods where buying now and buying later can substitute for each other, or where producing now and producing later are substitutes. In particular, the existence of the price ceiling affects the shape of the demand and supply curve. Moreover, the nature of the ceiling (whether it's a fixed price ceiling or a price change ceiling, and how people expect the price ceiling itself to evolve) plays a part in how this effect plays out. We will ignore these considerations.
* Interaction with price ceilings on substitute goods and complementary goods

===Non-binding price ceiling: price ceilings have no effect when they are above the market-clearing price===

A price ceiling that is set above the [[market price]] of the good has no direct short-run effect.

===Binding price ceiling: price ceilings create excess demand when they are below the market-clearing price===

If the price ceiling is below the [[market price]], the quantity demand for the good exceeds the quantity supplied for the good, resulting in a situation of scarcity or [[excess demand]]. This results in a loss of economic surplus compared to the situation of a market-clearing price.

For instance, in the figure below, if the price ceiling is set at the price level of the horizontal line AB, then there is a shortfall equal to the length of the segment AB.

Since a price ceiling creates a shortfall, it is not immediately clear which of the buyers willing to buy the good at the lower price will succeed in buying it (i.e., there is [[non-price competition]] among buyers, as discussed later in this page). Under the '''efficient allocation assumption''' (i.e., perfect sorting among buyers, ''and'' no costs imposed by non-price competition), the deadweight loss equals that arising from the case when the same quantity traded is accomplished by means of a [[sales tax]], and is described by the area of the [[Harberger triangle]], bounded by a vertical line through A and the demand and supply curves (so that two of its vertices are A and C). For more discussion, see [[Effect of price ceiling on economic surplus]].

[[File:Shortfallbelowmarketprice.png|500px]]

==Basic theory: the effects of price ceilings in monopolistic markets==

{{NeedsGraph}}

As was the case with the competitive markets analysis, the simple analysis in this section assumes a fixed price ceiling and ignores:

* Expectations regarding future prices
* Interaction with price ceilings on substitute goods and complementary goods

=== The basic case of increasing marginal costs ===

We restrict attention to cases where the monopolist's marginal cost curve is increasing, to avoid issues related to multiple optima. Many of the conclusions we draw are not dependent on this assumption.

There are three key price points relative to which price ceilings can be compared. For more context, see [[determination of price and quantity supplied by monopolistic firm in the short run]].

* The '''free market price''' (without any price ceiling), chosen by the monopolist for profit maximization.
* The '''optimal price''', which is the price point for the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market price would be if the market were competitive. This is based on the [[determination of quantity supplied by firm in perfectly competitive market in the short run]], where we find that the supply curve coincides with the short-run marginal cost curve if the latter is increasing.
* The '''free market marginal cost''', which is the marginal cost at the quantity being traded without any price ceiling. This is equal to the marginal revenue, since a monopolist optimizes at marginal cost equals marginal revenue.

There are two interesting values of quantity traded:

* The '''market quantity traded''', which is the quantity traded in the market without any price ceiling.
* The '''optimal quantity traded''', which is the maximum possible quantity traded, and is the quantity at the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market quantity traded would be if a competitive market were simulated with the same demand and supply structure.

We can now make cases based on the value of the price ceiling. We move the price ceiling ''down'', so the earlier rows discuss larger price ceilings and the later rows discuss lower price ceilings.

For any given price ceiling, there are two possibilities:

* It is a non-binding price ceiling, i.e., it is greater than or equal to the free market price. In this case, the market behavior remains the same as it would in a free market.
* It is a binding price ceiling in the sense of price, i.e., it is less than the free market price. In this case, the market price equals the binding price (note that this is no longer true with more complicated market structures, such as the case when the marginal cost curve is not increasing).

{| class="sortable" border="1"
! Price ceiling !! Binding or non-binding (binding means that the market price equals the ceiling, non-binding means it continues to equal the free market price) !! Quantity traded (compared to free market) !! Directional change in quantity traded as price decreases !! Location of the (price, quantity) pair !! Is there a shortfall?
|-
| Greater than or equal to than the free market price || Non-binding || Same || No change || On the market demand curve, same as without any price ceiling || No
|-
| Less than the free market price, but more than the optimal price || Binding || More || Increasing || On the market demand curve, moving down and right along the curve. The price being charged is the ''maximum'' possible price for the given quantity traded || No
|-
| Equal to the optimal price || Binding || More || Maximized || At the intersection of the market demand curve and short-run marginal cost curve || No
|-
| Less than the optimal price, but more than the free market marginal cost || Binding || More || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Equal to the free market marginal cost || Binding || Same || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Less than the free market marginal cost || Binding || Less || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|}

==Short-run impact of binding price ceilings in perfectly competitive markets==

===Non-price competition mechanisms===

The key problem that needs to be solved in case of a binding price ceiling is the problem: given that the quantity supplied is less than the quantity demanded, who among the different potential buyers of the good gets how much of it? There are two broad categories of approaches:

* Queueing, rationing, and queue-rationing
* Black markets

====Queueing, rationing, and queue-rationing====

{{further|[[Queueing, rationing, and queue-rationing]]}}

* Queueing is an approach where buyers are served in some form of a queue. The simplest is a time-based queue (first-come-first-serve) though other forms of priority queue are also possible.
* Rationing is an approach that limits the amount that each buyer can buy.
* Queue-rationing refers to a mix of queueing and rationing. For instance, each buyer can buy only a fixed amount in each iteration of purchase, and a buyer can take only one other position in the queue at a time (or even within a time period, for instance, per day). For instance, if the ration is 5 units per purchase, and the buyer wants to buy 48 units, the buyer will have to stand in the queue 10 times.

A key idea to keep in mind when thinking about these policies (queueing, rationing, and queue-rationing) is that the policies are determined mainly by sellers, but sellers do not internalize most of the gains from selecting policies that improve the efficiency of allocation between buyers. Sellers may, however, gain indirectly through reputational benefits, or spillover benefits to other goods the seller is selling.

====Black markets====

A [[black market]], or an illegal market in the good, is one way around the problem of a price ceiling. In this scenario, a small quantity of the good is sold in the legal market at a price equal to the price ceiling, whereas the rest of the good is sold in the black market at the true equilibrium price. In fact, the black market price may well be ''higher'' than the market price would be in the absence of a price ceiling, because of the added costs incurred by sellers to evade the law.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Under most sets of assumptions (in particular, assuming that there are no [[external cost]]s or [[external benefit]]s), price ceilings have a negative effect on economic surplus in competitive markets. In general, the following are true:

* Non-binding price ceilings have no effect on economic surplus.
* Binding price ceilings have negative effects on economic surplus as well as producer surplus, with the magnitude of the effect increasing as the ceiling price goes lower. The effect on consumer surplus is ambiguous. This is a [[deadweight loss]].

Note that there are three components to the deadweight loss arising due to a binding price ceiling:

* The ''inevitable'' deadweight loss, that is given by the area of the [[Harberger triangle]].
* The deadweight loss that arises due to imperfect sorting among buyers (i.e., buyers who value a good less get it). In other words, this occurs because non-price competition did not do its job well.
* The deadweight loss arising from the transaction costs associated with non-price competition.

==Short-run impact of binding price ceilings in monopolistic markets==

===Non-price competition mechanisms===

Similar to the case of a competitive market, binding price ceilings can create shortfalls, leading to non-price competition among buyers. However, unlike the case of competitive markets, not every binding price ceiling leads to a shortfall and to non-price competition. More specifically, a binding price ceiling leads to shortfalls only if it is set to below the optimal price as defined in [[#Basic theory: the effects of price ceilings in monopolistic markets]], i.e., the price at which the marginal cost curve and market demand curve intersect.

When the price ceiling is set to below the optimal price, the non-price competition mechanisms are similar to those in a competitive market, namely:

* Queueing, rationing, and queue-rationing
* Black markets

One difference is that since the monopolist has complete control over the supply of the market, it may be easier for the monopolist to choose the non-price competition strategy more freely.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Here we assume that the good being sold has no [[external cost|external costs]] or [[external benefit|external benefits]].

The discussion here builds on that in [[#Basic theory: the effects of price ceilings in monopolistic markets]]. You may need to reference that for more context around some of the terminology used.

For some of the rows, we can draw definite conclusions only under the '''efficient allocation assumption''': perfect sorting among buyers (the buyers who acquire the good are those who value it most highly), ''and'' the non-price competition imposes no extra costs on buyers and sellers. The caveats are noted in the corresponding cells where they apply.

The "optimal price" in the table below is obtained as the price point at the intersection of the marginal cost curve and the market demand curve. This is essentially what the price would be if the seller could be made to behave as if operating in perfect competition.
{| class="sortable" border="1"
! Price ceiling range !! economic surplus compared to no price ceiling !! Producer surplus compared to no price ceiling !! Consumer surplus compared to no price ceiling !! Direction of change of economic surplus with decreasing price ceiling !! Direction of change of producer surplus with decreasing price ceiling !! Direction of change of consumer surplus with decreasing price ceiling !! Qualitative comments
|-
| Greater than or equal to the free market price || Same || Same || Same || None || None || None || Deadweight loss is intact as the price ceiling has no effect
|-
| Less than the free market price and greater than the optimal price || More || Less || More || Increasing || Decreasing || Increasing || Deadweight loss due to monopoly is ameliorated by the price ceiling
|-
| Equal to the optimal price || More || Less || More || Maximized || Decreasing || Ambiguous || Deadweight loss is eliminated as perfect competition is emulated
|-
| Less than the optimal price and greater than the free market marginal cost || More (assuming efficient allocation), indeterminate otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || Deadweight loss is now no longer due to monopolistic pricing but rather due to price ceilings cutting off beneficial transactions
|-
| Equal to the free market marginal cost || Same (assuming efficient allocation), less otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || The quantity traded mimics that in the no-ceiling case, but the price at which the trades occur is lower. Assuming efficient allocation (i.e., the goods go to the buyers valuing them most highly), the economic surplus is the same but it is distributed more to consumers. Without the efficient allocation assumption, total economic surplus is down, with producer surplus down and the effect on consumer surplus indeterminate.
|-
| Less than the free market marginal cost || Less || Less || Starts out as more (assuming efficient allocation), may later becomes less. Without the efficient allocation assumption, indeterminate. || Decreasing || Decreasing || Ambiguous || Deadweight loss now exceeds that of monopoly, even under the efficient allocation assumption.
|}

==Long-run impact of price ceilings==

The long-run impact of a price ceiling is a much more complicated matter than the short-run impact. There are, roughly speaking, three sources of complication:

* Expectations regarding future demand and supply patterns: A price ceiling that is binding today may become non-binding in the future, and a price ceiling that is non-binding today may become binding in the future. Both the normal course of supply-and-demand changes as well as low-probability demand and supply shocks need to be examined in connection with the price ceiling.
* Intertemporal substitution with the future: Buyers and sellers who can substitute buying or selling now against buying or selling in the future, have to consider the effect of the price ceiling on how they distribute their buying or selling behavior over time. Note that this long-run consideration can also change the present-day shape of the supply and demand curves, thereby causing a short-run effect.
* The distinction between short-run and long-run supply, through reconfiguration: In the short run, sellers are generally constrained to a increasing short-run marginal cost curve. In the long run, the seller can change the mix of inputs, for instance, by acquiring more land and capital or hiring more people.

The type of impact a price ceiling has also depends on its structure. The analysis can differ quite a bit between uniform fixed price ceilings, price change ceilings, and profit ceilings. However, we can say a few broad things.

=== Price ceilings are more likely to cause firms to exit the market in the long run than in the short run, and have qualitatively different effects in increasing cost industries versus decreasing cost industries ===

In the short run, even in the face of a price ceiling, a firm may continue to produce as long as the minimum AVC value (at [[minimum efficient scale]]) is less than the price ceiling. That's because the firm has sunk its fixed costs. If the price ceiling is even lower than the firm's AVC, the firm may simply stay idle in the short run.

In the long run, however, firms are looking at their average total cost and comparing it with the minimum between what they expect the price to be (taking the minimum across the price ceiling and market price). There are two competing considerations here -- the ability to optimize better in the long run, and the ability to exit altogether in the long run. Here is how they interact for a firm in a large, competitive market:

* On the one hand, the long-run knowledge of the price ceiling allows the firm to choose a configuration of fixed and variable costs that is optimized for that price ceiling, rather than its prediction for the unrestricted price.
** For an [[increasing cost industry]], the firm will do so by reducing its fixed costs and reducing overall production. This can make the shortfall even worse than in the short run.
** For a [[constant cost industry]] or [[decreasing cost industry]], the firm (since it is small relative to the market) will still keep producing at maximum capacity. So there is no change.
* On the other hand, solving this problem might also show the firm that it does not have a configuration that allows for long-run profitability. Specifically, if the price ceiling is less than the minimum possible average total cost (ATC) for the firm, it will exit the market.
** For a constant cost industry or decreasing cost industry, the minimum ATC is attained at the maximum level of production. In other words, in such cases, if even at the maximum level of production, the firm is unable to make its ATC drop to below the price ceiling, it will exit the market. Over time, this might reduce the number of firms in the market, causing larger shortfalls.

The situation is a little different in a monopolistic firm, but the underlying trade-off remains the same: the firm can optimize better in the long run, but it can also choose to exit altogether.

=== Generally, price ceilings reduce seller incentives to prepare for demand and supply shocks, but the story is a little more complicated ===

A price ceiling that is non-binding now could become binding in the face of a demand shock or supply shock that increases market prices, especially in the short run when firms cannot reconfigure their factors of production.

If the price mechanism is allowed to operate freely, the firm may have stronger incentives to prepare for such situations, because the better prepared it is, the more it can sell and the more it can profit from the increased prices. Specifically, the firm may do one or more of these:

* Stockpile extra production that can be released into the market in the face of a demand or supply shock that raises price.
* Develop better forecasting so that shocks can be anticipated, and prepared for a little bit in advance (this can be combined with the previous point to give the idea of "speculative production" -- if the forecast shows increased demand, then start stockpiling).
* Configure their production process so that it is easier to reconfigure quickly (i.e., make the long run less long).

For instance, let's say a firm is one firm among many in a competitive market and an increasing cost industry (we'll assume an increasing cost industry because with a decreasing cost industry, firms are anyway maxed out on production capacity). The market price of a good under normal conditions is 1. The firm correctly forecasts a soon-to-happen demand shock that would cause the market price to go up to 3, with some probability. There is a price ceiling of 2.

* If there were no price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a market price of 3.
* Due to the price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a price of 2.

Comparing these two, we see that the price ceiling prevents the firm from capturing all the gains in market price. Therefore, even if the firm does increase its production, it will increase it to a lower level (enough for the price ceiling of 2) rather than to the higher level (enough for the market price of 3). Thus, although the firm's long-run planning will alleviate the shortfall a little bit compared to not being prepared at all, the shortfall is still not going to be eliminated.

The above assumes that the firm has definite knowledge of the demand shock. However, the situation gets more complicated when the demand shock is more probabilistic. For instance, if the firm believes that there is some probability that a demand shock will cause the market price to rise to 3. The firm has to choose to reconfigure its fixed costs to gear toward producing enough for the market price of 3, or stay with its current setup, or anything in between. Whatever choice the firm makes, it will have to compare the expected gain from that choice of both the options.

Even in this more complicated situation, the presence of the price ceiling reduces, overall, the extent to which the firm will increase its production, by reducing the upside. However, the specifics will depend on other questions such as whether the firm's production cycle, as well as its buyers, can engage in intertemporal substitution.

Note that this analysis is contingent on some assumptions:

* The price ceiling is a uniform fixed price ceiling: More complicated price ceiling formulas, like [[price change ceiling]]s and [[profit ceiling]]s, share some qualitative characteristics but are also different in other ways.
* The price ceiling is known in advance to the firm: A price ceiling imposed suddenly without warning after a demand shock will have a less detrimental effect on quantity; the firm that had ramped up production has now already invested the fixed costs (thinking it could profit more), and is therefore able to produce more.

=== Price ceilings can change the way buyers substitute intertemporally ===

For goods where present purchases can substitute for future purchases, buyers respond to expectations of future price increases by buying more now. In markets with price ceilings that may become binding, buyers have to factor in not just the future market prices but also future availability. This can change the buyers' decision of how much to buy now, but it's ambiguous in what direction the buyers' behavior will change. Specifically, the way the buyers' behavior changes depends partly on how much each buyer perceives as the costs of non-price competition and how much the buyer's individual reservation price compared with the market price.

For instance, let's say buyers expect a demand shock or supply shock in the future that would, in a free market, cause the price of toilet paper to rise. This might incentivize buyers to stock up on toilet paper right now. Now, if a price ceiling is implemented that prevents the price of toilet paper from rising, buyers' expectations will shift from an expectation of increased price to an expectation of reduced availability, and the possibility that the buyer may have to engage in non-price competition to get the good. This, too, might incentivize buyers to stock up on toilet paper right now. However, the relative strength of the incentive to stock up on toilet paper, between the free market and price ceiling case, is ambiguous.

This ambiguity is related to the idea that the effect of price ceilings on consumer surplus is ambiguous (though it's definitely negative for producer surplus and overall economic surplus).

Note that the possibility of [[black market]]s does increase the incentive to buy and hoard.

==Related notions==

* [[Maximum retail price]] is an upper limit that the producer or wholesale distributor puts on the price at which retailers can sell the commodity to customers. Maximum retail prices do not usually have the inefficiencies associated with price ceilings, because producers of the goods can vary maximum retail prices according to demand trends over the somewhat longer term.

Price ceiling

2020-03-31T04:14:00Z

Vipul: /* Queueing, rationing, and queue-rationing */

==Definition==

A '''price ceiling''' is an upper limit placed by a regulatory authority (such as a government, or regulatory authority with government sanction, or private party controlling a marketplace) on the price (per unit) of a good.

A price ceiling is a form of [[price control]]. Other forms of price control include [[minimum price]]s, [[price change ceiling]]s, and [[profit ceiling]]s.

At any given time, a price ceiling is one of these:

* '''Non-binding price ceiling''': This is a [[price ceiling]] that is greater than the current [[market price]].
* '''Binding price ceiling''': This is a [[price ceiling]] that is less than the current [[market price]]. Binding price ceilings cause a reduction in the price, and may increase or decrease the quantity traded depending on the market structure.

A particularly extreme form of price ceiling, which is not usually thought of that way, is a price ceiling of zero. This refers to situations where it is legal to give a good or service for free but it is illegal to offer the good or service in exchange for money. Price ceilings of zero are usually justified on aesthetic and ethical grounds as it is believed that the exchange of money sullies certain types of transaction. Since the market price for most forms of exchange is positive, price ceilings of zero are typically binding price ceilings. Examples include:

* [[Prostitution]] (the sale of sexual services), which is illegal, though not often rigorously prosecuted, in many countries
* [[Organ trade]], i.e., there are often jurisdictions where it is legal to donate an organ such as a kidney but illegal to buy or sell it.
* Adoption: In many places, it is not legal for a pregnant mother to sell her baby for adoption to a couple willing to adopt the kid, though it is legal to put the baby up for adoption.

== Type of price ceilings based on how they apply ==

=== Uniform fixed price ceiling ===

The simplest kind of price ceiling is a price ceiling that is fixed (i.e., a fixed price per unit) and imposed uniformly across all transactions, i.e., for all buyers and sellers. The value of this fixed price ceiling may change over time but generally does so through discrete policy changes. Therefore, in the short run, and possibly even the medium-to-long run, the price ceiling can be considered fixed.

There are two other kinds of variants of price ceilings.

=== Price change ceiling ===

{{further|[[Price change ceiling]]}}

This is a ceiling on how rapidly a price is allowed to increase. Price change ceilings may be any of these:
* Price change ceiling applied to the market as a whole: Here, no seller is allowed to sell at a price more than some percentage higher than the market price at some point in the recent past (e.g., no seller is allowed to sell at more than 10% of the average price in the market last week).
* Price change ceiling specific to a seller: Here, the price a seller is currently selling at is compared to the price the seller sold at in the past.
* Price change ceiling specific to a pair of buyer and seller: This makes sense in the context of a repeat transaction. Rent regulations of the "vacancy decontrol" form are like that -- the rent of a given housing unit is allowed to increase at some maximum annual rate for a given pair of landlord and tenant, but once the tenant moves out, the landlord may give the apartment out for rent at any price.

For static analysis at a single point in time, price change ceilings may seem to function effectively as price ceilings; however, the long-run analysis (across multiple time periods where price changes can be made) is quite different. In particular, the "expectation regarding future prices" by both buyers and sellers, that shapes both the demand and supply curves, is affected by the structure of the price change ceiling. Despite these differences, in the cases where unexpected demand or supply shocks cause price change ceilings to create binding price ceilings, they behave qualitatively like uniform fixed price ceilings.

=== Profit ceiling ===

{{further|[[Profit ceiling]]}}

Here, sellers are forbidden from selling a good at a price greater than some multiple of the cost of production, to prevent excessive profiteering, while taking into account the cost of production.

Profit ceilings are effectively fixed price ceilings in cases where the marginal cost of production is constant across quantities and between sellers. However, in most real-world cases, profit ceilings are reasonably different from fixed price ceilings. Please see the [[profit ceiling]] page for more detailed models of how profit ceilings work.

=== A note on "voluntary" price ceilings ===

In general, only sellers with [[market power]] (i.e., sellers who can influence the market price, either as monopoly sellers or part of a small oligopoly) can adhere to voluntary price ceilings. Small sellers in a competitive market who choose to adhere to voluntary price ceilings, not raising prices to the market equilibrium, will not be able to meet the huge amount of market demand directed at them.

In the face of huge demand shocks and supply shocks, it is possible for ''de facto'' price ceilings to take effect, not through a single regulatory authority or marketplace controller, but though all sellers deciding to not risk increasing prices, even if that means shortfalls and forgone profits. The two typical reasons are:

* Potential regulation and litigation: Sellers may fear that if they raise prices, they will attract the ire of regulators, even if no current regulations forbid them raising prices.
* Public opinion: Sellers may fear that negative public sentiment against [[price gouging]] may hurt their reputation more than any additional profits they will make by selling at a higher price, or any additional goodwill they will generate among actual customers who appreciate not having a shortfall. The idea here is that it's not just the actual buyers, but also others who are unable to buy, or even general spectators, who could create trouble for the seller. The more diversified the seller, the bigger this public opinion concern (so a seller who ''only'' sells the good affected by the price ceiling may be less concerned, but a seller who sells many other goods may be concerned about reputational impact on sales of those other goods).

It is worth keeping in mind that this sort of "voluntary" price ceiling can really be effective only if some sellers have market power, or if there is widespread agreement between sellers about the wisdom of adhering to the "voluntary" price ceilings.

== The distinction between price ceiling-like policies and other similar market controls ==

=== Price ceilings versus sales taxes ===

As we'll discuss later on this page, price ceilings and [[sales tax]]es have similar effects -- they generally reduce quantity traded relative to an unrestricted market, and they cause a deadweight loss (which, in simple cases, is given by the Harberger triangle). Moreover, each approach has many real-world variants, so we should really think of a cluster of "price ceiling-like" policies versus a cluster of "sales tax-like" policies.

Conceptually, the main difference between the clusters is that sales tax-like policies aim to mimic the behavior of an unrestricted market -- just one where buyers and sellers see different prices (with the difference pocketed by the taxing authority). They therefore retain many of the dynamics of an unregulated market as far as the buyers and sellers individually are concerned. In contrast, price ceiling-like policies are qualitatively different from unrestricted markets to the point that buyers and sellers can see and feel the differences directly.

Price ceilings and sales taxes also work quite differently in non-competitive markets. In a monopoly market, it is possible for a price ceiling to increase the quantity traded. In contrast, a sales tax will reduce quantity traded, even in a monopoly market.

=== Price ceilings versus quantity ceilings ===

Both price ceilings and [[quantity ceiling]]s effectively create a situation where the quantity traded is less than it would be without a ceiling. However, quantity ceilings favor sellers over buyers, and also shift the burden of non-price competition to sellers: sellers compete with each other for permission to produce a larger share of the quantity ceiling.

==Basic theory: the effects of price ceilings in competitive markets==

The simple analysis in this section assumes a fixed price ceiling and ignores some of the indirect effects of price ceilings:

* Expectations regarding future prices: Price ceilings affect not just current prices but also expectations regarding future prices, on both the demand and supply side. This is particularly important for goods where buying now and buying later can substitute for each other, or where producing now and producing later are substitutes. In particular, the existence of the price ceiling affects the shape of the demand and supply curve. Moreover, the nature of the ceiling (whether it's a fixed price ceiling or a price change ceiling, and how people expect the price ceiling itself to evolve) plays a part in how this effect plays out. We will ignore these considerations.
* Interaction with price ceilings on substitute goods and complementary goods

===Non-binding price ceiling: price ceilings have no effect when they are above the market-clearing price===

A price ceiling that is set above the [[market price]] of the good has no direct short-run effect.

===Binding price ceiling: price ceilings create excess demand when they are below the market-clearing price===

If the price ceiling is below the [[market price]], the quantity demand for the good exceeds the quantity supplied for the good, resulting in a situation of scarcity or [[excess demand]]. This results in a loss of economic surplus compared to the situation of a market-clearing price.

For instance, in the figure below, if the price ceiling is set at the price level of the horizontal line AB, then there is a shortfall equal to the length of the segment AB.

Since a price ceiling creates a shortfall, it is not immediately clear which of the buyers willing to buy the good at the lower price will succeed in buying it (i.e., there is [[non-price competition]] among buyers, as discussed later in this page). Under the '''efficient allocation assumption''' (i.e., perfect sorting among buyers, ''and'' no costs imposed by non-price competition), the deadweight loss equals that arising from the case when the same quantity traded is accomplished by means of a [[sales tax]], and is described by the area of the [[Harberger triangle]], bounded by a vertical line through A and the demand and supply curves (so that two of its vertices are A and C). For more discussion, see [[Effect of price ceiling on economic surplus]].

[[File:Shortfallbelowmarketprice.png|500px]]

==Basic theory: the effects of price ceilings in monopolistic markets==

{{NeedsGraph}}

As was the case with the competitive markets analysis, the simple analysis in this section assumes a fixed price ceiling and ignores:

* Expectations regarding future prices
* Interaction with price ceilings on substitute goods and complementary goods

=== The basic case of increasing marginal costs ===

We restrict attention to cases where the monopolist's marginal cost curve is increasing, to avoid issues related to multiple optima. Many of the conclusions we draw are not dependent on this assumption.

There are three key price points relative to which price ceilings can be compared. For more context, see [[determination of price and quantity supplied by monopolistic firm in the short run]].

* The '''free market price''' (without any price ceiling), chosen by the monopolist for profit maximization.
* The '''optimal price''', which is the price point for the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market price would be if the market were competitive. This is based on the [[determination of quantity supplied by firm in perfectly competitive market in the short run]], where we find that the supply curve coincides with the short-run marginal cost curve if the latter is increasing.
* The '''free market marginal cost''', which is the marginal cost at the quantity being traded without any price ceiling. This is equal to the marginal revenue, since a monopolist optimizes at marginal cost equals marginal revenue.

There are two interesting values of quantity traded:

* The '''market quantity traded''', which is the quantity traded in the market without any price ceiling.
* The '''optimal quantity traded''', which is the maximum possible quantity traded, and is the quantity at the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market quantity traded would be if a competitive market were simulated with the same demand and supply structure.

We can now make cases based on the value of the price ceiling. We move the price ceiling ''down'', so the earlier rows discuss larger price ceilings and the later rows discuss lower price ceilings.

For any given price ceiling, there are two possibilities:

* It is a non-binding price ceiling, i.e., it is greater than or equal to the free market price. In this case, the market behavior remains the same as it would in a free market.
* It is a binding price ceiling in the sense of price, i.e., it is less than the free market price. In this case, the market price equals the binding price (note that this is no longer true with more complicated market structures, such as the case when the marginal cost curve is not increasing).

{| class="sortable" border="1"
! Price ceiling !! Binding or non-binding (binding means that the market price equals the ceiling, non-binding means it continues to equal the free market price) !! Quantity traded (compared to free market) !! Directional change in quantity traded as price decreases !! Location of the (price, quantity) pair !! Is there a shortfall?
|-
| Greater than or equal to than the free market price || Non-binding || Same || No change || On the market demand curve, same as without any price ceiling || No
|-
| Less than the free market price, but more than the optimal price || Binding || More || Increasing || On the market demand curve, moving down and right along the curve. The price being charged is the ''maximum'' possible price for the given quantity traded || No
|-
| Equal to the optimal price || Binding || More || Maximized || At the intersection of the market demand curve and short-run marginal cost curve || No
|-
| Less than the optimal price, but more than the free market marginal cost || Binding || More || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Equal to the free market marginal cost || Binding || Same || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Less than the free market marginal cost || Binding || Less || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|}

==Short-run impact of binding price ceilings in perfectly competitive markets==

===Non-price competition mechanisms===

The key problem that needs to be solved in case of a binding price ceiling is the problem: given that the quantity supplied is less than the quantity demanded, who among the different potential buyers of the good gets how much of it? There are two broad categories of approaches:

* Queueing, rationing, and queue-rationing
* Black markets

====Queueing, rationing, and queue-rationing====

{{further|[[Queueing, rationing, and queue-rationing]]}}

* Queueing is an approach where buyers are served in some form of a queue. The simplest is a time-based queue (first-come-first-serve) though other forms of priority queue are also possible.
* Rationing is an approach that limits the amount that each buyer can buy.
* Queue-rationing refers to a mix of queueing and rationing. For instance, each buyer can buy only a fixed amount in each iteration of purchase, and a buyer can take only one other position in the queue at a time (or even within a time period, for instance, per day). For instance, if the ration is 5 units per purchase, and the buyer wants to buy 48 units, the buyer will have to stand in the queue 10 times.

A key idea to keep in mind when thinking about these policies (queueing, rationing, and queue-rationing) is that the policies are determined mainly by sellers, but sellers do not internalize most of the gains from selecting policies that improve the efficiency of allocation between buyers. Sellers may, however, gain indirectly through reputational benefits, or spillover benefits to other goods the seller is selling.

====Black markets====

A [[black market]], or an illegal market in the good, is one way around the problem of a price ceiling. In this scenario, a small quantity of the good is sold in the legal market at a price equal to the price ceiling, whereas the rest of the good is sold in the black market at the true equilibrium price. In fact, the black market price may well be ''higher'' than the market price would be in the absence of a price ceiling, because of the added costs incurred by sellers to evade the law.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Under most sets of assumptions (in particular, assuming that there are no [[external cost]]s or [[external benefit]]s), price ceilings have a negative effect on economic surplus in competitive markets. In general, the following are true:

* Non-binding price ceilings have no effect on economic surplus.
* Binding price ceilings have negative effects on economic surplus as well as producer surplus, with the magnitude of the effect increasing as the ceiling price goes lower. The effect on consumer surplus is ambiguous. This is a [[deadweight loss]].

Note that there are three components to the deadweight loss arising due to a binding price ceiling:

* The ''inevitable'' deadweight loss, that is given by the area of the [[Harberger triangle]].
* The deadweight loss that arises due to imperfect sorting among buyers (i.e., buyers who value a good less get it). In other words, this occurs because non-price competition did not do its job well.
* The deadweight loss arising from the transaction costs associated with non-price competition.

==Short-run impact of binding price ceilings in monopolistic markets==

===Non-price competition mechanisms===

Similar to the case of a competitive market, binding price ceilings can create shortfalls, leading to non-price competition among buyers. However, unlike the case of competitive markets, not every binding price ceiling leads to a shortfall and to non-price competition. More specifically, a binding price ceiling leads to shortfalls only if it is set to below the optimal price as defined in [[#Basic theory: the effects of price ceilings in monopolistic markets]], i.e., the price at which the marginal cost curve and market demand curve intersect.

When the price ceiling is set to below the optimal price, the non-price competition mechanisms are similar to those in a competitive market, namely:

* Queueing, rationing, and queue-rationing
* Black markets

One difference is that since the monopolist has complete control over the supply of the market, it may be easier for the monopolist to choose the non-price competition strategy more freely.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Here we assume that the good being sold has no [[external cost|external costs]] or [[external benefit|external benefits]].

The discussion here builds on that in [[#Basic theory: the effects of price ceilings in monopolistic markets]]. You may need to reference that for more context around some of the terminology used.

For some of the rows, we can draw definite conclusions only under the '''efficient allocation assumption''': perfect sorting among buyers (the buyers who acquire the good are those who value it most highly), ''and'' the non-price competition imposes no extra costs on buyers and sellers. The caveats are noted in the corresponding cells where they apply.

The "optimal price" in the table below is obtained as the price point at the intersection of the marginal cost curve and the market demand curve. This is essentially what the price would be if the seller could be made to behave as if operating in perfect competition.
{| class="sortable" border="1"
! Price ceiling range !! economic surplus compared to no price ceiling !! Producer surplus compared to no price ceiling !! Consumer surplus compared to no price ceiling !! Direction of change of economic surplus with decreasing price ceiling !! Direction of change of producer surplus with decreasing price ceiling !! Direction of change of consumer surplus with decreasing price ceiling !! Qualitative comments
|-
| Greater than or equal to the free market price || Same || Same || Same || None || None || None || Deadweight loss is intact as the price ceiling has no effect
|-
| Less than the free market price and greater than the optimal price || More || Less || More || Increasing || Decreasing || Increasing || Deadweight loss due to monopoly is ameliorated by the price ceiling
|-
| Equal to the optimal price || More || Less || More || Maximized || Decreasing || Ambiguous || Deadweight loss is eliminated as perfect competition is emulated
|-
| Less than the optimal price and greater than the free market marginal cost || More (assuming efficient allocation), indeterminate otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || Deadweight loss is now no longer due to monopolistic pricing but rather due to price ceilings cutting off beneficial transactions
|-
| Equal to the free market marginal cost || Same (assuming efficient allocation), less otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || The quantity traded mimics that in the no-ceiling case, but the price at which the trades occur is lower. Assuming efficient allocation (i.e., the goods go to the buyers valuing them most highly), the economic surplus is the same but it is distributed more to consumers. Without the efficient allocation assumption, total economic surplus is down, with producer surplus down and the effect on consumer surplus indeterminate.
|-
| Less than the free market marginal cost || Less || Less || Starts out as more (assuming efficient allocation), may later becomes less. Without the efficient allocation assumption, indeterminate. || Decreasing || Decreasing || Ambiguous || Deadweight loss now exceeds that of monopoly, even under the efficient allocation assumption.
|}

==Long-run impact of price ceilings==

The long-run impact of a price ceiling is a much more complicated matter than the short-run impact. There are, roughly speaking, three sources of complication:

* Expectations regarding future demand and supply patterns: A price ceiling that is binding today may become non-binding in the future, and a price ceiling that is non-binding today may become binding in the future. Both the normal course of supply-and-demand changes as well as low-probability demand and supply shocks need to be examined in connection with the price ceiling.
* Intertemporal substitution with the future: Buyers and sellers who can substitute buying or selling now against buying or selling in the future, have to consider the effect of the price ceiling on how they distribute their buying or selling behavior over time. Note that this long-run consideration can also change the present-day shape of the supply and demand curves, thereby causing a short-run effect.
* The distinction between short-run and long-run supply, through reconfiguration: In the short run, sellers are generally constrained to a increasing short-run marginal cost curve. In the long run, the seller can change the mix of inputs, for instance, by acquiring more land and capital or hiring more people. Long-run supply curves are more likely to be flat or even declining. This complicates the analysis of the impact of price ceilings.

The type of impact a price ceiling has also depends on its structure. The analysis can differ quite a bit between uniform fixed price ceilings, price change ceilings, and profit ceilings. However, we can say a few broad things.

=== Price ceilings are more likely to cause firms to exit the market in the long run than in the short run, and have qualitatively different effects in increasing cost industries versus decreasing cost industries ===

In the short run, even in the face of a price ceiling, a firm may continue to produce as long as the minimum AVC value (at [[minimum efficient scale]]) is less than the price ceiling. That's because the firm has sunk its fixed costs. If the price ceiling is even lower than the firm's AVC, the firm may simply stay idle in the short run.

In the long run, however, firms are looking at their average total cost and comparing it with the minimum between what they expect the price to be (taking the minimum across the price ceiling and market price). There are two competing considerations here -- the ability to optimize better in the long run, and the ability to exit altogether in the long run. Here is how they interact for a firm in a large, competitive market:

* On the one hand, the long-run knowledge of the price ceiling allows the firm to choose a configuration of fixed and variable costs that is optimized for that price ceiling, rather than its prediction for the unrestricted price.
** For an [[increasing cost industry]], the firm will do so by reducing its fixed costs and reducing overall production. This can make the shortfall even worse than in the short run.
** For a [[constant cost industry]] or [[decreasing cost industry]], the firm (since it is small relative to the market) will still keep producing at maximum capacity. So there is no change.
* On the other hand, solving this problem might also show the firm that it does not have a configuration that allows for long-run profitability. Specifically, if the price ceiling is less than the minimum possible average total cost (ATC) for the firm, it will exit the market.
** For a constant cost industry or decreasing cost industry, the minimum ATC is attained at the maximum level of production. In other words, in such cases, if even at the maximum level of production, the firm is unable to make its ATC drop to below the price ceiling, it will exit the market. Over time, this might reduce the number of firms in the market, causing larger shortfalls.

The situation is a little different in a monopolistic firm, but the underlying trade-off remains the same: the firm can optimize better in the long run, but it can also choose to exit altogether.

=== Generally, price ceilings reduce seller incentives to prepare for demand and supply shocks, but the story is a little more complicated ===

A price ceiling that is non-binding now could become binding in the face of a demand shock or supply shock that increases market prices, especially in the short run when firms cannot reconfigure their factors of production.

If the price mechanism is allowed to operate freely, the firm may have stronger incentives to prepare for such situations, because the better prepared it is, the more it can sell and the more it can profit from the increased prices. Specifically, the firm may do one or more of these:

* Stockpile extra production that can be released into the market in the face of a demand or supply shock that raises price.
* Develop better forecasting so that shocks can be anticipated, and prepared for a little bit in advance (this can be combined with the previous point to give the idea of "speculative production" -- if the forecast shows increased demand, then start stockpiling).
* Configure their production process so that it is easier to reconfigure quickly (i.e., make the long run less long).

For instance, let's say a firm is one firm among many in a competitive market and an increasing cost industry (we'll assume an increasing cost industry because with a decreasing cost industry, firms are anyway maxed out on production capacity). The market price of a good under normal conditions is 1. The firm correctly forecasts a soon-to-happen demand shock that would cause the market price to go up to 3, with some probability. There is a price ceiling of 2.

* If there were no price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a market price of 3.
* Due to the price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a price of 2.

Comparing these two, we see that the price ceiling prevents the firm from capturing all the gains in market price. Therefore, even if the firm does increase its production, it will increase it to a lower level (enough for the price ceiling of 2) rather than to the higher level (enough for the market price of 3). Thus, although the firm's long-run planning will alleviate the shortfall a little bit compared to not being prepared at all, the shortfall is still not going to be eliminated.

The above assumes that the firm has definite knowledge of the demand shock. However, the situation gets more complicated when the demand shock is more probabilistic. For instance, if the firm believes that there is some probability that a demand shock will cause the market price to rise to 3. The firm has to choose to reconfigure its fixed costs to gear toward producing enough for the market price of 3, or stay with its current setup, or anything in between. Whatever choice the firm makes, it will have to compare the expected gain from that choice of both the options.

Even in this more complicated situation, the presence of the price ceiling reduces, overall, the extent to which the firm will increase its production, by reducing the upside. However, the specifics will depend on other questions such as whether the firm's production cycle, as well as its buyers, can engage in intertemporal substitution.

Note that this analysis is contingent on some assumptions:

* The price ceiling is a uniform fixed price ceiling: More complicated price ceiling formulas, like [[price change ceiling]]s and [[profit ceiling]]s, share some qualitative characteristics but are also different in other ways.
* The price ceiling is known in advance to the firm: A price ceiling imposed suddenly without warning after a demand shock will have a less detrimental effect on quantity; the firm that had ramped up production has now already invested the fixed costs (thinking it could profit more), and is therefore able to produce more.

=== Price ceilings can change the way buyers substitute intertemporally ===

For goods where present purchases can substitute for future purchases, buyers respond to expectations of future price increases by buying more now. In markets with price ceilings that may become binding, buyers have to factor in not just the future market prices but also future availability. This can change the buyers' decision of how much to buy now, but it's ambiguous in what direction the buyers' behavior will change. Specifically, the way the buyers' behavior changes depends partly on how much each buyer perceives as the costs of non-price competition and how much the buyer's individual reservation price compared with the market price.

For instance, let's say buyers expect a demand shock or supply shock in the future that would, in a free market, cause the price of toilet paper to rise. This might incentivize buyers to stock up on toilet paper right now. Now, if a price ceiling is implemented that prevents the price of toilet paper from rising, buyers' expectations will shift from an expectation of increased price to an expectation of reduced availability, and the possibility that the buyer may have to engage in non-price competition to get the good. This, too, might incentivize buyers to stock up on toilet paper right now. However, the relative strength of the incentive to stock up on toilet paper, between the free market and price ceiling case, is ambiguous.

This ambiguity is related to the idea that the effect of price ceilings on consumer surplus is ambiguous (though it's definitely negative for producer surplus and overall economic surplus).

Note that the possibility of [[black market]]s does increase the incentive to buy and hoard.

==Related notions==

* [[Maximum retail price]] is an upper limit that the producer or wholesale distributor puts on the price at which retailers can sell the commodity to customers. Maximum retail prices do not usually have the inefficiencies associated with price ceilings, because producers of the goods can vary maximum retail prices according to demand trends over the somewhat longer term.

Price ceiling

2020-03-31T04:12:47Z

Vipul: /* Price ceilings versus quantity ceilings */

==Definition==

A '''price ceiling''' is an upper limit placed by a regulatory authority (such as a government, or regulatory authority with government sanction, or private party controlling a marketplace) on the price (per unit) of a good.

A price ceiling is a form of [[price control]]. Other forms of price control include [[minimum price]]s, [[price change ceiling]]s, and [[profit ceiling]]s.

At any given time, a price ceiling is one of these:

* '''Non-binding price ceiling''': This is a [[price ceiling]] that is greater than the current [[market price]].
* '''Binding price ceiling''': This is a [[price ceiling]] that is less than the current [[market price]]. Binding price ceilings cause a reduction in the price, and may increase or decrease the quantity traded depending on the market structure.

A particularly extreme form of price ceiling, which is not usually thought of that way, is a price ceiling of zero. This refers to situations where it is legal to give a good or service for free but it is illegal to offer the good or service in exchange for money. Price ceilings of zero are usually justified on aesthetic and ethical grounds as it is believed that the exchange of money sullies certain types of transaction. Since the market price for most forms of exchange is positive, price ceilings of zero are typically binding price ceilings. Examples include:

* [[Prostitution]] (the sale of sexual services), which is illegal, though not often rigorously prosecuted, in many countries
* [[Organ trade]], i.e., there are often jurisdictions where it is legal to donate an organ such as a kidney but illegal to buy or sell it.
* Adoption: In many places, it is not legal for a pregnant mother to sell her baby for adoption to a couple willing to adopt the kid, though it is legal to put the baby up for adoption.

== Type of price ceilings based on how they apply ==

=== Uniform fixed price ceiling ===

The simplest kind of price ceiling is a price ceiling that is fixed (i.e., a fixed price per unit) and imposed uniformly across all transactions, i.e., for all buyers and sellers. The value of this fixed price ceiling may change over time but generally does so through discrete policy changes. Therefore, in the short run, and possibly even the medium-to-long run, the price ceiling can be considered fixed.

There are two other kinds of variants of price ceilings.

=== Price change ceiling ===

{{further|[[Price change ceiling]]}}

This is a ceiling on how rapidly a price is allowed to increase. Price change ceilings may be any of these:
* Price change ceiling applied to the market as a whole: Here, no seller is allowed to sell at a price more than some percentage higher than the market price at some point in the recent past (e.g., no seller is allowed to sell at more than 10% of the average price in the market last week).
* Price change ceiling specific to a seller: Here, the price a seller is currently selling at is compared to the price the seller sold at in the past.
* Price change ceiling specific to a pair of buyer and seller: This makes sense in the context of a repeat transaction. Rent regulations of the "vacancy decontrol" form are like that -- the rent of a given housing unit is allowed to increase at some maximum annual rate for a given pair of landlord and tenant, but once the tenant moves out, the landlord may give the apartment out for rent at any price.

For static analysis at a single point in time, price change ceilings may seem to function effectively as price ceilings; however, the long-run analysis (across multiple time periods where price changes can be made) is quite different. In particular, the "expectation regarding future prices" by both buyers and sellers, that shapes both the demand and supply curves, is affected by the structure of the price change ceiling. Despite these differences, in the cases where unexpected demand or supply shocks cause price change ceilings to create binding price ceilings, they behave qualitatively like uniform fixed price ceilings.

=== Profit ceiling ===

{{further|[[Profit ceiling]]}}

Here, sellers are forbidden from selling a good at a price greater than some multiple of the cost of production, to prevent excessive profiteering, while taking into account the cost of production.

Profit ceilings are effectively fixed price ceilings in cases where the marginal cost of production is constant across quantities and between sellers. However, in most real-world cases, profit ceilings are reasonably different from fixed price ceilings. Please see the [[profit ceiling]] page for more detailed models of how profit ceilings work.

=== A note on "voluntary" price ceilings ===

In general, only sellers with [[market power]] (i.e., sellers who can influence the market price, either as monopoly sellers or part of a small oligopoly) can adhere to voluntary price ceilings. Small sellers in a competitive market who choose to adhere to voluntary price ceilings, not raising prices to the market equilibrium, will not be able to meet the huge amount of market demand directed at them.

In the face of huge demand shocks and supply shocks, it is possible for ''de facto'' price ceilings to take effect, not through a single regulatory authority or marketplace controller, but though all sellers deciding to not risk increasing prices, even if that means shortfalls and forgone profits. The two typical reasons are:

* Potential regulation and litigation: Sellers may fear that if they raise prices, they will attract the ire of regulators, even if no current regulations forbid them raising prices.
* Public opinion: Sellers may fear that negative public sentiment against [[price gouging]] may hurt their reputation more than any additional profits they will make by selling at a higher price, or any additional goodwill they will generate among actual customers who appreciate not having a shortfall. The idea here is that it's not just the actual buyers, but also others who are unable to buy, or even general spectators, who could create trouble for the seller. The more diversified the seller, the bigger this public opinion concern (so a seller who ''only'' sells the good affected by the price ceiling may be less concerned, but a seller who sells many other goods may be concerned about reputational impact on sales of those other goods).

It is worth keeping in mind that this sort of "voluntary" price ceiling can really be effective only if some sellers have market power, or if there is widespread agreement between sellers about the wisdom of adhering to the "voluntary" price ceilings.

== The distinction between price ceiling-like policies and other similar market controls ==

=== Price ceilings versus sales taxes ===

As we'll discuss later on this page, price ceilings and [[sales tax]]es have similar effects -- they generally reduce quantity traded relative to an unrestricted market, and they cause a deadweight loss (which, in simple cases, is given by the Harberger triangle). Moreover, each approach has many real-world variants, so we should really think of a cluster of "price ceiling-like" policies versus a cluster of "sales tax-like" policies.

Conceptually, the main difference between the clusters is that sales tax-like policies aim to mimic the behavior of an unrestricted market -- just one where buyers and sellers see different prices (with the difference pocketed by the taxing authority). They therefore retain many of the dynamics of an unregulated market as far as the buyers and sellers individually are concerned. In contrast, price ceiling-like policies are qualitatively different from unrestricted markets to the point that buyers and sellers can see and feel the differences directly.

Price ceilings and sales taxes also work quite differently in non-competitive markets. In a monopoly market, it is possible for a price ceiling to increase the quantity traded. In contrast, a sales tax will reduce quantity traded, even in a monopoly market.

=== Price ceilings versus quantity ceilings ===

Both price ceilings and [[quantity ceiling]]s effectively create a situation where the quantity traded is less than it would be without a ceiling. However, quantity ceilings favor sellers over buyers, and also shift the burden of non-price competition to sellers: sellers compete with each other for permission to produce a larger share of the quantity ceiling.

==Basic theory: the effects of price ceilings in competitive markets==

The simple analysis in this section assumes a fixed price ceiling and ignores some of the indirect effects of price ceilings:

* Expectations regarding future prices: Price ceilings affect not just current prices but also expectations regarding future prices, on both the demand and supply side. This is particularly important for goods where buying now and buying later can substitute for each other, or where producing now and producing later are substitutes. In particular, the existence of the price ceiling affects the shape of the demand and supply curve. Moreover, the nature of the ceiling (whether it's a fixed price ceiling or a price change ceiling, and how people expect the price ceiling itself to evolve) plays a part in how this effect plays out. We will ignore these considerations.
* Interaction with price ceilings on substitute goods and complementary goods

===Non-binding price ceiling: price ceilings have no effect when they are above the market-clearing price===

A price ceiling that is set above the [[market price]] of the good has no direct short-run effect.

===Binding price ceiling: price ceilings create excess demand when they are below the market-clearing price===

If the price ceiling is below the [[market price]], the quantity demand for the good exceeds the quantity supplied for the good, resulting in a situation of scarcity or [[excess demand]]. This results in a loss of economic surplus compared to the situation of a market-clearing price.

For instance, in the figure below, if the price ceiling is set at the price level of the horizontal line AB, then there is a shortfall equal to the length of the segment AB.

Since a price ceiling creates a shortfall, it is not immediately clear which of the buyers willing to buy the good at the lower price will succeed in buying it (i.e., there is [[non-price competition]] among buyers, as discussed later in this page). Under the '''efficient allocation assumption''' (i.e., perfect sorting among buyers, ''and'' no costs imposed by non-price competition), the deadweight loss equals that arising from the case when the same quantity traded is accomplished by means of a [[sales tax]], and is described by the area of the [[Harberger triangle]], bounded by a vertical line through A and the demand and supply curves (so that two of its vertices are A and C). For more discussion, see [[Effect of price ceiling on economic surplus]].

[[File:Shortfallbelowmarketprice.png|500px]]

==Basic theory: the effects of price ceilings in monopolistic markets==

{{NeedsGraph}}

As was the case with the competitive markets analysis, the simple analysis in this section assumes a fixed price ceiling and ignores:

* Expectations regarding future prices
* Interaction with price ceilings on substitute goods and complementary goods

=== The basic case of increasing marginal costs ===

We restrict attention to cases where the monopolist's marginal cost curve is increasing, to avoid issues related to multiple optima. Many of the conclusions we draw are not dependent on this assumption.

There are three key price points relative to which price ceilings can be compared. For more context, see [[determination of price and quantity supplied by monopolistic firm in the short run]].

* The '''free market price''' (without any price ceiling), chosen by the monopolist for profit maximization.
* The '''optimal price''', which is the price point for the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market price would be if the market were competitive. This is based on the [[determination of quantity supplied by firm in perfectly competitive market in the short run]], where we find that the supply curve coincides with the short-run marginal cost curve if the latter is increasing.
* The '''free market marginal cost''', which is the marginal cost at the quantity being traded without any price ceiling. This is equal to the marginal revenue, since a monopolist optimizes at marginal cost equals marginal revenue.

There are two interesting values of quantity traded:

* The '''market quantity traded''', which is the quantity traded in the market without any price ceiling.
* The '''optimal quantity traded''', which is the maximum possible quantity traded, and is the quantity at the intersection of the market demand curve and the monopolist's short-run marginal cost curve. We can also think of this as what the market quantity traded would be if a competitive market were simulated with the same demand and supply structure.

We can now make cases based on the value of the price ceiling. We move the price ceiling ''down'', so the earlier rows discuss larger price ceilings and the later rows discuss lower price ceilings.

For any given price ceiling, there are two possibilities:

* It is a non-binding price ceiling, i.e., it is greater than or equal to the free market price. In this case, the market behavior remains the same as it would in a free market.
* It is a binding price ceiling in the sense of price, i.e., it is less than the free market price. In this case, the market price equals the binding price (note that this is no longer true with more complicated market structures, such as the case when the marginal cost curve is not increasing).

{| class="sortable" border="1"
! Price ceiling !! Binding or non-binding (binding means that the market price equals the ceiling, non-binding means it continues to equal the free market price) !! Quantity traded (compared to free market) !! Directional change in quantity traded as price decreases !! Location of the (price, quantity) pair !! Is there a shortfall?
|-
| Greater than or equal to than the free market price || Non-binding || Same || No change || On the market demand curve, same as without any price ceiling || No
|-
| Less than the free market price, but more than the optimal price || Binding || More || Increasing || On the market demand curve, moving down and right along the curve. The price being charged is the ''maximum'' possible price for the given quantity traded || No
|-
| Equal to the optimal price || Binding || More || Maximized || At the intersection of the market demand curve and short-run marginal cost curve || No
|-
| Less than the optimal price, but more than the free market marginal cost || Binding || More || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Equal to the free market marginal cost || Binding || Same || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|-
| Less than the free market marginal cost || Binding || Less || Decreasing || On the short-run marginal cost curve, moving downward and leftward. The price being charged is the ''minimum'' possible price for the given quantity traded || Yes
|}

==Short-run impact of binding price ceilings in perfectly competitive markets==

===Non-price competition mechanisms===

The key problem that needs to be solved in case of a binding price ceiling is the problem: given that the quantity supplied is less than the quantity demanded, who among the different potential buyers of the good gets how much of it? There are two broad categories of approaches:

* Queueing, rationing, and queue-rationing
* Black markets

====Queueing, rationing, and queue-rationing====

* [[Queueing]] is an approach where buyers are served in some form of a queue. The simplest is a time-based queue (first-come-first-serve) though other forms of priority queue are also possible.
* [[Rationing]] is an approach that limits the amount that each buyer can buy.
* [[Queue-rationing]] refers to a mix of queueing and rationing. For instance, each buyer can buy only a fixed amount in each iteration of purchase, and a buyer can take only one other position in the queue at a time (or even within a time period, for instance, per day). For instance, if the ration is 5 units per purchase, and the buyer wants to buy 48 units, the buyer will have to stand in the queue 10 times.

A key idea to keep in mind when thinking about these policies (queueing, rationing, and queue-rationing) is that the policies are determined mainly by sellers, but sellers do not internalize most of the gains from selecting policies that improve the efficiency of allocation between buyers. Sellers may, however, gain indirectly through reputational benefits, or spillover benefits to other goods the seller is selling.

====Black markets====

A [[black market]], or an illegal market in the good, is one way around the problem of a price ceiling. In this scenario, a small quantity of the good is sold in the legal market at a price equal to the price ceiling, whereas the rest of the good is sold in the black market at the true equilibrium price. In fact, the black market price may well be ''higher'' than the market price would be in the absence of a price ceiling, because of the added costs incurred by sellers to evade the law.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Under most sets of assumptions (in particular, assuming that there are no [[external cost]]s or [[external benefit]]s), price ceilings have a negative effect on economic surplus in competitive markets. In general, the following are true:

* Non-binding price ceilings have no effect on economic surplus.
* Binding price ceilings have negative effects on economic surplus as well as producer surplus, with the magnitude of the effect increasing as the ceiling price goes lower. The effect on consumer surplus is ambiguous. This is a [[deadweight loss]].

Note that there are three components to the deadweight loss arising due to a binding price ceiling:

* The ''inevitable'' deadweight loss, that is given by the area of the [[Harberger triangle]].
* The deadweight loss that arises due to imperfect sorting among buyers (i.e., buyers who value a good less get it). In other words, this occurs because non-price competition did not do its job well.
* The deadweight loss arising from the transaction costs associated with non-price competition.

==Short-run impact of binding price ceilings in monopolistic markets==

===Non-price competition mechanisms===

Similar to the case of a competitive market, binding price ceilings can create shortfalls, leading to non-price competition among buyers. However, unlike the case of competitive markets, not every binding price ceiling leads to a shortfall and to non-price competition. More specifically, a binding price ceiling leads to shortfalls only if it is set to below the optimal price as defined in [[#Basic theory: the effects of price ceilings in monopolistic markets]], i.e., the price at which the marginal cost curve and market demand curve intersect.

When the price ceiling is set to below the optimal price, the non-price competition mechanisms are similar to those in a competitive market, namely:

* Queueing, rationing, and queue-rationing
* Black markets

One difference is that since the monopolist has complete control over the supply of the market, it may be easier for the monopolist to choose the non-price competition strategy more freely.

===Effect on economic surplus===

{{further|[[effect of price ceiling on economic surplus]]}}

Here we assume that the good being sold has no [[external cost|external costs]] or [[external benefit|external benefits]].

The discussion here builds on that in [[#Basic theory: the effects of price ceilings in monopolistic markets]]. You may need to reference that for more context around some of the terminology used.

For some of the rows, we can draw definite conclusions only under the '''efficient allocation assumption''': perfect sorting among buyers (the buyers who acquire the good are those who value it most highly), ''and'' the non-price competition imposes no extra costs on buyers and sellers. The caveats are noted in the corresponding cells where they apply.

The "optimal price" in the table below is obtained as the price point at the intersection of the marginal cost curve and the market demand curve. This is essentially what the price would be if the seller could be made to behave as if operating in perfect competition.
{| class="sortable" border="1"
! Price ceiling range !! economic surplus compared to no price ceiling !! Producer surplus compared to no price ceiling !! Consumer surplus compared to no price ceiling !! Direction of change of economic surplus with decreasing price ceiling !! Direction of change of producer surplus with decreasing price ceiling !! Direction of change of consumer surplus with decreasing price ceiling !! Qualitative comments
|-
| Greater than or equal to the free market price || Same || Same || Same || None || None || None || Deadweight loss is intact as the price ceiling has no effect
|-
| Less than the free market price and greater than the optimal price || More || Less || More || Increasing || Decreasing || Increasing || Deadweight loss due to monopoly is ameliorated by the price ceiling
|-
| Equal to the optimal price || More || Less || More || Maximized || Decreasing || Ambiguous || Deadweight loss is eliminated as perfect competition is emulated
|-
| Less than the optimal price and greater than the free market marginal cost || More (assuming efficient allocation), indeterminate otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || Deadweight loss is now no longer due to monopolistic pricing but rather due to price ceilings cutting off beneficial transactions
|-
| Equal to the free market marginal cost || Same (assuming efficient allocation), less otherwise || Less || More (assuming efficient allocation), indeterminate otherwise || Decreasing || Decreasing || Ambiguous || The quantity traded mimics that in the no-ceiling case, but the price at which the trades occur is lower. Assuming efficient allocation (i.e., the goods go to the buyers valuing them most highly), the economic surplus is the same but it is distributed more to consumers. Without the efficient allocation assumption, total economic surplus is down, with producer surplus down and the effect on consumer surplus indeterminate.
|-
| Less than the free market marginal cost || Less || Less || Starts out as more (assuming efficient allocation), may later becomes less. Without the efficient allocation assumption, indeterminate. || Decreasing || Decreasing || Ambiguous || Deadweight loss now exceeds that of monopoly, even under the efficient allocation assumption.
|}

==Long-run impact of price ceilings==

The long-run impact of a price ceiling is a much more complicated matter than the short-run impact. There are, roughly speaking, three sources of complication:

* Expectations regarding future demand and supply patterns: A price ceiling that is binding today may become non-binding in the future, and a price ceiling that is non-binding today may become binding in the future. Both the normal course of supply-and-demand changes as well as low-probability demand and supply shocks need to be examined in connection with the price ceiling.
* Intertemporal substitution with the future: Buyers and sellers who can substitute buying or selling now against buying or selling in the future, have to consider the effect of the price ceiling on how they distribute their buying or selling behavior over time. Note that this long-run consideration can also change the present-day shape of the supply and demand curves, thereby causing a short-run effect.
* The distinction between short-run and long-run supply, through reconfiguration: In the short run, sellers are generally constrained to a increasing short-run marginal cost curve. In the long run, the seller can change the mix of inputs, for instance, by acquiring more land and capital or hiring more people. Long-run supply curves are more likely to be flat or even declining. This complicates the analysis of the impact of price ceilings.

The type of impact a price ceiling has also depends on its structure. The analysis can differ quite a bit between uniform fixed price ceilings, price change ceilings, and profit ceilings. However, we can say a few broad things.

=== Price ceilings are more likely to cause firms to exit the market in the long run than in the short run, and have qualitatively different effects in increasing cost industries versus decreasing cost industries ===

In the short run, even in the face of a price ceiling, a firm may continue to produce as long as the minimum AVC value (at [[minimum efficient scale]]) is less than the price ceiling. That's because the firm has sunk its fixed costs. If the price ceiling is even lower than the firm's AVC, the firm may simply stay idle in the short run.

In the long run, however, firms are looking at their average total cost and comparing it with the minimum between what they expect the price to be (taking the minimum across the price ceiling and market price). There are two competing considerations here -- the ability to optimize better in the long run, and the ability to exit altogether in the long run. Here is how they interact for a firm in a large, competitive market:

* On the one hand, the long-run knowledge of the price ceiling allows the firm to choose a configuration of fixed and variable costs that is optimized for that price ceiling, rather than its prediction for the unrestricted price.
** For an [[increasing cost industry]], the firm will do so by reducing its fixed costs and reducing overall production. This can make the shortfall even worse than in the short run.
** For a [[constant cost industry]] or [[decreasing cost industry]], the firm (since it is small relative to the market) will still keep producing at maximum capacity. So there is no change.
* On the other hand, solving this problem might also show the firm that it does not have a configuration that allows for long-run profitability. Specifically, if the price ceiling is less than the minimum possible average total cost (ATC) for the firm, it will exit the market.
** For a constant cost industry or decreasing cost industry, the minimum ATC is attained at the maximum level of production. In other words, in such cases, if even at the maximum level of production, the firm is unable to make its ATC drop to below the price ceiling, it will exit the market. Over time, this might reduce the number of firms in the market, causing larger shortfalls.

The situation is a little different in a monopolistic firm, but the underlying trade-off remains the same: the firm can optimize better in the long run, but it can also choose to exit altogether.

=== Generally, price ceilings reduce seller incentives to prepare for demand and supply shocks, but the story is a little more complicated ===

A price ceiling that is non-binding now could become binding in the face of a demand shock or supply shock that increases market prices, especially in the short run when firms cannot reconfigure their factors of production.

If the price mechanism is allowed to operate freely, the firm may have stronger incentives to prepare for such situations, because the better prepared it is, the more it can sell and the more it can profit from the increased prices. Specifically, the firm may do one or more of these:

* Stockpile extra production that can be released into the market in the face of a demand or supply shock that raises price.
* Develop better forecasting so that shocks can be anticipated, and prepared for a little bit in advance (this can be combined with the previous point to give the idea of "speculative production" -- if the forecast shows increased demand, then start stockpiling).
* Configure their production process so that it is easier to reconfigure quickly (i.e., make the long run less long).

For instance, let's say a firm is one firm among many in a competitive market and an increasing cost industry (we'll assume an increasing cost industry because with a decreasing cost industry, firms are anyway maxed out on production capacity). The market price of a good under normal conditions is 1. The firm correctly forecasts a soon-to-happen demand shock that would cause the market price to go up to 3, with some probability. There is a price ceiling of 2.

* If there were no price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a market price of 3.
* Due to the price ceiling, the question before the firm is whether to reconfigure its production process to optimize the amount produced for a price of 2.

Comparing these two, we see that the price ceiling prevents the firm from capturing all the gains in market price. Therefore, even if the firm does increase its production, it will increase it to a lower level (enough for the price ceiling of 2) rather than to the higher level (enough for the market price of 3). Thus, although the firm's long-run planning will alleviate the shortfall a little bit compared to not being prepared at all, the shortfall is still not going to be eliminated.

The above assumes that the firm has definite knowledge of the demand shock. However, the situation gets more complicated when the demand shock is more probabilistic. For instance, if the firm believes that there is some probability that a demand shock will cause the market price to rise to 3. The firm has to choose to reconfigure its fixed costs to gear toward producing enough for the market price of 3, or stay with its current setup, or anything in between. Whatever choice the firm makes, it will have to compare the expected gain from that choice of both the options.

Even in this more complicated situation, the presence of the price ceiling reduces, overall, the extent to which the firm will increase its production, by reducing the upside. However, the specifics will depend on other questions such as whether the firm's production cycle, as well as its buyers, can engage in intertemporal substitution.

Note that this analysis is contingent on some assumptions:

* The price ceiling is a uniform fixed price ceiling: More complicated price ceiling formulas, like [[price change ceiling]]s and [[profit ceiling]]s, share some qualitative characteristics but are also different in other ways.
* The price ceiling is known in advance to the firm: A price ceiling imposed suddenly without warning after a demand shock will have a less detrimental effect on quantity; the firm that had ramped up production has now already invested the fixed costs (thinking it could profit more), and is therefore able to produce more.

=== Price ceilings can change the way buyers substitute intertemporally ===

For goods where present purchases can substitute for future purchases, buyers respond to expectations of future price increases by buying more now. In markets with price ceilings that may become binding, buyers have to factor in not just the future market prices but also future availability. This can change the buyers' decision of how much to buy now, but it's ambiguous in what direction the buyers' behavior will change. Specifically, the way the buyers' behavior changes depends partly on how much each buyer perceives as the costs of non-price competition and how much the buyer's individual reservation price compared with the market price.

For instance, let's say buyers expect a demand shock or supply shock in the future that would, in a free market, cause the price of toilet paper to rise. This might incentivize buyers to stock up on toilet paper right now. Now, if a price ceiling is implemented that prevents the price of toilet paper from rising, buyers' expectations will shift from an expectation of increased price to an expectation of reduced availability, and the possibility that the buyer may have to engage in non-price competition to get the good. This, too, might incentivize buyers to stock up on toilet paper right now. However, the relative strength of the incentive to stock up on toilet paper, between the free market and price ceiling case, is ambiguous.

This ambiguity is related to the idea that the effect of price ceilings on consumer surplus is ambiguous (though it's definitely negative for producer surplus and overall economic surplus).

Note that the possibility of [[black market]]s does increase the incentive to buy and hoard.

==Related notions==

* [[Maximum retail price]] is an upper limit that the producer or wholesale distributor puts on the price at which retailers can sell the commodity to customers. Maximum retail prices do not usually have the inefficiencies associated with price ceilings, because producers of the goods can vary maximum retail prices according to demand trends over the somewhat longer term.

Income tax

2020-03-30T04:23:23Z

Vipul:

== Definition ==

An '''income tax''' is a [[tax]] that is levied on, and is generally an increasing function of, [[income]]. Income taxes are levied on persons (individuals or households). There is a related notion of income tax for corporations, which is discussed on the separate [[corporate tax]] page.

== Mechanics ==

=== Burden of remitting the tax ===

* Income taxes are usually paid by the individual or household as part of an annual process of filing a tax return. The tax return is a statement of the income over the tax year as well as the calculation of tax based on the income. A tax return includes filled versions of forms created by the taxing authority.
* Many payers of income, including employers paying wage income, as well as banks offering interest income, may be required to deduct taxes from the employee's income and send it to the taxing authority. These deducted taxes are called ''tax withholdings'', and represent an advance payment of the eventual tax obligation of the individual or household. Tax withholdings help the tax authority obtain a steady stream of income tax revenue throughout the year, increase tax compliance, and reduce the visibility of taxation to individuals and households.

=== Structure of tax rates ===

Income tax rates are quoted inclusively. For instance, an income tax rate of 10% means that the taxpaper pays 10% of income, leaving the taxpayer with the remaining 90%. This is in contrast with sales taxes, which are quoted exclusively.

== Structure and applicability ==

=== Generally progressive structure ===

In most jurisdictions, the income tax formula is progressive: the higher the income, the higher the average tax rate. Marginal income tax rates are generally constant over income ranges and jump discretely. These income ranges are sometimes called ''tax brackets'' or ''tax slabs''. The lowest marginal tax rate is generally zero (though this might be operationalized in the form of a "standard deduction" or "personal exemption" on taxable income rather than a 0% marginal tax rate) and the highest marginal tax rate can vary from 1% to 90% depending on jurisdiction.

Some jurisdictions have a flat income tax rate, though even these jurisdictions support some basic exemption, so they effectively have a two-tiered tax rate: 0% for the exempted income, and then a fixed rate.

Income taxes are almost never regressive; however, [[social security tax]]es, which are in many ways similar to income taxes, may be regressive or even capped.

=== Types of income ===

There are a few categories of income to which income tax applies:

* Earned income: Income earned by doing work. This is the most common kind of income for the majority of people who file income tax returns, in most jurisdictions. Earned income is subject not just to income tax but also to [[social security tax]] in some jurisdictions.
* Capital gains: Income earned through a gain in the value of assets held. Capital gains are realized at the time of sale, though they may also be realized using a "mark-to-market" method. Capital gains are most likely to have a lower tax rate, possibly even a zero tax rate. There are theoretical arguments for a different treatment of capital gains than other kinds of income.
* Interest and dividend income: Income earned from deposits in bank accounts, and dividends earned from shares held in companies. Although the arguments for lower tax rates on capital gains may also apply to interest income, interest income is generally taxed the same way as regular earned income, though it is not subject to social security tax.
* Other income: Any other kinds of income that does not fall within the above categories.

=== Sensitivity to distribution across persons and time periods ===

Since income tax rates are progressive and not flat, the total income tax burden over a multi-year time period cannot be determined by looking at the total income over the time period. Rather, the distribution of income across the multi-year time period determines the amount of tax. In general, assuming no significant changes to tax rates or tax brackets between the years, the tax is least when the income is evenly distributed across the time periods.

Similarly, the total income tax burden across a set of people is not determined purely by the total income of those people, but also by the distribution, The closer to even the distribution of income, the lower the total income tax.

=== Individual versus household ===

Tax treatment generally provides lower tax rates on the same income to a married couple filing jointly than to an individual, but the tax rates are higher than if they both reported their separate incomes as individuals. Households with children may have to pay less in taxes for each child, up to some limit.

=== Deductions ===

Taxes in general have three justifications: revenue justification, incentive justification, and group/class warfare justification. Tax laws include a large number of deductions for politically or socially favored categories of expenses, such as charitable donations or healthcare payments. This ties with the incentive justification, as the tax law wants to incentivize people to donate to charity and take care of their health.

Deductions generally add to the complexity of the tax code, significantly adding to the overhead of tax preparation.

=== Taxation by multiple jurisdictions ===

In some cases, an individual or household may be required to pay taxes to multiple jurisdictions on the same income. There are two kinds of situations:

* Jurisdictions at different levels, such as a national government and a state or provincial government: Generally, since a given state or provincial governments is inside a fixed national government, the state's tax laws already take into account the nation's tax laws. In fact, many of the tax calculations for the state's taxes may rely on tax calculations for the nation's taxes. Generally, the same income is subject to being taxes at both levels; however, taxes paid to one level may be a deduction one can take for taxes paid to another level.
* Multiple independent jurisdictions, such as two countries (for people who have citizenship and/or residency and/or income sources in multiple countries): In such cases, it may be possible to exclude income that has been taxed in one jurisdiction from taxation in the other.

== Effect of income tax ==

It is worth keeping in mind that because income tax laws affect large numbers of people, the study of behavioral responses to income taxes, to be done properly, must take into account the interaction between responses. This section will discuss the effect of income taxes at the micro level, but a fuller understanding would require unfolding what this does to the whole economy. In particular, the secondary and tertiary effects of changes to income tax policies would result in changes to the general price level of the economy.

=== Effect on earned income ===

Income taxes have incentive effects on earned incomes in both directions:

{| class="sortable" border="1"
! Explanation of effect !! What does this effect predict about the effect on earned income of increasing income tax rates? !! What does this effect predict about the effect on tax revenue of increasing income tax rates? !! What kind of people would this effect be strongest in
|-
| The marginal benefit (financial) of earning more is less, because the after-tax income is reduced. This reduces people's incentive to work more, or to look for higher-paying (but potentially less pleasant) jobs. This is a [[substitution effect]] in action. || Decreases || Ambiguous || People who are already earning enough to meet their basic needs; people who have a range of options either for the kind of job or the amount of time spent on the job, that differ significantly in the amount of personal pleasantness or satisfaction. This may also apply to families that already have some earners, and where additional earners have a choice between working and not working.
|-
| To have a given amount of after-tax income (needed to sustain a lifestyle) the person needs to earn more pre-tax income. This is an [[income effect]] in action. || Increases || Increases || People who have a relatively inflexible budget, and who come close to spending most of their income (living paycheck-to-paycheck), or have very specific financial savings goals.
|}

Although there is ambiguity about the effect on earned income, there are other, less ambiguous things we can conclude:

* The progressive structure of tax rates incentivizes people toward having a more steady income rather than having large incomes in one year and small incomes in other years. This may not change behavior much for salaried workers, but for contract workers, who have more flexibility in how to distribute their work between years, it could affect behavior. This could also affect the way employers structure bonuses (so that bonuses that have less-than-annual frequency would be rare).

=== Effect on interest income ===

Income taxes on interest income cause the ''effective interest rate'' on savings to be correspondingly lower than the interest rate offered by the bank or financial institution. Generally speaking, this should move people away from saving money in interest-bearing accounts, toward one of these:

* Consumption.
* Saving money in cash or non-interest-bearing accounts, if saving money in this way offers some other advantages.
* Buying assets, on which taxes would be paid as capital gains, and likely only at the time of sale (thus allowing for more tax-free compounding over time). Also, capital gains may have a lower tax rate.
* Putting money in interest-bearing accounts that are exempt from taxes; usually, some kinds of retirement accounts enjoy this exemption.

=== Effect on capital gains ===

Capital gains tax rates are generally lower than tax rates on earned income or interest income. Some jurisdictions make a distinction between short-term capital gains, which are taxed at ordinary income tax rates, and long-term capital gains, which are taxed at a reduced rate. Moreover, capital gains taxes are generally paid only at the time of sale, though some assets may be taxed on a "mark-to-market" basis where the appreciation in value every year is taxed.

* The gap between ordinary income tax rates and capital gains tax rates is one factor that determines whether people save in the form of deposits or assets. The larger the gap, the more likely savings are to be in the form of assets.
* If capital gains tax rates are based on total income level, this might incentivize people to time the sale of their capital assets to years when their other income is lower, so as to pay a lower effective tax rate on the capital gain.
* If tax law itself is subject to changes, people with the flexibility to time things may time the sales of capital assets to years when capital gains treatment is particularly favorable.

=== Effect on favored activities ===

Tax code often provides favorable treatment in the following forms:

* Deductions are allowed for charitable contributions, some healthcare expenses, health insurance, and education expenses. As is partly the intent of such deductions, these deductions cause more of these expenses than would otherwise be the case. This money may substitute away from money that would be spent on other forms of consumption or saving.
* Money (income or otherwise) saved in special kinds of savings accounts called retirement accounts may benefit from reduced tax rates relative to money saved in normal interest-bearing accounts. This may encourage people to use retirement accounts rather than ordinary savings accounts or direct purchase of assets, even though ordinary savings accounts and purchase of assets offer more liquidity. It may also shift people to move money away from consumption toward retirement accounts.

Income tax

2020-03-30T04:22:30Z

Vipul:

== Definition ==

An '''income tax''' is a [[tax]] that is levied on, and is generally an increasing function of, [[income]]. Income taxes are levied on persons (individuals or households). There is a related notion of income tax for corporations, which is discussed on the separate [[corporate tax]] page.

== Mechanics ==

=== Burden of remitting the tax ===

* Income taxes are usually paid by the individual or household as part of an annual process of filing a tax return. The tax return is a statement of the income over the tax year as well as the calculation of tax based on the income. A tax return includes filled versions of forms created by the taxing authority.
* Many payers of income, including employers paying wage income, as well as banks offering interest income, may be required to deduct taxes from the employee's income and send it to the taxing authority. These deducted taxes are called ''tax withholdings'', and represent an advance payment of the eventual tax obligation of the individual or household. Tax withholdings help the tax authority obtain a steady stream of income tax revenue throughout the year, increase tax compliance, and reduce the visibility of taxation to individuals and households.

=== Structure of tax rates ===

Income tax rates are quoted inclusively. For instance, an income tax rate of 10% means that the taxpaper pays 10% of income, leaving the taxpayer with the remaining 90%. This is in contrast with sales taxes, which are quoted exclusively.

== Structure and applicability ==

=== Generally progressive structure ===

In most jurisdictions, the income tax formula is progressive: the higher the income, the higher the average tax rate. Marginal income tax rates are generally constant over income ranges and jump discretely. These income ranges are sometimes called ''tax brackets'' or ''tax slabs''. The lowest marginal tax rate is generally zero (though this might be operationalized in the form of a "standard deduction" or "personal exemption" on taxable income rather than a 0% marginal tax rate) and the highest marginal tax rate can vary from 1% to 90% depending on jurisdiction.

Some jurisdictions have a flat income tax rate, though even these jurisdictions support some basic exemption, so they effectively have a two-tiered tax rate: 0% for the exempted income, and then a fixed rate.

Income taxes are almost never regressive; however, [[payroll tax]]es, which are in many ways similar to income taxes, may be regressive or even capped.

=== Types of income ===

There are a few categories of income to which income tax applies:

* Earned income: Income earned by doing work. This is the most common kind of income for the majority of people who file income tax returns, in most jurisdictions. Earned income is subject not just to income tax but also to [[payroll tax]] in some jurisdictions.
* Capital gains: Income earned through a gain in the value of assets held. Capital gains are realized at the time of sale, though they may also be realized using a "mark-to-market" method. Capital gains are most likely to have a lower tax rate, possibly even a zero tax rate. There are theoretical arguments for a different treatment of capital gains than other kinds of income.
* Interest and dividend income: Income earned from deposits in bank accounts, and dividends earned from shares held in companies. Although the arguments for lower tax rates on capital gains may also apply to interest income, interest income is generally taxed the same way as regular earned income, though it is not subject to social security tax.
* Other income: Any other kinds of income that does not fall within the above categories.

=== Sensitivity to distribution across persons and time periods ===

Since income tax rates are progressive and not flat, the total income tax burden over a multi-year time period cannot be determined by looking at the total income over the time period. Rather, the distribution of income across the multi-year time period determines the amount of tax. In general, assuming no significant changes to tax rates or tax brackets between the years, the tax is least when the income is evenly distributed across the time periods.

Similarly, the total income tax burden across a set of people is not determined purely by the total income of those people, but also by the distribution, The closer to even the distribution of income, the lower the total income tax.

=== Individual versus household ===

Tax treatment generally provides lower tax rates on the same income to a married couple filing jointly than to an individual, but the tax rates are higher than if they both reported their separate incomes as individuals. Households with children may have to pay less in taxes for each child, up to some limit.

=== Deductions ===

Taxes in general have three justifications: revenue justification, incentive justification, and group/class warfare justification. Tax laws include a large number of deductions for politically or socially favored categories of expenses, such as charitable donations or healthcare payments. This ties with the incentive justification, as the tax law wants to incentivize people to donate to charity and take care of their health.

Deductions generally add to the complexity of the tax code, significantly adding to the overhead of tax preparation.

=== Taxation by multiple jurisdictions ===

In some cases, an individual or household may be required to pay taxes to multiple jurisdictions on the same income. There are two kinds of situations:

* Jurisdictions at different levels, such as a national government and a state or provincial government: Generally, since a given state or provincial governments is inside a fixed national government, the state's tax laws already take into account the nation's tax laws. In fact, many of the tax calculations for the state's taxes may rely on tax calculations for the nation's taxes. Generally, the same income is subject to being taxes at both levels; however, taxes paid to one level may be a deduction one can take for taxes paid to another level.
* Multiple independent jurisdictions, such as two countries (for people who have citizenship and/or residency and/or income sources in multiple countries): In such cases, it may be possible to exclude income that has been taxed in one jurisdiction from taxation in the other.

== Effect of income tax ==

It is worth keeping in mind that because income tax laws affect large numbers of people, the study of behavioral responses to income taxes, to be done properly, must take into account the interaction between responses. This section will discuss the effect of income taxes at the micro level, but a fuller understanding would require unfolding what this does to the whole economy. In particular, the secondary and tertiary effects of changes to income tax policies would result in changes to the general price level of the economy.

=== Effect on earned income ===

Income taxes have incentive effects on earned incomes in both directions:

{| class="sortable" border="1"
! Explanation of effect !! What does this effect predict about the effect on earned income of increasing income tax rates? !! What does this effect predict about the effect on tax revenue of increasing income tax rates? !! What kind of people would this effect be strongest in
|-
| The marginal benefit (financial) of earning more is less, because the after-tax income is reduced. This reduces people's incentive to work more, or to look for higher-paying (but potentially less pleasant) jobs. This is a [[substitution effect]] in action. || Decreases || Ambiguous || People who are already earning enough to meet their basic needs; people who have a range of options either for the kind of job or the amount of time spent on the job, that differ significantly in the amount of personal pleasantness or satisfaction. This may also apply to families that already have some earners, and where additional earners have a choice between working and not working.
|-
| To have a given amount of after-tax income (needed to sustain a lifestyle) the person needs to earn more pre-tax income. This is an [[income effect]] in action. || Increases || Increases || People who have a relatively inflexible budget, and who come close to spending most of their income (living paycheck-to-paycheck), or have very specific financial savings goals.
|}

Although there is ambiguity about the effect on earned income, there are other, less ambiguous things we can conclude:

* The progressive structure of tax rates incentivizes people toward having a more steady income rather than having large incomes in one year and small incomes in other years. This may not change behavior much for salaried workers, but for contract workers, who have more flexibility in how to distribute their work between years, it could affect behavior. This could also affect the way employers structure bonuses (so that bonuses that have less-than-annual frequency would be rare).

=== Effect on interest income ===

Income taxes on interest income cause the ''effective interest rate'' on savings to be correspondingly lower than the interest rate offered by the bank or financial institution. Generally speaking, this should move people away from saving money in interest-bearing accounts, toward one of these:

* Consumption.
* Saving money in cash or non-interest-bearing accounts, if saving money in this way offers some other advantages.
* Buying assets, on which taxes would be paid as capital gains, and likely only at the time of sale (thus allowing for more tax-free compounding over time). Also, capital gains may have a lower tax rate.
* Putting money in interest-bearing accounts that are exempt from taxes; usually, some kinds of retirement accounts enjoy this exemption.

=== Effect on capital gains ===

Capital gains tax rates are generally lower than tax rates on earned income or interest income. Some jurisdictions make a distinction between short-term capital gains, which are taxed at ordinary income tax rates, and long-term capital gains, which are taxed at a reduced rate. Moreover, capital gains taxes are generally paid only at the time of sale, though some assets may be taxed on a "mark-to-market" basis where the appreciation in value every year is taxed.

* The gap between ordinary income tax rates and capital gains tax rates is one factor that determines whether people save in the form of deposits or assets. The larger the gap, the more likely savings are to be in the form of assets.
* If capital gains tax rates are based on total income level, this might incentivize people to time the sale of their capital assets to years when their other income is lower, so as to pay a lower effective tax rate on the capital gain.
* If tax law itself is subject to changes, people with the flexibility to time things may time the sales of capital assets to years when capital gains treatment is particularly favorable.

=== Effect on favored activities ===

Tax code often provides favorable treatment in the following forms:

* Deductions are allowed for charitable contributions, some healthcare expenses, health insurance, and education expenses. As is partly the intent of such deductions, these deductions cause more of these expenses than would otherwise be the case. This money may substitute away from money that would be spent on other forms of consumption or saving.
* Money (income or otherwise) saved in special kinds of savings accounts called retirement accounts may benefit from reduced tax rates relative to money saved in normal interest-bearing accounts. This may encourage people to use retirement accounts rather than ordinary savings accounts or direct purchase of assets, even though ordinary savings accounts and purchase of assets offer more liquidity. It may also shift people to move money away from consumption toward retirement accounts.

Income tax

2020-03-30T04:21:23Z

Vipul: /* Effect of income tax */

Income tax

2020-03-30T04:16:45Z

Vipul: /* Effect on capital gains */

Income tax

2020-03-30T04:14:29Z

Vipul:

== Definition ==

An '''income tax''' is a [[tax]] that is levied on, and is generally an increasing function of, [[income]]. Income taxes are levied on persons (individuals or households). There is a related notion of income tax for corporations, which is discussed on the separate [[corporate tax]] page.

== Mechanics ==

=== Burden of remitting the tax ===

* Income taxes are usually paid by the individual or household as part of an annual process of filing a tax return. The tax return is a statement of the income over the tax year as well as the calculation of tax based on the income. A tax return includes filled versions of forms created by the taxing authority.
* Many payers of income, including employers paying wage income, as well as banks offering interest income, may be required to deduct taxes from the employee's income and send it to the taxing authority. These deducted taxes are called ''tax withholdings'', and represent an advance payment of the eventual tax obligation of the individual or household. Tax withholdings help the tax authority obtain a steady stream of income tax revenue throughout the year, increase tax compliance, and reduce the visibility of taxation to individuals and households.

=== Structure of tax rates ===

Income tax rates are quoted inclusively. For instance, an income tax rate of 10% means that the taxpaper pays 10% of income, leaving the taxpayer with the remaining 90%. This is in contrast with sales taxes, which are quoted exclusively.

== Structure and applicability ==

=== Generally progressive structure ===

In most jurisdictions, the income tax formula is progressive: the higher the income, the higher the average tax rate. Marginal income tax rates are generally constant over income ranges and jump discretely. These income ranges are sometimes called ''tax brackets'' or ''tax slabs''. The lowest marginal tax rate is generally zero (though this might be operationalized in the form of a "standard deduction" or "personal exemption" on taxable income rather than a 0% marginal tax rate) and the highest marginal tax rate can vary from 1% to 90% depending on jurisdiction.

Some jurisdictions have a flat income tax rate, though even these jurisdictions support some basic exemption, so they effectively have a two-tiered tax rate: 0% for the exempted income, and then a fixed rate.

Income taxes are almost never regressive; however, [[social security tax]]es, which are in many ways similar to income taxes, may be regressive or even capped.

=== Types of income ===

There are a few categories of income to which income tax applies:

* Earned income: Income earned by doing work. This is the most common kind of income for the majority of people who file income tax returns, in most jurisdictions. Earned income is subject not just to income tax but also to [[social security tax]] in some jurisdictions.
* Capital gains: Income earned through a gain in the value of assets held. Capital gains are realized at the time of sale, though they may also be realized using a "mark-to-market" method. Capital gains are most likely to have a lower tax rate, possibly even a zero tax rate. There are theoretical arguments for a different treatment of capital gains than other kinds of income.
* Interest and dividend income: Income earned from deposits in bank accounts, and dividends earned from shares held in companies. Although the arguments for lower tax rates on capital gains may also apply to interest income, interest income is generally taxed the same way as regular earned income, though it is not subject to social security tax.
* Other income: Any other kinds of income that does not fall within the above categories.

=== Sensitivity to distribution across persons and time periods ===

Since income tax rates are progressive and not flat, the total income tax burden over a multi-year time period cannot be determined by looking at the total income over the time period. Rather, the distribution of income across the multi-year time period determines the amount of tax. In general, assuming no significant changes to tax rates or tax brackets between the years, the tax is least when the income is evenly distributed across the time periods.

Similarly, the total income tax burden across a set of people is not determined purely by the total income of those people, but also by the distribution, The closer to even the distribution of income, the lower the total income tax.

=== Individual versus household ===

Tax treatment generally provides lower tax rates on the same income to a married couple filing jointly than to an individual, but the tax rates are higher than if they both reported their separate incomes as individuals. Households with children may have to pay less in taxes for each child, up to some limit.

=== Deductions ===

Taxes in general have three justifications: revenue justification, incentive justification, and group/class warfare justification. Tax laws include a large number of deductions for politically or socially favored categories of expenses, such as charitable donations or healthcare payments. This ties with the incentive justification, as the tax law wants to incentivize people to donate to charity and take care of their health.

Deductions generally add to the complexity of the tax code, significantly adding to the overhead of tax preparation.

=== Taxation by multiple jurisdictions ===

In some cases, an individual or household may be required to pay taxes to multiple jurisdictions on the same income. There are two kinds of situations:

* Jurisdictions at different levels, such as a national government and a state or provincial government: Generally, since a given state or provincial governments is inside a fixed national government, the state's tax laws already take into account the nation's tax laws. In fact, many of the tax calculations for the state's taxes may rely on tax calculations for the nation's taxes. Generally, the same income is subject to being taxes at both levels; however, taxes paid to one level may be a deduction one can take for taxes paid to another level.
* Multiple independent jurisdictions, such as two countries (for people who have citizenship and/or residency and/or income sources in multiple countries): In such cases, it may be possible to exclude income that has been taxed in one jurisdiction from taxation in the other.

== Effect of income tax ==

It is worth keeping in mind that because income tax laws affect large numbers of people, the study of behavioral responses to income taxes, to be done properly, must take into account the interaction between responses. This section will discuss the effect of income taxes at the micro level, but a fuller understanding would require unfolding what this does to the whole economy. In particular, the secondary and tertiary effects of changes to income tax policies would result in changes to the general price level of the economy.

=== Effect on earned income ===

Income taxes have incentive effects on earned incomes in both directions:

{| class="sortable" border="1"
! Explanation of effect !! What does this effect predict about the effect on earned income of increasing income tax rates? !! What does this effect predict about the effect on tax revenue of increasing income tax rates? !! What kind of people would this effect be strongest in
|-
| The marginal benefit (financial) of earning more is less, because the after-tax income is reduced. This reduces people's incentive to work more, or to look for higher-paying (but potentially less pleasant) jobs. This is a [[substitution effect]] in action. || Decreases || Ambiguous || People who are already earning enough to meet their basic needs; people who have a range of options either for the kind of job or the amount of time spent on the job, that differ significantly in the amount of personal pleasantness or satisfaction. This may also apply to families that already have some earners, and where additional earners have a choice between working and not working.
|-
| To have a given amount of after-tax income (needed to sustain a lifestyle) the person needs to earn more pre-tax income. This is an [[income effect]] in action. || Increases || Increases || People who have a relatively inflexible budget, and who come close to spending most of their income (living paycheck-to-paycheck), or have very specific financial savings goals.
|}

Although there is ambiguity about the effect on earned income, there are other, less ambiguous things we can conclude:

* The progressive structure of tax rates incentivizes people toward having a more steady income rather than having large incomes in one year and small incomes in other years. This may not change behavior much for salaried workers, but for contract workers, who have more flexibility in how to distribute their work between years, it could affect behavior. This could also affect the way employers structure bonuses (so that bonuses that have less-than-annual frequency would be rare).

=== Effect on interest income ===

Income taxes on interest income cause the ''effective interest rate'' on savings to be correspondingly lower than the interest rate offered by the bank or financial institution. Generally speaking, this should move people away from saving money in interest-bearing accounts, toward one of these:

* Consumption.
* Saving money in cash or non-interest-bearing accounts, if saving money in this way offers some other advantages.
* Buying assets, on which taxes would be paid as capital gains, and likely only at the time of sale (thus allowing for more tax-free compounding over time). Also, capital gains may have a lower tax rate.
* Putting money in interest-bearing accounts that are exempt from taxes; usually, some kinds of retirement accounts enjoy this exemption.

=== Effect on capital gains ===

Capital gains tax rates are generally lower than tax rates on earned income or interest income. Moreover, capital gains taxes are generally paid only at the time of sale, though some assets may be taxed on a "mark-to-market" basis where the appreciation in value every year is taxed.

* The gap between ordinary income tax rates and capital gains tax rates is one factor that determines whether people save in the form of deposits or assets. The larger the gap, the more likely savings are to be in the form of assets.
* If capital gains tax rates are based on total income level, this might incentivize people to time the sale of their capital assets to years when their other income is lower, so as to pay a lower effective tax rate on the capital gain.

Income tax

2020-03-30T03:49:24Z

Vipul: /* Structure and applicability */

Income tax

2020-03-30T03:36:42Z

Vipul: /* = Generally progressive structure */

Income tax

2020-03-30T03:30:13Z

Vipul: Created page with "== Definition == An '''income tax''' is a tax that is levied on, and is generally an increasing function of, income. Income taxes are levied on persons (individuals o..."

Substitute goods

2020-03-30T02:30:25Z

Vipul: /* In terms of effect on consumption */

This page is about substitution for goods for consumers. For substitution in the context of factors of production to a production process, see [[substitute factors of production]].

==Definition==

===In terms of partial derivative of individual utility function===

Two goods are said to be substitutes in terms of the utility function of an individual or household if the [[calculus:second-order mixed partial derivative|second-order mixed partial derivative]] of personal utility with respect to the quantities of the two goods consumed is negative. Note that under reasonable assumptions, this definition is equivalent to the other two definitions.

===In terms of effect on consumption===

Two goods are said to be '''substitute goods''' if an increase in consumption of either one of them leads to a decrease in demand (i.e., a contraction in the demand curve) for the other.

===In terms of price and quantity demanded===

Assuming the [[law of demand]], the definition in terms of substitution is equivalent to the condition that:

* A decrease in the unit price of one of the goods should cause a ''decrease'' in demand for the other, i.e., reduce the quantity demanded for the other good holding its unit price constant.
* Equivalently, an increase in the unit price of one of the goods should cause an ''increase'' in demand for the other, i.e., increase the quantity demanded for the other good holding its unit price constant.

==Algebra of substitution==

===Reflexivity===

We generally do not talk of goods as being substitutes for themselves. However, this does make conceptual sense when interpreted appropriately: a good is self-substituting if the second derivative of the utility function with respect to the quantity consumed is negative (i.e., diminishing returns from consumption). Most goods are self-substituting in this sense, at least in the consumption range at which people would finally be consuming the good.
===Symmetry===

The general conceptual definition as well as its mathematical formulations imply that the relation of being substitute goods is ''symmetric'', i.e., if ''A'' is a substitute good for ''B'', then ''B'' is a substitute good for ''A''. While it is possible to come up with contrived counterexamples to symmetry, the assumption of symmetry is practically harmless.

===Transitivity===

Transitivity is the statement that if ''A'' and B'' are substitutes and ''B'' and ''C'' are substitutes, then ''A'' and ''C'' are substitutes.

The mathematical formulation of substitute goods does not say anything conclusive about transitivity. From a conceptual perspective, there is a strong reason to believe that the relation of being substitute goods is generally transitive, and more so if at least one of the substitution relations is close. One common reason why goods are substitutes is that they meet the same common need. In this case, the relation would be transitive (for instance, the case where ''A'', ''B'', and ''C'' are all different brands of wine).

The reason why transitivity might fail is that the "common need" that ''A'' and ''B'' fulfill might differ from the "common need" that ''B'' and ''C'' fulfill. For instance, ''A'' might be a ''phone Internet access plan'', ''B'' might be a ''home broadband Internet and cable TV connection'', ''C'' might be a ''pure cable connection without Internet.'' ''A'' and ''B'' fulfill a common need for Internet access, whereas ''B'' and ''C'' fulfill a common need for cable TV, but ''A'' and ''C'' do not have a common need that they fulfill.

==Combined analysis of substitute goods==

If two goods are perfect substitutes, then the prices for the goods are likely to converge (with the appropriate unit conversion factors). In such cases, it is possible to do an analysis of them as a single good. Combined analysis may also serve as a first-order approximation for goods that are fairly close but not perfect substitutes.

Queueing, rationing, and queue-rationing

2020-03-30T01:32:55Z

Vipul: /* Efficiency of allocation of queueing, rationing, and queue-rationing */

==Definition==

'''Queueing, rationing, and queue-rationing''' are a family of forms of [[defining ingredient::non-price competition]] where a seller or regulatory authority deals with a shortfall ([[excess demand]] -- more demanded than supplied) by controlling who can buy how much when.

'''Queueing''': Here, potential buyers have to wait in a queue, generally a first-come-first-serve queue. This could be a physical queue; for instance, shoppers waiting in line outside a store in order to enter and claim items, or waiting in line at a checkout counter in order to complete the transaction. If a good is sold out by the time a buyer gets to the front of the queue, the buyer is out of luck. A buyer can have only one position in a queue at a time.

'''Rationing''': Here, potential buyers are limiting in the total quantity of an item they can purchase. The limit may be imposed per unit time (for instance, at most one loaf of bread a day). Unused rations are usually not tradable, though it may be possible to roll them over.

'''Queue-rationing''': A mix of queueing and rationing: buyers have to wait in a queue, generally a first-come-first-serve queue. However, even when it's the buyer's turn, the buyer is constrained by rationing. There are different variants: in one variant, the buyer can immediately go to the back of the queue after completing the purchase, for the next turn. In another version, the ration is over a time period (like a day or month) so the buyer has to wait for the next time period to get in the queue again.

==Causes of queueing, rationing, and queue-rationing==

===Excess demand due to inability of prices to adjust===

Queueing typically occurs in a case of [[excess demand]] because prices are unable to adjust to [[market price|market-clearing levels]] due to [[sticky price]]s, [[price ceiling]]s or other factors.

=== A deliberate choice by sellers to shape their customers ===

In some cases, producers/suppliers may deliberately maintain shortages and not raise prices in order to make the good appear more attractive. Some possible advantages of queueing and rationing are:

* By queueing, sellers may be able to get a profile of customers who may be better for them in the long run.
* By rationing, sellers increase the ''number'' of people who buy the good, which may have long-term value for the sellers.
* Standing in a long queue itself makes people buy more: There are often a lot of items for ''impulse purchase'' at the checkout counters in supermarkets, so the longer people have to stand in queue, the more such purchases they may make. Similarly, people on a waiting list for a good sold through a website may check the website more frequently, and may as a result make many other auxiliary purchases.

===More fairness===

For queueing: Standing in line may be considered a fairer way of distributing resources among people with varying degrees of wealth, compared to charging a high price. This is particularly true for goods that are highly valued by all, but for which [[wealth effect]]s make it much easier for the rich to purchase them. This includes, for instance, goods such as education and health care.

For rationing: Rationing distributes a scarce good more equally among people, thereby being more fair.

===Tamping down on panic buying===

[[Panic buying]] is a situation where buyers' "true" demand for a good does not change, but buyers still try to purchase larger quantities because of fear that other buyers will use up the existing stock. This is most common for cases where intertemporal substitution is easy: one can buy now and stock up for the future.

Panic buying can become a self-fulfilling prophecy, causing shortages. Moreover, it can lead to the [[bullwhip effect]], where sellers incorrectly conclude that demand has intrinsically increased, leading to them producing more, but then find reduced demand in the next time period as buyers start using up their existing stocks rather than buying more.

Done correctly, rationing is most helpful for panic buying because it provides a solution to the coordination problem of buyers not trusting each other. By committing all buyers to purchasing a limited quantity of the good, rationing increases the confidence of all buyers that there will be enough for them.

== Efficiency of allocation of queueing, rationing, and queue-rationing ==

In a situation of a shortfall, where the quantity demanded exceeds the quantity supplied, there is some [[deadweight loss]] compared to what there would be if prices reached the market price. The inevitable deadweight loss is represented by the area of a [[Harberger triangle]] (see [[effect of price ceiling on economic surplus]]).

Beyond this inevitable deadweight loss, there is further loss that may happen if the non-price competition between buyers fails in one of these two ways:

* It does not allocate the good to the buyers who value it most, i.e., it does not generate the most high-value part of the [[consumer surplus]]
* It imposes transaction costs on buyers and sellers

Setting aside transaction costs, we now discuss the question of the efficiency of allocation of queueing, rationing, and queue-rationing.

=== Pure rationing allocates efficiently when buyers have similar reservation prices and there are sharp diminishing returns to each individual buyer after the ration ===

If all buyers have sharply diminishing returns after buying the first two units of a good, so much so that any buyer's first two units have a higher reservation price for that buyer than any other buyer's third or later unit, and there is enough for everybody to buy two units, then rationing to two units leads to an efficient allocation.

Even if the above isn't strictly true, if it's generally true that the reservation prices of buyers are similar, and see sharp diminishing returns, setting a ration to before the point of diminishing returns, if feasible, is likely to lead to an efficient or close-to-efficient allocation.

=== Pure queueing allocates efficiently when reservation prices differ between buyers, don't differ much across the quantity range for each buyer, and the order of buyers in the queue mirrors their reservation price ===

If some buyers value a good more than others, and this effect is stronger than any diminishing returns within the range that a buyer may buy in, then queueing to give the higher-value buyers priority makes sense. However, without buyers explicitly bidding to indicate how much they value a good, it may be hard for a queue that forms in practice to reflect the relative value placed by buyers.

If it is possible for buyers to pay people to stand in a queue for them, and the transaction costs are negligible, then we might expect queueing to give more priority to higher-value buyers (as they will be willing to bid higher to pay somebody to stand in queue for them and grab an earlier slot) and lead to an efficient allocation.

=== A suitable queue-rationing strategy can be found for a wide range of intermediate situations ===

The "queue" part of queue-rationing helps prioritize between different buyers, and the "ration" part helps deal with diminishing marginal returns. By combining these two tools through queue-rationing, it is possible to design strategies for efficient allocation for many situations.

=== Sellers in general may not have incentives to allocate efficiently ===

Regardless of how sellers allocate the good, they will sell it all, because quantity demanded exceeds quantity supplied. Therefore, viewed naively, sellers have no incentive to allocate efficiently.

However, sellers do have some incentives. First, they care about perceived fairness, which often relates with efficiency of allocation. Second, a single seller is often selling not just the one good that has a shortfall, but many other goods that don't. The seller is also interested in long-term buyer loyalty. These considerations push the seller in the general direction of allocating efficiently. However, the considerations don't align perfectly with efficient allocation.

For instance, a seller may adopt a rationing strategy even though a queueing strategy would be more efficient, because a rationing strategy gives more of an appearance of full shelves (by slowing down the rate at which a good is sold) thereby giving others looking at the store the perception that it is well-stocked.