Market - User contributions [en]

Price ceiling

2016-07-24T19:47:37Z

MiloKing: /* Effect on social surplus */

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above marginal cost at the pre-ceiling level of production===

Before a price ceiling is imposed, the monopolist will produce at a point where the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. (The price charged will be higher than this point). In this section, we are considering the impact of a price ceiling above this point described. (Since the price ceiling is binding, by definition it must be below the price charged by the monopolist.)

'''Effects on the market price''': Price ceilings in this range will reduce the market price of the good sold.

'''Effects on the quantity traded''': Price ceilings in this range will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run|maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus|total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below marginal cost at the pre-ceiling level of production===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

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

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Short-run impact of binding price ceilings in monopolistic markets==

===Reduction of monopoly profits===

A monopolist enjoys an economic profit that firms in perfect competition do not receive, because they are able to set the price and quantity sold in the whole market to maximize their profits. This excess profit is reduced when a price control is imposed, as it constrains the monopolist and requires them to offer the good at a price and quantity which does not maximize their profits (or else they would have chosen that price and quantity in the first place).

===Effect on social surplus===

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

Here we assume that the good being sold has no [[external cost|external costs]] or [[external benefit|external benefits]].

In the case in which the price control [[Price_ceiling#Binding_price_ceilings_above_marginal_cost_at_the_pre-ceiling_level_of_production|actually raises the quantity of the good sold]] in the short run, the effect on social surplus is positive, as it removes some of the [[deadweight loss]] of the monopoly and moves the price and quantity closer to what they would be in a perfectly competitive market.

Conversely, in the case in which the price control [[Price_ceiling#Binding_price_ceilings_below_marginal_cost_at_the_pre-ceiling_level_of_production|reduces the quantity of the good sold]] in the short run, the effect on social surplus is negative, as it prevents some mutually beneficial exchanges from occurring.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-24T19:47:12Z

MiloKing: /* Effect on social surplus */

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above marginal cost at the pre-ceiling level of production===

Before a price ceiling is imposed, the monopolist will produce at a point where the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. (The price charged will be higher than this point). In this section, we are considering the impact of a price ceiling above this point described. (Since the price ceiling is binding, by definition it must be below the price charged by the monopolist.)

'''Effects on the market price''': Price ceilings in this range will reduce the market price of the good sold.

'''Effects on the quantity traded''': Price ceilings in this range will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run|maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus|total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below marginal cost at the pre-ceiling level of production===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

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

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Short-run impact of binding price ceilings in monopolistic markets==

===Reduction of monopoly profits===

A monopolist enjoys an economic profit that firms in perfect competition do not receive, because they are able to set the price and quantity sold in the whole market to maximize their profits. This excess profit is reduced when a price control is imposed, as it constrains the monopolist and requires them to offer the good at a price and quantity which does not maximize their profits (or else they would have chosen that price and quantity in the first place).

===Effect on social surplus===

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

Note: here we assume that the good being sold has no [[external cost|external costs]] or [[external benefit|external benefits]].

In the case in which the price control [[Price_ceiling#Binding_price_ceilings_above_marginal_cost_at_the_pre-ceiling_level_of_production|actually raises the quantity of the good sold]] in the short run, the effect on social surplus is positive, as it removes some of the [[deadweight loss]] of the monopoly and moves the price and quantity closer to what they would be in a perfectly competitive market.

Conversely, in the case in which the price control [[Price_ceiling#Binding_price_ceilings_below_marginal_cost_at_the_pre-ceiling_level_of_production|reduces the quantity of the good sold]] in the short run, the effect on social surplus is negative, as it prevents some mutually beneficial exchanges from occurring.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-24T19:44:28Z

MiloKing: New section

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above marginal cost at the pre-ceiling level of production===

Before a price ceiling is imposed, the monopolist will produce at a point where the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. (The price charged will be higher than this point). In this section, we are considering the impact of a price ceiling above this point described. (Since the price ceiling is binding, by definition it must be below the price charged by the monopolist.)

'''Effects on the market price''': Price ceilings in this range will reduce the market price of the good sold.

'''Effects on the quantity traded''': Price ceilings in this range will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run|maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus|total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below marginal cost at the pre-ceiling level of production===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

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

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Short-run impact of binding price ceilings in monopolistic markets==

===Reduction of monopoly profits===

A monopolist enjoys an economic profit that firms in perfect competition do not receive, because they are able to set the price and quantity sold in the whole market to maximize their profits. This excess profit is reduced when a price control is imposed, as it constrains the monopolist and requires them to offer the good at a price and quantity which does not maximize their profits (or else they would have chosen that price and quantity in the first place).

===Effect on social surplus===

In the case in which the price control [[Price_ceiling#Binding_price_ceilings_above_marginal_cost_at_the_pre-ceiling_level_of_production|actually raises the quantity of the good sold]] in the short run, the effect on social surplus is positive, as it removes some of the [[deadweight loss]] of the monopoly and moves the price and quantity closer to what they would be in a perfectly competitive market.

Conversely, in the case in which the price control [[Price_ceiling#Binding_price_ceilings_below_marginal_cost_at_the_pre-ceiling_level_of_production|reduces the quantity of the good sold]] in the short run, the effect on social surplus is negative, as it prevents some mutually beneficial exchanges from occurring.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-24T19:30:56Z

MiloKing: /* Basic theory: the effects of price ceilings in monopolistic markets */

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above marginal cost at the pre-ceiling level of production===

Before a price ceiling is imposed, the monopolist will produce at a point where the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. (The price charged will be higher than this point). In this section, we are considering the impact of a price ceiling above this point described. (Since the price ceiling is binding, by definition it must be below the price charged by the monopolist.)

'''Effects on the market price''': Price ceilings in this range will reduce the market price of the good sold.

'''Effects on the quantity traded''': Price ceilings in this range will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run|maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus|total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below marginal cost at the pre-ceiling level of production===

'''Effects on the market price''': Price ceilings in this range will reduce the market price of the good sold.

'''Effects on the quantity traded''': Price ceilings in this range will reduce the quantity of the good sold.

This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

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

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-24T19:26:31Z

MiloKing: Clarification /* Basic theory: the effects of price ceilings in monopolistic markets */

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above marginal cost at the pre-ceiling level of production===

Before a price ceiling is imposed, the monopolist will produce at a point where the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. (The price charged will be higher than this point). In this section, we are considering the impact of a price ceiling above this point described. (Since the price ceiling is binding, by definition it must be below the price charged by the monopolist.)

'''Effects on the market price''': Price ceilings in this range will reduce the market price of the good sold.

'''Effects on the quantity traded''': Price ceilings in this range will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run|maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus|total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below marginal cost at the pre-ceiling level of production===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

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

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-24T19:03:02Z

MiloKing: syntax error/* Binding price ceilings above the point at which marginal revenue equals marginal cost */

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above the point at which marginal revenue equals marginal cost===

Here we consider binding price ceilings above the point at which the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. Price ceilings in this range will reduce the market price of the good sold, and they will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run|maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus|total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below the point at which marginal revenue equals marginal cost===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

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

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-24T19:00:37Z

MiloKing: changing title, b/c new section will be added on monopoly /* Short-run impact of binding price ceilings */

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above the point at which marginal revenue equals marginal cost===

Here we consider binding price ceilings above the point at which the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. Price ceilings in this range will reduce the market price of the good sold, and they will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run||maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus||total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below the point at which marginal revenue equals marginal cost===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

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

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-18T21:09:03Z

MiloKing: /* Long-run impact of price ceiling */

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above the point at which marginal revenue equals marginal cost===

Here we consider binding price ceilings above the point at which the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. Price ceilings in this range will reduce the market price of the good sold, and they will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run||maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus||total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below the point at which marginal revenue equals marginal cost===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

==Short-run impact of binding price ceilings==

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these, the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

===Firms in declining-cost industries may leave the market===

There are some industries where the average cost of producing a unit of the good actually declines as more units are produced. This often happens if there are fixed costs of production. The result is that the average cost of producing a unit will exceed the marginal cost of producing a unit, and generally only one firm will supply the market. This is often called a case of ''natural monopoly''. The problem is that when a price control is established that would otherwise raise the quantity sold (as described above), the new price will be below the average cost of producing a unit, and so the monopolist firm will no longer be profitable.

In order to raise total surplus in this sort of monopoly situation, a price control set at the marginal cost of production will be insufficient. The firm will either have to be allowed to engage in [[price discrimination]] so that the profit-maximizing level of production will be closer to the socially optimal level of production, will have to be subsidized by the government so that it can sell units closer to marginal cost, or will have to be allowed to sell units at or above the average cost of production. This last option has less potential to raise total surplus, as it cannot allow the socially optimal level of production to prevail. However, the other options can also present difficulties, including distributional issues with price discrimination (more of the total surplus is taken up by the monopolist) and funding issues with subsidies (funding subsidies via distortionary taxes can actually create another deadweight loss).

==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

2016-07-18T20:57:37Z

MiloKing: Note: be sure to add in explanations of new terms! Also the part about firm shutdown

==Definition==

A '''price ceiling''' is an upper limit placed by the government or a regulatory authority with government sanction on the price (per unit) of a commodity.

A price ceiling is a form of [[price control]]. The other form of price control is a [[minimum price]].

There are two types of price ceilings:

* '''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]].

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.

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

===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 commodity has no direct effect. Such price ceilings may be put in place to prevent [[price gouging]] in the event of an emergency (not currently happening) or to prevent rapid fluctuations in prices due to other unforeseen circumstances. A price ceiling that is above the market price is termed a ''non-binding price ceiling''.

===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 social 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. The loss in social surplus relative to the market price situation is given by the area of the triangle ABC.

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

<center>{{#widget:YouTube|id=L9P-_OdT1vg}}</center>

<center>{{#widget:YouTube|id=rU6gXsrs1Pk}}</center>

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

{{NeedsGraph}}

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

This is essentially the same situation as in the competitive market case.

===Binding price ceilings above the point at which marginal revenue equals marginal cost===

Here we consider binding price ceilings above the point at which the monopolist's marginal revenue from selling a unit equals its marginal cost of producing a unit. Price ceilings in this range will reduce the market price of the good sold, and they will actually ''raise'' the quantity of the good sold (not lower it as in the competitive case).

The reason why is that the marginal revenue function for the monopolist effectively changes. The marginal revenue from selling the first unit is the price paid for that unit (which is fixed at the price ceiling). If it chooses to sell another unit, the price of the first unit does not change, as both units are sold at the maximum price allowed. So the marginal revenue is still equal to the price charged. This is true until the point at which consumers are willing to pay less than the price ceiling, at which point the marginal revenue of selling units falls below the price sold.

The monopolist will then [[Determination of price and quantity supplied by monopolistic firm in the short run||maximize its profits]] in the short run by producing more than it previously was, because the marginal revenue gained from selling an additional unit is greater. This raises [[economic surplus||total surplus]] by removing part of the [[deadweight loss]] associated with the monopoly. In particular, if the price ceiling is set at the point that would prevail in a competitive market (that is, the point where the demand curve intersects the marginal cost curve), total surplus will be maximized and the deadweight loss from the monopoly will be completely eliminated.

An exception to this is discussed below. Namely, there are some cases in which a price control in this range will make a monopoly firm unprofitable, causing it to exit. In this situation, it may be necessary to allow [[price discrimination]] or subsidize the monopoly firm in order to increase total surplus.

===Binding price ceilings below the point at which marginal revenue equals marginal cost===

Price ceilings in this range will reduce the market price of the good sold, and will lower the quantity of the good sold. This is the same as the competitive case. The basic reasoning behind this is that the price ceiling reduces the marginal revenue from selling an additional unit at the current point of production, and thereby causes the monopolist to reduce the quantity it sells.

==Short-run impact of binding price ceilings==

===Non-price competition among buyers===

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? Note that this problem does not arise in case there is a single buyer.

One solution to this problem is [[non-price competition]] among potential buyers. An example of non-price competition is [[queueing]] -- the buyers stand in line to buy the good, and those who are too far behind in line end up not getting any of the good. There are other mechanisms of non-price competition.

The chief drawback of non-price competition is that it results in a [[deadweight loss]] because the buyers spend effort competing with each other but there are no net gains to society from this effort.

===Black market===

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 commodity 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 social surplus===

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

Under most sets of assumptions, price ceilings have a negative effect on social surplus. There are, however, some theoretical exceptions, whose incidence in practice is debated.

==Long-run impact of price ceiling==

===Innovation and substitution between product lines===

Price ceilings, both binding and non-binding, can have important long-run effects, including:

* Sellers may choose to rebrand or redefine their products so as to make cheaper or lower quality products that fit in the same category as the original product, or to shift the costs on to auxiliary products. For instance, if a price ceiling is imposed on the sale of cellphones, but what a "cellphone" is is not clearly specified, sellers may shift to stocking more of the cheaper and low cost cellphones. Alternatively, sellers may choose to shift costs from the cellphone to the payment plans so they end up selling the cellphones cheap but raise the price of the payment plans.
* Conversely, sellers may be reluctant to create new products in the category for fear that they will not be able to charge a higher price for the new product to recoup the cost of creation. This concern applies even in the case of non-binding price ceilings. Goods with high upfront investment costs command a high price at the beginning, and sellers then engage in [[price skimming]] as competitors catch up, and eventually the new products become as cheap as the older products used to be, and perhaps even cheaper. ''It is thus possible that the existence of a price ceiling scares away innovation that would ultimately have a more beneficial long run impact in terms of reducing cost and improving quality''.

To avoid these,the following are usually done:

* Price ceilings are typically applied for commodities like oil or grain where the unit measurements are reasonably clear and the problem above of a new technology does not arise.
* Sometimes, price ceilings are applied only to certain brands and products and the same sellers are allowed to sell alternate or new products at unrestricted prices.

===Disaster planning===

Non-binding price ceilings are sometimes put in place to prevent [[price gouging]] in the event of natural disasters. This may reduce incentives for sellers to be well stocked with goods for natural disasters as they will be unable to command the full market price for the good in the event of a disaster.

==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.

User:MiloKing/Determination PQ Monopsonist SR

2016-07-16T20:37:26Z

MiloKing: /* Determining the price paid by the monopsonist */

Note: this article is eventually intended to become a companion to [[Determination of price and quantity supplied by monopolistic firm in the short run]].

{{NeedsGraph}}

This article describes the process by which a [[Monopsony|monopsonist]] firm, i.e., a firm that is the only firm buying a particular commodity, selects the ''quantity to purchase'' and the ''price to set'' for the commodity.

Monopsonists are usually either firms who have a monopsony in the market for one of their inputs or non-firm buyers who have a monopsony in some consumption good they choose to buy. In the former case, there is a prominent subcase of ''labor monopsony'', in which a firm is the only employer in a certain labor market. This is especially relevant when examining [[Minimum_wage#Effects_of_minimum_wages_in_a_monopsonistic_labor_market|minimum wages applied to such firms]]. In this article, we consider several different types of monopsony buyers, including non-firm buyers and several different types of firms differing by firm structure.

==Non-firm monopsonists==

Some monopsonists are not firms who possess a monopsony in one of their input markets. Some are just individual buyers purchasing consumption goods. As with the other cases, we are trying to determine the price the buyer pays and the quantity they purchase. In this case, the relevant factors are the buyer's willingness to pay for an additional unit and the cost to the buyer of buying an additional unit (called the ''marginal revenue cost'' here). The latter factor is derived from the supply curve.

One important observation is that the marginal revenue cost of a given unit ''exceeds'' the actual price of that unit, assuming the [[law of supply]] holds and that there is no [[price discrimination]]. The reason why is that, when the buyer decides to buy an additional unit, not only do they have to pay the price for that unit, but they also have to pay that new, higher price on all the other units they are buying.

So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units.

===Determining the quantity purchased by the monopsonist===

The monopsonist chooses the total number of units to buy that maximizes the difference between the total willingness to pay and the total cost of buying the units. The monopsonist's relevant consideration for buying an additional unit is how much the buyer is willing to pay for the additional unit versus the marginal revenue cost. We assume here that the buyer's willingness to pay for an additional unit falls as they purchase more units. We already assumed that the [[law of supply]] holds, and so that the marginal
revenue cost for an additional unit rises as the number of units purchased rises.

Therefore, the monopsonist will either buy zero units (if it is not willing to pay the marginal revenue cost for the first unit), or it will buy units until the marginal revenue cost exceeds its marginal willingness to pay.

===Determining the price paid by the monopsonist===

The monopsonist has absolute [[market power]], and will pay the lowest price it can for the last unit it wishes to purchase. Therefore, the monopsonist will set the price it pays at whatever the minimum amount is that the sellers would accept for the last unit the monopsonist buys.

User:MiloKing/Determination PQ Monopsonist SR

2016-07-16T20:14:48Z

MiloKing: The NeedsGraph template definitely applies here, lol

Note: this article is eventually intended to become a companion to [[Determination of price and quantity supplied by monopolistic firm in the short run]].

{{NeedsGraph}}

This article describes the process by which a [[Monopsony|monopsonist]] firm, i.e., a firm that is the only firm buying a particular commodity, selects the ''quantity to purchase'' and the ''price to set'' for the commodity.

Monopsonists are usually either firms who have a monopsony in the market for one of their inputs or non-firm buyers who have a monopsony in some consumption good they choose to buy. In the former case, there is a prominent subcase of ''labor monopsony'', in which a firm is the only employer in a certain labor market. This is especially relevant when examining [[Minimum_wage#Effects_of_minimum_wages_in_a_monopsonistic_labor_market|minimum wages applied to such firms]]. In this article, we consider several different types of monopsony buyers, including non-firm buyers and several different types of firms differing by firm structure.

==Non-firm monopsonists==

Some monopsonists are not firms who possess a monopsony in one of their input markets. Some are just individual buyers purchasing consumption goods. As with the other cases, we are trying to determine the price the buyer pays and the quantity they purchase. In this case, the relevant factors are the buyer's willingness to pay for an additional unit and the cost to the buyer of buying an additional unit (called the ''marginal revenue cost'' here). The latter factor is derived from the supply curve.

One important observation is that the marginal revenue cost of a given unit ''exceeds'' the actual price of that unit, assuming the [[law of supply]] holds and that there is no [[price discrimination]]. The reason why is that, when the buyer decides to buy an additional unit, not only do they have to pay the price for that unit, but they also have to pay that new, higher price on all the other units they are buying.

So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units.

===Determining the quantity purchased by the monopsonist===

The monopsonist chooses the total number of units to buy that maximizes the difference between the total willingness to pay and the total cost of buying the units. The monopsonist's relevant consideration for buying an additional unit is how much the buyer is willing to pay for the additional unit versus the marginal revenue cost. We assume here that the buyer's willingness to pay for an additional unit falls as they purchase more units. We already assumed that the [[law of supply]] holds, and so that the marginal
revenue cost for an additional unit rises as the number of units purchased rises.

Therefore, the monopsonist will either buy zero units (if it is not willing to pay the marginal revenue cost for the first unit), or it will buy units until the marginal revenue cost exceeds its marginal willingness to pay.

===Determining the price paid by the monopsonist===

The monopsonist has absolute market power, and will pay the lowest price it can for the last unit it wishes to purchase. Therefore, the monopsonist will set the price it pays at whatever the minimum amount is that the sellers would accept for the last unit the monopsonist buys.

User:MiloKing/Determination PQ Monopsonist SR

2016-07-12T18:44:40Z

MiloKing: Note: explanation of marginal factor cost may be moved to another section

Price floor

2016-07-12T18:07:15Z

MiloKing: adding template to indicate potential need for a graph /* Basic theory in monopsonistic markets */

==Definition==

A '''price floor''' or '''minimum price''' is a lower limit placed by a government or regulatory authority on the price (per unit) of a commodity.

A price floor is a form of [[price control]]. Another form of price control is a [[price ceiling]].

There are two types of price floors:

* '''Non-binding price floor''': This is a price floor that is less than the current [[market price]].
* '''Binding price floor''': This is a price floor that is greater than the current [[market price]].

There are two extreme forms of price floors:

* A price floor of infinity can be thought of as analogous to making the exchange or selling of the commodity illegal.
* A price floor of zero (non-inclusive) can be thought of as a requirement that the good cannot be given away for free.

==Basic theory in perfectly competitive markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Market_price|perfectly competitive]].

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price, it has no effect on the market price.

===Binding price floors: price floors set above the market price cause excess supply===

A price floor set above the market price causes [[excess supply]], or a surplus, of the good, because suppliers, tempted by the higher prices, increase production, while buyers, put off by the high prices, decide to buy less. This leads to a [[deadweight loss]]. The picture below illustrates this. Here, the distance AB measures the surplus when the price floor is set at the price level of the line AB, which is higher than the equilibrium price (i.e., the market price).

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

==Basic theory in monopsonistic markets==

{{NeedsGraph}}

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Monopsony|monopsonistic]]. That is, we assume that there is only one buyer in the market, which is trying to maximize consumer surplus. We also assume that there is no [[Price_discrimination|price discrimination]] in this market; that is, all sellers are paid the same price for the good they are selling.

We also invoke the concept of a '''marginal revenue cost''' for the buyer. This is the cost, from the buyer's perspective, of buying another unit of the good. We do not just call it the "marginal cost", because that generally refers to the cost of ''producing'' one additional unit of the good in question.

Finally, we refer to the monopsonist's '''willingness to pay''', not a "demand curve". This is because the concept of a demand curve technically relies on the existence of perfect competition.

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price (the price at which the good is actually sold, not what the price would be in perfect competition), it has no effect on the market price or quantity traded.

===Binding price floors set below the point at which marginal revenue cost equals willingness to pay increase quantity sold===

Suppose there is no price floor (or a non-binding price floor) in a monopsonistic market. Then the marginal revenue cost of buying a unit is greater than what sellers would be willing to sell the unit for. The reason why is that not only must the monopsonist pay for the additional unit, they also now have to pay the higher price for ''all the other units they buy''. (As stated above, here we assume that there is no price discrimination.) So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units. The monopsonist will choose to buy units until the marginal revenue cost of buying another unit exceeds their willingness to pay for that unit. Since they have absolute [[Market_power|market power]], the monopolist can set the price they pay, and so the market price will equal whatever the seller is willing to accept for the last unit described.

However, now suppose a price floor is imposed that is between the prevailing market price and the point at which the monopsonist's marginal revenue cost equals its willingness to pay. The monopsonist's effective marginal revenue cost curve shifts. For the first unit, its marginal revenue cost is equal to the price floor. For units after the first unit, as long as the price floor exceeds the supply curve, the marginal revenue cost ''still equals the price floor''. The reason is that the monopsonist can still buy another unit at a rate equal to the price floor without having to pay a higher price for any other units (because those units would have to be bought at the price floor as well). So the monopolist will still buy units until its marginal revenue cost exceeds its willingness to pay, but its effective marginal revenue cost curve has shifted ''downwards''.

The result is that they will choose to buy more units than they did before the price floor was imposed. The prevailing market price will also increase. The effect on [[Economic_surplus|total surplus]] is positive, as the price floor removes some of the deadweight loss from the monopsony.

===Binding price floors set above the point at which marginal revenue cost equals willingness to pay cause excess supply===

A binding price floor set above the point at which the original marginal revenue cost curve exceeds willingness to pay will shift the marginal revenue cost curve, but it will shift it upward. Namely, marginal revenue cost will be equal to the price floor until the price floor no longer exceeds what sellers are willing to sell the good for. This causes the monopsonist to buy fewer units as the marginal revenue cost of the good increases. Also, sellers will want to sell more units at this price, creating an excess supply of the good in question. This adds to the deadweight loss from the monopsony.

===A binding price floor set at the point where willingness to pay intersects the supply curve maximizes total surplus===

If this example were in perfect competition, the willingness to pay curve would be called the ''demand curve'' instead. A price floor set at the point described causes the monopsonist to purchase units until the point at which the monopsonist's willingness to pay no longer exceeds what the suppliers will accept for their goods. This is the quantity traded and price which would exist in the case of perfect competition, and so total surplus is maximized. This eliminates all [[deadweight loss]] caused by the monopsony.

==Effects of price floors==

===Regulatory agency may buy up the surplus===

The regulatory agency setting the price floor may agree to purchase all excess inventory.

===Non-price competition among sellers===

Lower effective prices by means of additional services (a form of [[non-price competition]]) or special discounts and rebates on related products.

===Black market===

A [[black market]], where the goods are sold for less than the price floor (typically, though, black markets are used to handle shortages or scarcity due to [[price ceiling]]s).

Template:NeedsGraph

2016-07-12T18:06:22Z

MiloKing: Created page with "{| class="wikitable" border="1" ! This article or section could be in use of a graph or other visual aid. Relevant discussion may be found on the talk page. |}"

{| class="wikitable" border="1"
! This article or section could be in use of a graph or other visual aid. Relevant discussion may be found on the talk page.
|}

User:MiloKing/Determination PQ Monopsonist SR

2016-07-12T18:04:35Z

MiloKing:

Note: this article is eventually intended to become a companion to [[Determination of price and quantity supplied by monopolistic firm in the short run]].

This article describes the process by which a [[Monopsony|monopsonist]] firm, i.e., a firm that is the only firm buying a particular commodity, selects the ''quantity to purchase'' and the ''price to set'' for the commodity.

Monopsonists are usually either firms who have a monopsony in the market for one of their inputs or non-firm buyers who have a monopsony in some consumption good they choose to buy. In the former case, there is a prominent subcase of ''labor monopsony'', in which a firm is the only employer in a certain labor market. This is especially relevant when examining [[Minimum_wage#Effects_of_minimum_wages_in_a_monopsonistic_labor_market|minimum wages applied to such firms]]. In this article, we consider several different types of monopsony buyers

==Non-firm monopsonists==

Some monopsonists are not firms who possess a monopsony in one of their input markets. Some are just individual buyers purchasing consumption goods. As with the other cases, we are trying to determine the price the buyer pays and the quantity they purchase. In this case, the relevant factors are the buyer's willingness to pay for an additional unit and the cost to the buyer of buying an additional unit (called the ''marginal revenue cost'' in the other cases). The latter factor is derived from the supply curve.

User:MiloKing/Determination PQ Monopsonist SR

2016-07-12T17:57:51Z

MiloKing:

{|This article or section could be in use of a graph or other visual aid. Relevant discussion may be found on the talk page.|}

Note: this article is eventually intended to become a companion to [[Determination of price and quantity supplied by monopolistic firm in the short run]].

This article describes the process by which a [[Monopsony|monopsonist]] firm, i.e., a firm that is the only firm buying a particular commodity, selects the ''quantity to purchase'' and the ''price to set'' for the commodity.

Monopsonists are usually either firms who have a monopsony in the market for one of their inputs or non-firm buyers who have a monopsony in some consumption good they choose to buy. In the former case, there is a prominent subcase of ''labor monopsony'', in which a firm is the only employer in a certain labor market. This is especially relevant when examining [[Minimum_wage#Effects_of_minimum_wages_in_a_monopsonistic_labor_market|minimum wages applied to such firms]]. In this article, we consider several different types of monopsony buyers

==Non-firm monopsonists==

Some monopsonists are not firms who possess a monopsony in one of their input markets. Some are just individual buyers purchasing consumption goods. As with the other cases, we are trying to determine the price the buyer pays and the quantity they purchase. In this case, the relevant factors are the buyer's willingness to pay for an additional unit and the cost to the buyer of buying an additional unit (called the ''marginal revenue cost'' in the other cases). The latter factor is derived from the supply curve.

User:MiloKing/Determination PQ Monopsonist SR

2016-07-12T17:57:33Z

MiloKing:

{|This article or section could be in use of a graph or other visual aid.
Relevant discussion may be found on the talk page.|}

Note: this article is eventually intended to become a companion to [[Determination of price and quantity supplied by monopolistic firm in the short run]].

This article describes the process by which a [[Monopsony|monopsonist]] firm, i.e., a firm that is the only firm buying a particular commodity, selects the ''quantity to purchase'' and the ''price to set'' for the commodity.

Monopsonists are usually either firms who have a monopsony in the market for one of their inputs or non-firm buyers who have a monopsony in some consumption good they choose to buy. In the former case, there is a prominent subcase of ''labor monopsony'', in which a firm is the only employer in a certain labor market. This is especially relevant when examining [[Minimum_wage#Effects_of_minimum_wages_in_a_monopsonistic_labor_market|minimum wages applied to such firms]]. In this article, we consider several different types of monopsony buyers

==Non-firm monopsonists==

Some monopsonists are not firms who possess a monopsony in one of their input markets. Some are just individual buyers purchasing consumption goods. As with the other cases, we are trying to determine the price the buyer pays and the quantity they purchase. In this case, the relevant factors are the buyer's willingness to pay for an additional unit and the cost to the buyer of buying an additional unit (called the ''marginal revenue cost'' in the other cases). The latter factor is derived from the supply curve.

User:MiloKing/Determination PQ Monopsonist SR

2016-07-12T17:55:40Z

MiloKing:

User:MiloKing/Determination PQ Monopsonist SR

2016-07-12T17:22:43Z

MiloKing: starting userspace article on monopsony buyers and how they make their decisions

This article describes the process by which a [[Monopsony|monopsonist]] firm, i.e., a firm that is the only firm buying a particular commodity, selects the ''quantity to purchase'' and the ''price to set'' for the commodity.

Price floor

2016-07-12T16:31:04Z

MiloKing: /* A binding price floor set at the point where willingness to pay intersects the supply curve maximizes total surplus */

==Definition==

A '''price floor''' or '''minimum price''' is a lower limit placed by a government or regulatory authority on the price (per unit) of a commodity.

A price floor is a form of [[price control]]. Another form of price control is a [[price ceiling]].

There are two types of price floors:

* '''Non-binding price floor''': This is a price floor that is less than the current [[market price]].
* '''Binding price floor''': This is a price floor that is greater than the current [[market price]].

There are two extreme forms of price floors:

* A price floor of infinity can be thought of as analogous to making the exchange or selling of the commodity illegal.
* A price floor of zero (non-inclusive) can be thought of as a requirement that the good cannot be given away for free.

==Basic theory in perfectly competitive markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Market_price|perfectly competitive]].

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price, it has no effect on the market price.

===Binding price floors: price floors set above the market price cause excess supply===

A price floor set above the market price causes [[excess supply]], or a surplus, of the good, because suppliers, tempted by the higher prices, increase production, while buyers, put off by the high prices, decide to buy less. This leads to a [[deadweight loss]]. The picture below illustrates this. Here, the distance AB measures the surplus when the price floor is set at the price level of the line AB, which is higher than the equilibrium price (i.e., the market price).

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

==Basic theory in monopsonistic markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Monopsony|monopsonistic]]. That is, we assume that there is only one buyer in the market, which is trying to maximize consumer surplus. We also assume that there is no [[Price_discrimination|price discrimination]] in this market; that is, all sellers are paid the same price for the good they are selling.

We also invoke the concept of a '''marginal revenue cost''' for the buyer. This is the cost, from the buyer's perspective, of buying another unit of the good. We do not just call it the "marginal cost", because that generally refers to the cost of ''producing'' one additional unit of the good in question.

Finally, we refer to the monopsonist's '''willingness to pay''', not a "demand curve". This is because the concept of a demand curve technically relies on the existence of perfect competition.

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price (the price at which the good is actually sold, not what the price would be in perfect competition), it has no effect on the market price or quantity traded.

===Binding price floors set below the point at which marginal revenue cost equals willingness to pay increase quantity sold===

Suppose there is no price floor (or a non-binding price floor) in a monopsonistic market. Then the marginal revenue cost of buying a unit is greater than what sellers would be willing to sell the unit for. The reason why is that not only must the monopsonist pay for the additional unit, they also now have to pay the higher price for ''all the other units they buy''. (As stated above, here we assume that there is no price discrimination.) So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units. The monopsonist will choose to buy units until the marginal revenue cost of buying another unit exceeds their willingness to pay for that unit. Since they have absolute [[Market_power|market power]], the monopolist can set the price they pay, and so the market price will equal whatever the seller is willing to accept for the last unit described.

However, now suppose a price floor is imposed that is between the prevailing market price and the point at which the monopsonist's marginal revenue cost equals its willingness to pay. The monopsonist's effective marginal revenue cost curve shifts. For the first unit, its marginal revenue cost is equal to the price floor. For units after the first unit, as long as the price floor exceeds the supply curve, the marginal revenue cost ''still equals the price floor''. The reason is that the monopsonist can still buy another unit at a rate equal to the price floor without having to pay a higher price for any other units (because those units would have to be bought at the price floor as well). So the monopolist will still buy units until its marginal revenue cost exceeds its willingness to pay, but its effective marginal revenue cost curve has shifted ''downwards''.

The result is that they will choose to buy more units than they did before the price floor was imposed. The prevailing market price will also increase. The effect on [[Economic_surplus|total surplus]] is positive, as the price floor removes some of the deadweight loss from the monopsony.

===Binding price floors set above the point at which marginal revenue cost equals willingness to pay cause excess supply===

A binding price floor set above the point at which the original marginal revenue cost curve exceeds willingness to pay will shift the marginal revenue cost curve, but it will shift it upward. Namely, marginal revenue cost will be equal to the price floor until the price floor no longer exceeds what sellers are willing to sell the good for. This causes the monopsonist to buy fewer units as the marginal revenue cost of the good increases. Also, sellers will want to sell more units at this price, creating an excess supply of the good in question. This adds to the deadweight loss from the monopsony.

===A binding price floor set at the point where willingness to pay intersects the supply curve maximizes total surplus===

If this example were in perfect competition, the willingness to pay curve would be called the ''demand curve'' instead. A price floor set at the point described causes the monopsonist to purchase units until the point at which the monopsonist's willingness to pay no longer exceeds what the suppliers will accept for their goods. This is the quantity traded and price which would exist in the case of perfect competition, and so total surplus is maximized. This eliminates all [[deadweight loss]] caused by the monopsony.

==Effects of price floors==

===Regulatory agency may buy up the surplus===

The regulatory agency setting the price floor may agree to purchase all excess inventory.

===Non-price competition among sellers===

Lower effective prices by means of additional services (a form of [[non-price competition]]) or special discounts and rebates on related products.

===Black market===

A [[black market]], where the goods are sold for less than the price floor (typically, though, black markets are used to handle shortages or scarcity due to [[price ceiling]]s).

Minimum wage

2016-07-12T16:29:46Z

MiloKing: /* Effects of minimum wages in a monopsonistic labor market */

==Definition==

A '''minimum wage''' is a legally enforceable government-imposed lower bound on the wage that can be paid to a worker. It thus acts as a [[price floor]] in the [[labor market]].

==Mechanics==

===Basic structure of the minimum wage===

Minimum wages are usually specified for work per unit time. For instance, a minimum wage might be imposed of $5 per hour worked.

===Sources of minimum wage arrangements===

Formally established minimum wages involve the government directly regulating labor arrangements to prevent employers from paying workers less than the minimum wage rate. There also exist some agreements between labor unions and businesses creating a minimum pay rate, but this can have some differences from the minimum wages we describe in this article.

==Effects of minimum wages in perfect competition==

The effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, the effects can vary depending on the assumptions in the model, particularly regarding assumptions concerning the degree of market power. Whether a labor market is perfectly competitive or monopsonistic affects the analysis present. (In the analysis below, we assume that the labor market is perfectly competitive.) This analysis also is done in partial equilibrium.

===Effects on quantity traded===

In a perfectly competitive market, the effect on the equilibrium quantity traded is either zero or negative. In the case of a minimum wage which is below the market wage for the market is applied to, the analysis is essentially that of a [[Price_floor#Non-binding_price_floor:_price_floors_set_below_the_market_price_have_no_effect|non-binding price floor]], and we expect that there will be no effect on either the wage paid or the quantity of labor bought.

In the case of a minimum wage which is higher than the market wage for the market it is applied to, the effect will be an [[Price_floor#Binding_price_floors:_price_floors_set_above_the_market_price_cause_excess_supply|excess supply of labor]]. Namely, workers will want to sell a greater amount of labor, while employers will want to buy less labor. This has both an '''unemployment effect''' and a '''disemployment effect'''. The unemployment effect is the effect on the number (or fraction) of workers who wish to be employed, but cannot find additional work at the existing wage. The disemployment effect is the effect on workers who are previously employed for some number of hours, but have their hours cut or lose their jobs. In other words, the unemployment effect is an increase in excess supply in the labor market, while the disemployment effect is a reduction of quantity traded in the labor market.

===Effects on social surplus===

To determine the effect of a minimum wage on [[Economic surplus|social surplus]], we must compare the level of social surplus in a market with no minimum wage to the level of social surplus in a market with a minimum wage at the rate being considered. A binding minimum wage, like a binding price floor, will lead to a [[Deadweight loss|deadweight loss]], which is a loss of social surplus.

[[File:Surplusabovemarketprice.png]]

(Note: in the image linked above, the label "Surplus" refers to the excess supply of the good in question, not the social surplus. The deadweight loss is represented by the quasi-triangular area between the demand and supply curves between the new quantity sold and the old quantity sold.)

===Effects on the distribution of social surplus===

As described in the previous section, the effects of a binding minimum wage on total social surplus are negative. However, the minimum wage also redistributes some of the remaining social surplus in the labor market. Consumer surplus decreases, as employers have to pay a higher wage for labor (and choose, as a whole, to buy less labor). However, the effect on producer surplus is indeterminate, as workers (as a whole) can no longer sell as many units of labor, but do receive a higher wage for the units they do sell. If the demand for labor is sufficiently inelastic, producer surplus could increase.

An intuitive way of thinking about the latter statement is as follows: if employers are very sensitive to a new minimum wage (or an increase in an existing one), there will be a large cutback in hours or employees, and while remaining workers will be paid a higher wage for the hours they work, employees' total income (and producer surplus) falls. But if employers barely react to a minimum wage increase, there will be little or no cutback in hours or employees, and workers will receive a higher wage.

==Effects of minimum wages in a monopsonistic labor market==

As with the perfectly competitive case, the effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, in this case, we are concerned with the effects of a minimum wage when there is a [[monopsony]] in the labor market; that is, when there is only one buyer of a certain type of labor. We also assume that the workers in this market compete with each other, and do not collaborate together (such as via a labor union) to gain [[market power]].

Here, the effects of a binding minimum wage mirror what we would expect from [[Price_floor#Basic_theory_in_monopsonistic_markets|other cases of monopsony]]. Namely:

* '''In [[Price_floor#Non-binding_price_floor:_price_floors_set_below_the_market_price_have_no_effect_2|the case of a non-binding minimum wage]]:''' the minimum wage will have no effect on the market wage or the quantity of labor bought.

* '''In [[Price_floor#Binding_price_floors_set_below_the_point_at_which_marginal_revenue_cost_equals_willingness_to_pay_increase_quantity_sold|the case of a binding minimum wage set at or below the point where the cost to the employer of buying an additional unit of labor equals the employer's willingness to pay for additional units of labor]]''': the minimum wage will raise the market wage and raise the quantity of labor bought (compared to the case of a monopsony with no minimum wage).

* '''In [[Price_floor#Binding_price_floors_set_above_the_point_at_which_marginal_revenue_cost_equals_willingness_to_pay_cause_excess_supply|the case of a binding minimum wage set above the point where the cost to the employer of buying an additional unit of labor equals the employer's willingness to pay for additional units of labor]]''': the minimum wage will raise the market wage and lower the quantity of labor bought (compared to the case of a monopsony with no minimum wage).

Also, in [[Price_floor#A_binding_price_floor_set_at_the_point_where_willingness_to_pay_intersects_the_supply_curve_maximizes_total_surplus|the case of a binding minimum wage set at the wage which would exist in perfect competition]], the minimum wage will eliminate the [[deadweight loss]] associated with the monopsony.

Minimum wage

2016-07-12T16:08:06Z

MiloKing: added links /* Effects of minimum wages in a monopsonistic labor market */

Minimum wage

2016-07-12T16:06:33Z

MiloKing: /* Effects of minimum wages in a monopsonistic labor market */

==Definition==

A '''minimum wage''' is a legally enforceable government-imposed lower bound on the wage that can be paid to a worker. It thus acts as a [[price floor]] in the [[labor market]].

==Mechanics==

===Basic structure of the minimum wage===

Minimum wages are usually specified for work per unit time. For instance, a minimum wage might be imposed of $5 per hour worked.

===Sources of minimum wage arrangements===

Formally established minimum wages involve the government directly regulating labor arrangements to prevent employers from paying workers less than the minimum wage rate. There also exist some agreements between labor unions and businesses creating a minimum pay rate, but this can have some differences from the minimum wages we describe in this article.

==Effects of minimum wages in perfect competition==

The effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, the effects can vary depending on the assumptions in the model, particularly regarding assumptions concerning the degree of market power. Whether a labor market is perfectly competitive or monopsonistic affects the analysis present. (In the analysis below, we assume that the labor market is perfectly competitive.) This analysis also is done in partial equilibrium.

===Effects on quantity traded===

In a perfectly competitive market, the effect on the equilibrium quantity traded is either zero or negative. In the case of a minimum wage which is below the market wage for the market is applied to, the analysis is essentially that of a [[Price_floor#Non-binding_price_floor:_price_floors_set_below_the_market_price_have_no_effect|non-binding price floor]], and we expect that there will be no effect on either the wage paid or the quantity of labor bought.

In the case of a minimum wage which is higher than the market wage for the market it is applied to, the effect will be an [[Price_floor#Binding_price_floors:_price_floors_set_above_the_market_price_cause_excess_supply|excess supply of labor]]. Namely, workers will want to sell a greater amount of labor, while employers will want to buy less labor. This has both an '''unemployment effect''' and a '''disemployment effect'''. The unemployment effect is the effect on the number (or fraction) of workers who wish to be employed, but cannot find additional work at the existing wage. The disemployment effect is the effect on workers who are previously employed for some number of hours, but have their hours cut or lose their jobs. In other words, the unemployment effect is an increase in excess supply in the labor market, while the disemployment effect is a reduction of quantity traded in the labor market.

===Effects on social surplus===

To determine the effect of a minimum wage on [[Economic surplus|social surplus]], we must compare the level of social surplus in a market with no minimum wage to the level of social surplus in a market with a minimum wage at the rate being considered. A binding minimum wage, like a binding price floor, will lead to a [[Deadweight loss|deadweight loss]], which is a loss of social surplus.

[[File:Surplusabovemarketprice.png]]

(Note: in the image linked above, the label "Surplus" refers to the excess supply of the good in question, not the social surplus. The deadweight loss is represented by the quasi-triangular area between the demand and supply curves between the new quantity sold and the old quantity sold.)

===Effects on the distribution of social surplus===

As described in the previous section, the effects of a binding minimum wage on total social surplus are negative. However, the minimum wage also redistributes some of the remaining social surplus in the labor market. Consumer surplus decreases, as employers have to pay a higher wage for labor (and choose, as a whole, to buy less labor). However, the effect on producer surplus is indeterminate, as workers (as a whole) can no longer sell as many units of labor, but do receive a higher wage for the units they do sell. If the demand for labor is sufficiently inelastic, producer surplus could increase.

An intuitive way of thinking about the latter statement is as follows: if employers are very sensitive to a new minimum wage (or an increase in an existing one), there will be a large cutback in hours or employees, and while remaining workers will be paid a higher wage for the hours they work, employees' total income (and producer surplus) falls. But if employers barely react to a minimum wage increase, there will be little or no cutback in hours or employees, and workers will receive a higher wage.

==Effects of minimum wages in a monopsonistic labor market==

As with the perfectly competitive case, the effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, in this case, we are concerned with the effects of a minimum wage when there is a [[monopsony]] in the labor market; that is, when there is only one buyer of a certain type of labor. We also assume that the workers in this market compete with each other, and do not collaborate together (such as via a labor union) to gain [[market power]].

Here, the effects of a binding minimum wage mirror what we would expect from [[Price_floor#Basic_theory_in_monopsonistic_markets|other cases of monopsony]]. Namely:

* '''In the case of a non-binding minimum wage:''' the minimum wage will have no effect on the market wage or the quantity of labor bought.

* '''In the case of a binding minimum wage set at or below the point where the cost to the employer of buying an additional unit of labor equals the employer's willingness to pay for additional units of labor''': the minimum wage will raise the market wage and raise the quantity of labor bought (compared to the case of a monopsony with no minimum wage).

* '''In the case of a binding minimum wage set above the point where the cost to the employer of buying an additional unit of labor equals the employer's willingness to pay for additional units of labor''': the minimum wage will raise the market wage and lower the quantity of labor bought (compared to the case of a monopsony with no minimum wage).

Price floor

2016-07-12T16:04:19Z

MiloKing: error /* A binding price floor set at the point where willingness to pay intersects the labor supply curve maximizes total surplus */

==Definition==

A '''price floor''' or '''minimum price''' is a lower limit placed by a government or regulatory authority on the price (per unit) of a commodity.

A price floor is a form of [[price control]]. Another form of price control is a [[price ceiling]].

There are two types of price floors:

* '''Non-binding price floor''': This is a price floor that is less than the current [[market price]].
* '''Binding price floor''': This is a price floor that is greater than the current [[market price]].

There are two extreme forms of price floors:

* A price floor of infinity can be thought of as analogous to making the exchange or selling of the commodity illegal.
* A price floor of zero (non-inclusive) can be thought of as a requirement that the good cannot be given away for free.

==Basic theory in perfectly competitive markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Market_price|perfectly competitive]].

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price, it has no effect on the market price.

===Binding price floors: price floors set above the market price cause excess supply===

A price floor set above the market price causes [[excess supply]], or a surplus, of the good, because suppliers, tempted by the higher prices, increase production, while buyers, put off by the high prices, decide to buy less. This leads to a [[deadweight loss]]. The picture below illustrates this. Here, the distance AB measures the surplus when the price floor is set at the price level of the line AB, which is higher than the equilibrium price (i.e., the market price).

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

==Basic theory in monopsonistic markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Monopsony|monopsonistic]]. That is, we assume that there is only one buyer in the market, which is trying to maximize consumer surplus. We also assume that there is no [[Price_discrimination|price discrimination]] in this market; that is, all sellers are paid the same price for the good they are selling.

We also invoke the concept of a '''marginal revenue cost''' for the buyer. This is the cost, from the buyer's perspective, of buying another unit of the good. We do not just call it the "marginal cost", because that generally refers to the cost of ''producing'' one additional unit of the good in question.

Finally, we refer to the monopsonist's '''willingness to pay''', not a "demand curve". This is because the concept of a demand curve technically relies on the existence of perfect competition.

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price (the price at which the good is actually sold, not what the price would be in perfect competition), it has no effect on the market price or quantity traded.

===Binding price floors set below the point at which marginal revenue cost equals willingness to pay increase quantity sold===

Suppose there is no price floor (or a non-binding price floor) in a monopsonistic market. Then the marginal revenue cost of buying a unit is greater than what sellers would be willing to sell the unit for. The reason why is that not only must the monopsonist pay for the additional unit, they also now have to pay the higher price for ''all the other units they buy''. (As stated above, here we assume that there is no price discrimination.) So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units. The monopsonist will choose to buy units until the marginal revenue cost of buying another unit exceeds their willingness to pay for that unit. Since they have absolute [[Market_power|market power]], the monopolist can set the price they pay, and so the market price will equal whatever the seller is willing to accept for the last unit described.

However, now suppose a price floor is imposed that is between the prevailing market price and the point at which the monopsonist's marginal revenue cost equals its willingness to pay. The monopsonist's effective marginal revenue cost curve shifts. For the first unit, its marginal revenue cost is equal to the price floor. For units after the first unit, as long as the price floor exceeds the supply curve, the marginal revenue cost ''still equals the price floor''. The reason is that the monopsonist can still buy another unit at a rate equal to the price floor without having to pay a higher price for any other units (because those units would have to be bought at the price floor as well). So the monopolist will still buy units until its marginal revenue cost exceeds its willingness to pay, but its effective marginal revenue cost curve has shifted ''downwards''.

The result is that they will choose to buy more units than they did before the price floor was imposed. The prevailing market price will also increase. The effect on [[Economic_surplus|total surplus]] is positive, as the price floor removes some of the deadweight loss from the monopsony.

===Binding price floors set above the point at which marginal revenue cost equals willingness to pay cause excess supply===

A binding price floor set above the point at which the original marginal revenue cost curve exceeds willingness to pay will shift the marginal revenue cost curve, but it will shift it upward. Namely, marginal revenue cost will be equal to the price floor until the price floor no longer exceeds what sellers are willing to sell the good for. This causes the monopsonist to buy fewer units as the marginal revenue cost of the good increases. Also, sellers will want to sell more units at this price, creating an excess supply of the good in question. This adds to the deadweight loss from the monopsony.

===A binding price floor set at the point where willingness to pay intersects the supply curve maximizes total surplus===

If this example were in perfect competition, the willingness to pay curve would be called the ''demand curve'' instead. A price floor set at the point described causes the monopsonist to purchase units until the point at which the monopsonist's willingness to pay no longer exceeds what the suppliers will accept for their goods. This is the quantity traded and price which would exist in the case of perfect competition, and so total surplus is maximized.

==Effects of price floors==

===Regulatory agency may buy up the surplus===

The regulatory agency setting the price floor may agree to purchase all excess inventory.

===Non-price competition among sellers===

Lower effective prices by means of additional services (a form of [[non-price competition]]) or special discounts and rebates on related products.

===Black market===

A [[black market]], where the goods are sold for less than the price floor (typically, though, black markets are used to handle shortages or scarcity due to [[price ceiling]]s).

Price floor

2016-07-12T16:03:58Z

MiloKing: /* Basic theory in monopsonistic markets */

==Definition==

A '''price floor''' or '''minimum price''' is a lower limit placed by a government or regulatory authority on the price (per unit) of a commodity.

A price floor is a form of [[price control]]. Another form of price control is a [[price ceiling]].

There are two types of price floors:

* '''Non-binding price floor''': This is a price floor that is less than the current [[market price]].
* '''Binding price floor''': This is a price floor that is greater than the current [[market price]].

There are two extreme forms of price floors:

* A price floor of infinity can be thought of as analogous to making the exchange or selling of the commodity illegal.
* A price floor of zero (non-inclusive) can be thought of as a requirement that the good cannot be given away for free.

==Basic theory in perfectly competitive markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Market_price|perfectly competitive]].

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price, it has no effect on the market price.

===Binding price floors: price floors set above the market price cause excess supply===

A price floor set above the market price causes [[excess supply]], or a surplus, of the good, because suppliers, tempted by the higher prices, increase production, while buyers, put off by the high prices, decide to buy less. This leads to a [[deadweight loss]]. The picture below illustrates this. Here, the distance AB measures the surplus when the price floor is set at the price level of the line AB, which is higher than the equilibrium price (i.e., the market price).

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

==Basic theory in monopsonistic markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Monopsony|monopsonistic]]. That is, we assume that there is only one buyer in the market, which is trying to maximize consumer surplus. We also assume that there is no [[Price_discrimination|price discrimination]] in this market; that is, all sellers are paid the same price for the good they are selling.

We also invoke the concept of a '''marginal revenue cost''' for the buyer. This is the cost, from the buyer's perspective, of buying another unit of the good. We do not just call it the "marginal cost", because that generally refers to the cost of ''producing'' one additional unit of the good in question.

Finally, we refer to the monopsonist's '''willingness to pay''', not a "demand curve". This is because the concept of a demand curve technically relies on the existence of perfect competition.

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price (the price at which the good is actually sold, not what the price would be in perfect competition), it has no effect on the market price or quantity traded.

===Binding price floors set below the point at which marginal revenue cost equals willingness to pay increase quantity sold===

Suppose there is no price floor (or a non-binding price floor) in a monopsonistic market. Then the marginal revenue cost of buying a unit is greater than what sellers would be willing to sell the unit for. The reason why is that not only must the monopsonist pay for the additional unit, they also now have to pay the higher price for ''all the other units they buy''. (As stated above, here we assume that there is no price discrimination.) So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units. The monopsonist will choose to buy units until the marginal revenue cost of buying another unit exceeds their willingness to pay for that unit. Since they have absolute [[Market_power|market power]], the monopolist can set the price they pay, and so the market price will equal whatever the seller is willing to accept for the last unit described.

However, now suppose a price floor is imposed that is between the prevailing market price and the point at which the monopsonist's marginal revenue cost equals its willingness to pay. The monopsonist's effective marginal revenue cost curve shifts. For the first unit, its marginal revenue cost is equal to the price floor. For units after the first unit, as long as the price floor exceeds the supply curve, the marginal revenue cost ''still equals the price floor''. The reason is that the monopsonist can still buy another unit at a rate equal to the price floor without having to pay a higher price for any other units (because those units would have to be bought at the price floor as well). So the monopolist will still buy units until its marginal revenue cost exceeds its willingness to pay, but its effective marginal revenue cost curve has shifted ''downwards''.

The result is that they will choose to buy more units than they did before the price floor was imposed. The prevailing market price will also increase. The effect on [[Economic_surplus|total surplus]] is positive, as the price floor removes some of the deadweight loss from the monopsony.

===Binding price floors set above the point at which marginal revenue cost equals willingness to pay cause excess supply===

A binding price floor set above the point at which the original marginal revenue cost curve exceeds willingness to pay will shift the marginal revenue cost curve, but it will shift it upward. Namely, marginal revenue cost will be equal to the price floor until the price floor no longer exceeds what sellers are willing to sell the good for. This causes the monopsonist to buy fewer units as the marginal revenue cost of the good increases. Also, sellers will want to sell more units at this price, creating an excess supply of the good in question. This adds to the deadweight loss from the monopsony.

===A binding price floor set at the point where willingness to pay intersects the labor supply curve maximizes total surplus===

If this example were in perfect competition, the willingness to pay curve would be called the ''demand curve'' instead. A price floor set at the point described causes the monopsonist to purchase units until the point at which the monopsonist's willingness to pay no longer exceeds what the suppliers will accept for their goods. This is the quantity traded and price which would exist in the case of perfect competition, and so total surplus is maximized.

==Effects of price floors==

===Regulatory agency may buy up the surplus===

The regulatory agency setting the price floor may agree to purchase all excess inventory.

===Non-price competition among sellers===

Lower effective prices by means of additional services (a form of [[non-price competition]]) or special discounts and rebates on related products.

===Black market===

A [[black market]], where the goods are sold for less than the price floor (typically, though, black markets are used to handle shortages or scarcity due to [[price ceiling]]s).

Minimum wage

2016-07-12T15:37:58Z

MiloKing: beginning section on monopsony

==Definition==

A '''minimum wage''' is a legally enforceable government-imposed lower bound on the wage that can be paid to a worker. It thus acts as a [[price floor]] in the [[labor market]].

==Mechanics==

===Basic structure of the minimum wage===

Minimum wages are usually specified for work per unit time. For instance, a minimum wage might be imposed of $5 per hour worked.

===Sources of minimum wage arrangements===

Formally established minimum wages involve the government directly regulating labor arrangements to prevent employers from paying workers less than the minimum wage rate. There also exist some agreements between labor unions and businesses creating a minimum pay rate, but this can have some differences from the minimum wages we describe in this article.

==Effects of minimum wages in perfect competition==

The effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, the effects can vary depending on the assumptions in the model, particularly regarding assumptions concerning the degree of market power. Whether a labor market is perfectly competitive or monopsonistic affects the analysis present. (In the analysis below, we assume that the labor market is perfectly competitive.) This analysis also is done in partial equilibrium.

===Effects on quantity traded===

In a perfectly competitive market, the effect on the equilibrium quantity traded is either zero or negative. In the case of a minimum wage which is below the market wage for the market is applied to, the analysis is essentially that of a [[Price_floor#Non-binding_price_floor:_price_floors_set_below_the_market_price_have_no_effect|non-binding price floor]], and we expect that there will be no effect on either the wage paid or the quantity of labor bought.

In the case of a minimum wage which is higher than the market wage for the market it is applied to, the effect will be an [[Price_floor#Binding_price_floors:_price_floors_set_above_the_market_price_cause_excess_supply|excess supply of labor]]. Namely, workers will want to sell a greater amount of labor, while employers will want to buy less labor. This has both an '''unemployment effect''' and a '''disemployment effect'''. The unemployment effect is the effect on the number (or fraction) of workers who wish to be employed, but cannot find additional work at the existing wage. The disemployment effect is the effect on workers who are previously employed for some number of hours, but have their hours cut or lose their jobs. In other words, the unemployment effect is an increase in excess supply in the labor market, while the disemployment effect is a reduction of quantity traded in the labor market.

===Effects on social surplus===

To determine the effect of a minimum wage on [[Economic surplus|social surplus]], we must compare the level of social surplus in a market with no minimum wage to the level of social surplus in a market with a minimum wage at the rate being considered. A binding minimum wage, like a binding price floor, will lead to a [[Deadweight loss|deadweight loss]], which is a loss of social surplus.

[[File:Surplusabovemarketprice.png]]

(Note: in the image linked above, the label "Surplus" refers to the excess supply of the good in question, not the social surplus. The deadweight loss is represented by the quasi-triangular area between the demand and supply curves between the new quantity sold and the old quantity sold.)

===Effects on the distribution of social surplus===

As described in the previous section, the effects of a binding minimum wage on total social surplus are negative. However, the minimum wage also redistributes some of the remaining social surplus in the labor market. Consumer surplus decreases, as employers have to pay a higher wage for labor (and choose, as a whole, to buy less labor). However, the effect on producer surplus is indeterminate, as workers (as a whole) can no longer sell as many units of labor, but do receive a higher wage for the units they do sell. If the demand for labor is sufficiently inelastic, producer surplus could increase.

An intuitive way of thinking about the latter statement is as follows: if employers are very sensitive to a new minimum wage (or an increase in an existing one), there will be a large cutback in hours or employees, and while remaining workers will be paid a higher wage for the hours they work, employees' total income (and producer surplus) falls. But if employers barely react to a minimum wage increase, there will be little or no cutback in hours or employees, and workers will receive a higher wage.

==Effects of minimum wages in a monopsonistic labor market==

As with the perfectly competitive case, the effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, in this case, we are concerned with the effects of a minimum wage when there is a [[monopsony]] in the labor market; that is, when there is only one buyer of a certain type of labor. We also assume that the workers in this market compete with each other, and do not collaborate together (such as via a labor union) to gain [[market power]]. Here, the effects of a binding minimum wage mirror what we would expect from [[Price_floor#Basic_theory_in_monopsonistic_markets|other cases of monopsony]].

Monopsony

2016-07-07T22:50:17Z

MiloKing:

A '''monopsony''' is a type of market where there is one buyer and many sellers who compete (in [[Market price|perfect competition]]) to serve that buyer. A market can be an '''oligopsony''' if there are relatively few buyers and many sellers who compete to serve them. A market of the former type can be described as '''monopsonistic''', where the single buyer is called the '''monopsonist'''. A market of the latter type can be described as '''oligopsonistic''', where the few buyers are called '''oligopsonists'''. In practice, oligopsonies are sometimes referred to with the same language used to describe monopsonies.

The concept of monopsony has parallels with [[Monopoly_pricing|monopoly]]. The former has only one ''buyer'' in a competitively-provided market, while the latter has only one ''seller'' in a market where buyers compete. Both involve forms of [[Market_power|market power]], since a single market participant has influence over the price in the market.

One interesting aspect of monopsonistic markets is that [[Price_floor|price floors]] may not affect such markets in the same ways as they affect perfectly competitive markets. In particular, [[Price_floor#Binding_price_floors_set_below_the_point_at_which_marginal_revenue_cost_equals_willingness_to_pay_increase_quantity_sold|it is possible]] in a monopsonistic market for price floors to actually ''raise'' the quantity of a good sold and ''increase'' social surplus.

Price floor

2016-07-07T22:49:30Z

MiloKing: /* Basic theory in monopsonistic markets */

==Definition==

A '''price floor''' or '''minimum price''' is a lower limit placed by a government or regulatory authority on the price (per unit) of a commodity.

A price floor is a form of [[price control]]. Another form of price control is a [[price ceiling]].

There are two types of price floors:

* '''Non-binding price floor''': This is a price floor that is less than the current [[market price]].
* '''Binding price floor''': This is a price floor that is greater than the current [[market price]].

There are two extreme forms of price floors:

* A price floor of infinity can be thought of as analogous to making the exchange or selling of the commodity illegal.
* A price floor of zero (non-inclusive) can be thought of as a requirement that the good cannot be given away for free.

==Basic theory in perfectly competitive markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Market_price|perfectly competitive]].

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price, it has no effect on the market price.

===Binding price floors: price floors set above the market price cause excess supply===

A price floor set above the market price causes [[excess supply]], or a surplus, of the good, because suppliers, tempted by the higher prices, increase production, while buyers, put off by the high prices, decide to buy less. This leads to a [[deadweight loss]]. The picture below illustrates this. Here, the distance AB measures the surplus when the price floor is set at the price level of the line AB, which is higher than the equilibrium price (i.e., the market price).

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

==Basic theory in monopsonistic markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Monopsony|monopsonistic]]. That is, we assume that there is only one buyer in the market, which is trying to maximize consumer surplus. We also assume that there is no [[Price_discrimination|price discrimination]] in this market; that is, all sellers are paid the same price for the good they are selling.

We also invoke the concept of a '''marginal revenue cost''' for the buyer. This is the cost, from the buyer's perspective, of buying another unit of the good. We do not just call it the "marginal cost", because that generally refers to the cost of ''producing'' one additional unit of the good in question.

Finally, we refer to the monopsonist's '''willingness to pay''', not a "demand curve". This is because the concept of a demand curve technically relies on the existence of perfect competition.

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price (the price at which the good is actually sold, not what the price would be in perfect competition), it has no effect on the market price or quantity traded.

===Binding price floors set below the point at which marginal revenue cost equals willingness to pay increase quantity sold===

Suppose there is no price floor (or a non-binding price floor) in a monopsonistic market. Then the marginal revenue cost of buying a unit is greater than what sellers would be willing to sell the unit for. The reason why is that not only must the monopsonist pay for the additional unit, they also now have to pay the higher price for ''all the other units they buy''. (As stated above, here we assume that there is no price discrimination.) So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units. The monopsonist will choose to buy units until the marginal revenue cost of buying another unit exceeds their willingness to pay for that unit. Since they have absolute [[Market_power|market power]], the monopolist can set the price they pay, and so the market price will equal whatever the seller is willing to accept for the last unit described.

However, now suppose a price floor is imposed that is between the prevailing market price and the point at which the monopsonist's marginal revenue cost equals its willingness to pay. The monopsonist's effective marginal revenue cost curve shifts. For the first unit, its marginal revenue cost is equal to the price floor. For units after the first unit, as long as the price floor exceeds the supply curve, the marginal revenue cost ''still equals the price floor''. The reason is that the monopsonist can still buy another unit at a rate equal to the price floor without having to pay a higher price for any other units (because those units would have to be bought at the price floor as well). So the monopolist will still buy units until its marginal revenue cost exceeds its willingness to pay, but its effective marginal revenue cost curve has shifted ''downwards''.

The result is that they will choose to buy more units than they did before the price floor was imposed. The prevailing market price will also increase. The effect on [[Economic_surplus|total surplus]] is positive, as the price floor removes some of the deadweight loss from the monopsony.

===Binding price floors set above the point at which marginal revenue cost equals willingness to pay cause excess supply===

A binding price floor set above the point at which the original marginal revenue cost curve exceeds willingness to pay will shift the marginal revenue cost curve, but it will shift it upward. Namely, marginal revenue cost will be equal to the price floor until the price floor no longer exceeds what sellers are willing to sell the good for. This causes the monopsonist to buy fewer units as the marginal revenue cost of the good increases. Also, sellers will want to sell more units at this price, creating an excess supply of the good in question. This adds to the deadweight loss from the monopsony.

==Effects of price floors==

===Regulatory agency may buy up the surplus===

The regulatory agency setting the price floor may agree to purchase all excess inventory.

===Non-price competition among sellers===

Lower effective prices by means of additional services (a form of [[non-price competition]]) or special discounts and rebates on related products.

===Black market===

A [[black market]], where the goods are sold for less than the price floor (typically, though, black markets are used to handle shortages or scarcity due to [[price ceiling]]s).

Monopsony

2016-07-07T22:49:02Z

MiloKing: Created page with "A '''monopsony''' is a type of market where there is one buyer and many sellers who compete (in perfect competition) to serve that buyer. A market can be an '..."

A '''monopsony''' is a type of market where there is one buyer and many sellers who compete (in [[Market price|perfect competition]]) to serve that buyer. A market can be an '''oligopsony''' if there are relatively few buyers and many sellers who compete to serve them. A market of the former type can be described as '''monopsonistic''', where the single buyer is called the '''monopsonist'''. A market of the latter type can be described as '''oligopsonistic''', where the few buyers are called '''oligopsonists'''. In practice, oligopsonies are sometimes referred to with the same language used to describe monopsonies.

The concept of monopsony has parallels with [[Monopoly_pricing|monopoly]]. The former has only one ''buyer'' in a competitively-provided market, while the latter has only one ''seller'' in a market where buyers compete. Both involve forms of [[Market_power|market power]], since a single market participant has influence over the price in the market.

One interesting aspect of monopsonistic markets is that [[Price_floor|price floors]] may not affect such markets in the same ways as they affect perfectly competitive markets. In particular, it is possible in a monopsonistic market for price floors to actually ''raise'' the quantity of a good sold and ''increase'' social surplus.

Price floor

2016-07-07T22:46:51Z

MiloKing: I should add some graphs to the monopsony part to explain it better

==Definition==

A '''price floor''' or '''minimum price''' is a lower limit placed by a government or regulatory authority on the price (per unit) of a commodity.

A price floor is a form of [[price control]]. Another form of price control is a [[price ceiling]].

There are two types of price floors:

* '''Non-binding price floor''': This is a price floor that is less than the current [[market price]].
* '''Binding price floor''': This is a price floor that is greater than the current [[market price]].

There are two extreme forms of price floors:

* A price floor of infinity can be thought of as analogous to making the exchange or selling of the commodity illegal.
* A price floor of zero (non-inclusive) can be thought of as a requirement that the good cannot be given away for free.

==Basic theory in perfectly competitive markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is [[Market_price|perfectly competitive]].

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price, it has no effect on the market price.

===Binding price floors: price floors set above the market price cause excess supply===

A price floor set above the market price causes [[excess supply]], or a surplus, of the good, because suppliers, tempted by the higher prices, increase production, while buyers, put off by the high prices, decide to buy less. This leads to a [[deadweight loss]]. The picture below illustrates this. Here, the distance AB measures the surplus when the price floor is set at the price level of the line AB, which is higher than the equilibrium price (i.e., the market price).

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

==Basic theory in monopsonistic markets==

As indicated in the title of this section, we assume here that for the good on which the price floor is imposed, its market is monopsonistic. That is, we assume that there is only one buyer in the market, which is trying to maximize consumer surplus. We also assume that there is no [[Price_discrimination|price discrimination]] in this market; that is, all sellers are paid the same price for the good they are selling.

We also invoke the concept of a '''marginal revenue cost''' for the buyer. This is the cost, from the buyer's perspective, of buying another unit of the good. We do not just call it the "marginal cost", because that generally refers to the cost of ''producing'' one additional unit of the good in question.

Finally, we refer to the monopsonist's '''willingness to pay''', not a "demand curve". This is because the concept of a demand curve technically relies on the existence of perfect competition.

===Non-binding price floor: price floors set below the market price have no effect===

If the price floor is set below the market price (the price at which the good is actually sold, not what the price would be in perfect competition), it has no effect on the market price or quantity traded.

===Binding price floors set below the point at which marginal revenue cost equals willingness to pay increase quantity sold===

Suppose there is no price floor (or a non-binding price floor) in a monopsonistic market. Then the marginal revenue cost of buying a unit is greater than what sellers would be willing to sell the unit for. The reason why is that not only must the monopsonist pay for the additional unit, they also now have to pay the higher price for ''all the other units they buy''. (As stated above, here we assume that there is no price discrimination.) So if, for example, the supply schedule for a good is $1 for one unit, $2 for two units, $3 for 3 units, ''et cetera'', the marginal revenue cost of buying a third unit is actually $5, not just $3. Instead of spending $4 to buy two units, the monopsonist would be spending $9 to buy three units. The monopsonist will choose to buy units until the marginal revenue cost of buying another unit exceeds their willingness to pay for that unit. Since they have absolute [[Market_power|market power]], the monopolist can set the price they pay, and so the market price will equal whatever the seller is willing to accept for the last unit described.

However, now suppose a price floor is imposed that is between the prevailing market price and the point at which the monopsonist's marginal revenue cost equals its willingness to pay. The monopsonist's effective marginal revenue cost curve shifts. For the first unit, its marginal revenue cost is equal to the price floor. For units after the first unit, as long as the price floor exceeds the supply curve, the marginal revenue cost ''still equals the price floor''. The reason is that the monopsonist can still buy another unit at a rate equal to the price floor without having to pay a higher price for any other units (because those units would have to be bought at the price floor as well). So the monopolist will still buy units until its marginal revenue cost exceeds its willingness to pay, but its effective marginal revenue cost curve has shifted ''downwards''.

The result is that they will choose to buy more units than they did before the price floor was imposed. The prevailing market price will also increase. The effect on [[Economic_surplus|total surplus]] is positive, as the price floor removes some of the deadweight loss from the monopsony.

===Binding price floors set above the point at which marginal revenue cost equals willingness to pay cause excess supply===

A binding price floor set above the point at which the original marginal revenue cost curve exceeds willingness to pay will shift the marginal revenue cost curve, but it will shift it upward. Namely, marginal revenue cost will be equal to the price floor until the price floor no longer exceeds what sellers are willing to sell the good for. This causes the monopsonist to buy fewer units as the marginal revenue cost of the good increases. Also, sellers will want to sell more units at this price, creating an excess supply of the good in question. This adds to the deadweight loss from the monopsony.

==Effects of price floors==

===Regulatory agency may buy up the surplus===

The regulatory agency setting the price floor may agree to purchase all excess inventory.

===Non-price competition among sellers===

Lower effective prices by means of additional services (a form of [[non-price competition]]) or special discounts and rebates on related products.

===Black market===

A [[black market]], where the goods are sold for less than the price floor (typically, though, black markets are used to handle shortages or scarcity due to [[price ceiling]]s).

Price floor

2016-07-07T21:57:57Z

MiloKing: adding in assumption. Will add section on monopsony

User:MiloKing/Monopsony

2016-07-06T19:34:43Z

MiloKing: Note: will add more details on the price floor page soon

A '''monopsony''' is a type of market where there is one buyer and many sellers who compete (in [[Market price|perfect competition]]) to serve that buyer. A market can be an '''oligopsony''' if there are relatively few buyers and many sellers who compete to serve them. A market of the former type can be described as '''monopsonistic''', where the single buyer is called the '''monopsonist'''. A market of the latter type can be described as '''oligopsonistic''', where the few buyers are called '''oligopsonists'''. In practice, oligopsonies are sometimes referred to with the same language used to describe monopsonies.

The concept of monopsony has parallels with [[Monopoly_pricing|monopoly]]. The former has only one ''buyer'' in a competitively-provided market, while the latter has only one ''seller'' in a market where buyers compete. Both involve forms of [[Market_power|market power]], since a single market participant has influence over the price in the market.

One interesting aspect of monopsonistic markets is that [[Price_floor|price floors]] may not affect such markets in the same ways as they affect perfectly competitive markets. In particular, it is possible in a monopsonistic market for price floors to actually ''raise'' the quantity of a good sold and ''increase'' social surplus.

Minimum wage

2016-07-06T19:21:05Z

MiloKing:

User:MiloKing/Monopsony

2016-06-30T15:29:00Z

MiloKing:

User:MiloKing/Monopsony

2016-06-30T15:27:45Z

MiloKing:

A '''monopsony''' is a type of market where there is one buyer and many sellers who compete (in [[Perfect competition|perfect competition]]) to serve that buyer. A market can be an '''oligopsony''' if there are relatively few buyers and many sellers who compete to serve them.

User:MiloKing/Monopsony

2016-06-30T15:27:32Z

MiloKing: Created page with "A '''monopsony''' is a type of market where there is one buyer and many sellers who compete (in Perfect competition|perfect competition) to serve that buyer. A market can be..."

A '''monopsony''' is a type of market where there is one buyer and many sellers who compete (in [[Perfect competition|perfect competition) to serve that buyer. A market can be an '''oligopsony''' if there are relatively few buyers and many sellers who compete to serve them.

Minimum wage

2016-06-28T21:21:28Z

MiloKing:

User:MiloKing/MinWage

2016-06-28T21:20:28Z

MiloKing: /* Effects of minimum wages in perfect competition */

User:MiloKing/MinWage

2016-06-28T20:48:23Z

MiloKing: /* Effects on social surplus */

User:MiloKing/MinWage

2016-06-28T20:34:55Z

MiloKing: /* Effects on social surplus */

User:MiloKing/MinWage

2016-06-28T15:52:32Z

MiloKing:

User:MiloKing/MinWage

2016-06-28T15:52:12Z

MiloKing:

==Definition==

A '''minimum wage''' is a legally enforceable government-imposed lower bound on the wage that can be paid to a worker. It thus acts as a [[price floor]] in the [[labor market]]. Minimum wages are usually specified for work per unit time.

==Mechanics==

===Basic structure of the minimum wage===

Minimum wages are usually specified for work per unit time. For instance, a minimum wage might be imposed of $5 per hour worked.

===Sources of minimum wage arrangements===

Formally established minimum wages involve the government directly regulating labor arrangements to prevent employers from paying workers less than the minimum wage rate. There also exist some agreements between labor unions and businesses creating a minimum pay rate, but this can have some differences from the minimum wages we describe in this article.

==Effects of minimum wages in perfect competition==

The effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, the effects can vary depending on the assumptions in the model, particularly regarding assumptions concerning the degree of market power. Whether a labor market is perfectly competitive or monopsonistic affects the analysis present. This analysis also is mainly in partial equilibrium.

===Effects on quantity traded===

In a perfectly competitive market, the effect on the equilibrium quantity traded is either zero or negative. In the case of a minimum wage which is below the market wage for the market is applied to, the analysis is essentially that of a [[Price_floor#Non-binding_price_floor:_price_floors_set_below_the_market_price_have_no_effect|non-binding price floor]], and we expect that there will be no effect on either the wage paid or the quantity of labor bought.

In the case of a minimum wage which is higher than the market wage for the market it is applied to, the effect will be an [[Price_floor#Binding_price_floors:_price_floors_set_above_the_market_price_cause_excess_supply|excess supply of labor]]. Namely, workers will want to sell a greater amount of labor, while employers will want to buy less labor. This has both an '''unemployment effect''' and a '''disemployment effect'''. The unemployment effect is the effect on the number (or fraction) of workers who wish to be employed, but cannot find additional work at the existing wage. The disemployment effect is the effect on workers who are previously employed for some number of hours, but have their hours cut or lose their jobs. In other words, the unemployment effect is an increase in excess supply in the labor market, while the disemployment effect is a reduction of quantity traded in the labor market.

===Effects on social surplus===

User:MiloKing/MinWage

2016-06-28T15:47:14Z

MiloKing:

==Mechanics==

===Basic structure of the minimum wage===

Minimum wages are usually specified for work per unit time. For instance, a minimum wage might be imposed of $5 per hour worked.

===Sources of minimum wage arrangements===

Formally established minimum wages involve the government directly regulating labor arrangements to prevent employers from paying workers less than the minimum wage rate. There also exist some agreements between labor unions and businesses creating a minimum pay rate, but this can have some differences from the minimum wages we describe in this article.

==Effects of minimum wages in perfect competition==

The effects of minimum wages can be analyzed by considering them as [[price floor|price floors]] on the sale of labor. However, the effects can vary depending on the assumptions in the model, particularly regarding assumptions concerning the degree of market power. Whether a labor market is perfectly competitive or monopsonistic affects the analysis present. This analysis also is mainly in partial equilibrium.

===Effects on quantity traded===

In a perfectly competitive market, the effect on the equilibrium quantity traded is either zero or negative. In the case of a minimum wage which is below the market wage for the market is applied to, the analysis is essentially that of a [[Price_floor#Non-binding_price_floor:_price_floors_set_below_the_market_price_have_no_effect|non-binding price floor]], and we expect that there will be no effect on either the wage paid or the quantity of labor bought.

In the case of a minimum wage which is higher than the market wage for the market it is applied to, the effect will be an [[Price_floor#Binding_price_floors:_price_floors_set_above_the_market_price_cause_excess_supply|excess supply of labor]]. Namely, workers will want to sell a greater amount of labor, while employers will want to buy less labor. This has both an '''unemployment effect''' and a '''disemployment effect'''. The unemployment effect is the effect on the number (or fraction) of workers who wish to be employed, but cannot find additional work at the existing wage. The disemployment effect is the effect on workers who are previously employed for some number of hours, but have their hours cut or lose their jobs. In other words, the unemployment effect is an increase in excess supply in the labor market, while the disemployment effect is a reduction of quantity traded in the labor market.

===Effects on social surplus===

User:MiloKing/MinWage

2016-06-28T15:14:21Z

MiloKing: creating draft part of article for the Minimum wage page

Effect of sales tax on market price and quantity traded

2016-06-26T20:18:29Z

MiloKing: /* Summary of several cases */ changed into table

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 ''price-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 social 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 social surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on social surplus]]
* [[Effect of price floor on social surplus]]
* [[Effect of quantity ceiling on social 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 price-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 price-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==

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.

Unlike in the previous section, here we assume that the market for the single good is supplied solely by one firm which is seeking to maximize its profits. Here, the demand curve the firm faces for its product is the same as the demand curve for the industry as a whole, so the price they receive for their goods declines as the quantity sold increases (assuming the law of demand holds). This means that the marginal revenue from selling a unit is lower than the price of that unit. Since maximizing profits involves setting marginal cost equal to marginal revenue, the monopolist will produce goods at a level where price exceeds the marginal cost of producing a good.

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 Product Rule of calculus, 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.

Furthermore, we avoid referring to a "supply curve" for a monopolist and instead refer to its "marginal cost curve". The latter refers to the relationship between the quantity of the good the monopolist produces and the marginal cost of producing each unit. The reason we do not call this the supply curve is that at the level of quantity traded, price exceeds marginal cost, and so the demand curve does not intersect the marginal cost curve at this point. Calling the marginal cost curve the "supply curve" would imply that it should, as supply and demand curves are normally expected to intersect when the market is in equilibrium.

===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 marginal cost, marginal revenue, 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 marginal cost, marginal revenue, and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply, marginal revenue, 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 marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''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.

'''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 price-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]]
|}

'''Marginal revenue curve''': The marginal revenue curve changes. In general, it moves downward in the case of a quantity-proportional sales tax, and closer to zero in the case of a price-proportional sales tax. (This means that in the case of a price-proportional sales tax, if marginal revenue is negative at a given quantity sold, marginal revenue will actually increase at that point, as it will be less negative.) Assuming the law of demand, the marginal revenue curve slopes downwards, so that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new marginal revenue curve is related to the old marginal revenue curve as follows:
{| class="sortable" border="1"
! Case !! What happens to the marginal revenue curve algebraically !! Pictorial depiction
|-
| price-propotional sales tax || For a price-proportional sales tax with a factor of <math>x</math>, the new marginal revenue function equals <math>(1/(1+x))*(Q*(dP/dQ) + P)</math>. The reason is that the demand curve is multiplied by 1/(1+x), so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d(PQ/(1+x))/dQ</math>. || An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. INSERT IMAGE
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new marginal revenue function equals <math>Q*(dP/dQ) + P - b</math>. The reason is that the demand curve shifts downward by b, so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d((P-b)Q)/dQ</math>.|| An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue 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. INSERT IMAGE
|}

The upshot is that the marginal cost curve remains the same and the demand and marginal revenue curves move inward. We can therefore determine that the equilibrium quantity traded falls. However, we cannot necessarily determine whether the pre-tax price will rise or fall. In most cases, we would expect the pre-tax price to fall, as demand falls. However, it is possible for the pre-tax price to rise if the monopolist switches from one potential equilibrium to another.

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.

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

To analyze the imposition of a sales tax on a monopolistic market, it is easiest to take the analysis for pre-tax prices and simply apply the sales tax on top of those prices. The net effect of the tax on the equilibrium quantity traded is negative. The net effect of the tax on the post-tax price is zero or positive. (Even in the case where the pre-tax price falls, it cannot fall by more than the level of the tax imposed. At maximum, the pre-tax price will fall by the full amount of the tax; this happens in the case where the marginal cost curve is completely inelastic.)

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price may be lower or 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 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)
* The sales tax effectively adds additional deadweight loss on top of the existing deadweight loss caused by the monopoly

===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 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes up and the post-tax price goes up too, while the equilibrium quantity traded rises.
* The combined effect on the pre-tax price is ambiguous (in the first approximation, it goes down, but the substitution effect pushes it back up, and it is unclear which effect dominates). The combined effect on the equilibrium quantity traded is also ambiguous. However, the combined effect on the post-tax price is unambiguous: both reasons cause it to go up.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the post-tax price goes up. However, it does not clearly show the conclusions mentioned about pre-tax price and quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods, similar to that done for substitution effects.

* In the first approximation, ignore the complementarity effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes down and the post-tax price goes down too, while the equilibrium quantity traded falls.
* The combined effect on the post-tax price is ambiguous (in the first approximation, it goes up, but the complementarity effect pushes it back down, and it is unclear which effect dominates). The combined effects on the pre-tax price and equilibrium quantity traded are unambiguous, however: both reasons cause them to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price and quantity traded both go down. However, it does not clearly show the conclusions mentioned about the post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

Effect of sales tax on market price and quantity traded

2016-06-26T20:06:50Z

MiloKing: /* Extreme cases of elastic and inelastic supply and demand */ removing flawed section

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 ''price-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==

* In the case of a single good provided in a perfectly competitive market, a sales tax (either price-proportional or quantity-proportional) will reduce the pre-tax market price, increase the post-tax market price, and reduce the equilibrium quantity traded.

* In the case of a single good provided by a monopoly firm, a sales tax (either price-proportional or quantity-proportional) will have an ambiguous effect on the pre-tax market price, increase the post-tax market price, and reduce the equilibrium quantity traded.

* In the case of two partial substitute goods each sold in perfectly competitive markets, a sales tax (either price-proportional or quantity-proportional) will decrease the pre-tax market price for at least one good, increase the post-tax market prices for both goods, and reduce the equilibrium quantity traded for at least one good.

* In the case of two complementary goods each sold in perfectly competitive markets, a sales tax (either price-proportional or quantity-proportional) will decrease the pre-tax market prices for both goods, raise the post-tax market price for at least one good, and reduce the equilibrium quantity traded for both goods.

==Relationship with other analyses==

===Other effects of sales tax===

* [[Effect of sales tax on social 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 social surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on social surplus]]
* [[Effect of price floor on social surplus]]
* [[Effect of quantity ceiling on social 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 price-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 price-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==

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.

Unlike in the previous section, here we assume that the market for the single good is supplied solely by one firm which is seeking to maximize its profits. Here, the demand curve the firm faces for its product is the same as the demand curve for the industry as a whole, so the price they receive for their goods declines as the quantity sold increases (assuming the law of demand holds). This means that the marginal revenue from selling a unit is lower than the price of that unit. Since maximizing profits involves setting marginal cost equal to marginal revenue, the monopolist will produce goods at a level where price exceeds the marginal cost of producing a good.

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 Product Rule of calculus, 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.

Furthermore, we avoid referring to a "supply curve" for a monopolist and instead refer to its "marginal cost curve". The latter refers to the relationship between the quantity of the good the monopolist produces and the marginal cost of producing each unit. The reason we do not call this the supply curve is that at the level of quantity traded, price exceeds marginal cost, and so the demand curve does not intersect the marginal cost curve at this point. Calling the marginal cost curve the "supply curve" would imply that it should, as supply and demand curves are normally expected to intersect when the market is in equilibrium.

===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 marginal cost, marginal revenue, 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 marginal cost, marginal revenue, and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply, marginal revenue, 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 marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''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.

'''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 price-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]]
|}

'''Marginal revenue curve''': The marginal revenue curve changes. In general, it moves downward in the case of a quantity-proportional sales tax, and closer to zero in the case of a price-proportional sales tax. (This means that in the case of a price-proportional sales tax, if marginal revenue is negative at a given quantity sold, marginal revenue will actually increase at that point, as it will be less negative.) Assuming the law of demand, the marginal revenue curve slopes downwards, so that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new marginal revenue curve is related to the old marginal revenue curve as follows:
{| class="sortable" border="1"
! Case !! What happens to the marginal revenue curve algebraically !! Pictorial depiction
|-
| price-propotional sales tax || For a price-proportional sales tax with a factor of <math>x</math>, the new marginal revenue function equals <math>(1/(1+x))*(Q*(dP/dQ) + P)</math>. The reason is that the demand curve is multiplied by 1/(1+x), so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d(PQ/(1+x))/dQ</math>. || An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. INSERT IMAGE
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new marginal revenue function equals <math>Q*(dP/dQ) + P - b</math>. The reason is that the demand curve shifts downward by b, so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d((P-b)Q)/dQ</math>.|| An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue 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. INSERT IMAGE
|}

The upshot is that the marginal cost curve remains the same and the demand and marginal revenue curves move inward. We can therefore determine that the equilibrium quantity traded falls. However, we cannot necessarily determine whether the pre-tax price will rise or fall. In most cases, we would expect the pre-tax price to fall, as demand falls. However, it is possible for the pre-tax price to rise if the monopolist switches from one potential equilibrium to another.

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.

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

To analyze the imposition of a sales tax on a monopolistic market, it is easiest to take the analysis for pre-tax prices and simply apply the sales tax on top of those prices. The net effect of the tax on the equilibrium quantity traded is negative. The net effect of the tax on the post-tax price is zero or positive. (Even in the case where the pre-tax price falls, it cannot fall by more than the level of the tax imposed. At maximum, the pre-tax price will fall by the full amount of the tax; this happens in the case where the marginal cost curve is completely inelastic.)

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price may be lower or 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 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)
* The sales tax effectively adds additional deadweight loss on top of the existing deadweight loss caused by the monopoly

===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 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes up and the post-tax price goes up too, while the equilibrium quantity traded rises.
* The combined effect on the pre-tax price is ambiguous (in the first approximation, it goes down, but the substitution effect pushes it back up, and it is unclear which effect dominates). The combined effect on the equilibrium quantity traded is also ambiguous. However, the combined effect on the post-tax price is unambiguous: both reasons cause it to go up.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the post-tax price goes up. However, it does not clearly show the conclusions mentioned about pre-tax price and quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods, similar to that done for substitution effects.

* In the first approximation, ignore the complementarity effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes down and the post-tax price goes down too, while the equilibrium quantity traded falls.
* The combined effect on the post-tax price is ambiguous (in the first approximation, it goes up, but the complementarity effect pushes it back down, and it is unclear which effect dominates). The combined effects on the pre-tax price and equilibrium quantity traded are unambiguous, however: both reasons cause them to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price and quantity traded both go down. However, it does not clearly show the conclusions mentioned about the post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

Effect of sales tax on market price and quantity traded

2016-06-26T20:02:05Z

MiloKing: added a summary section

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 ''price-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==

* In the case of a single good provided in a perfectly competitive market, a sales tax (either price-proportional or quantity-proportional) will reduce the pre-tax market price, increase the post-tax market price, and reduce the equilibrium quantity traded.

* In the case of a single good provided by a monopoly firm, a sales tax (either price-proportional or quantity-proportional) will have an ambiguous effect on the pre-tax market price, increase the post-tax market price, and reduce the equilibrium quantity traded.

* In the case of two partial substitute goods each sold in perfectly competitive markets, a sales tax (either price-proportional or quantity-proportional) will decrease the pre-tax market price for at least one good, increase the post-tax market prices for both goods, and reduce the equilibrium quantity traded for at least one good.

* In the case of two complementary goods each sold in perfectly competitive markets, a sales tax (either price-proportional or quantity-proportional) will decrease the pre-tax market prices for both goods, raise the post-tax market price for at least one good, and reduce the equilibrium quantity traded for both goods.

==Relationship with other analyses==

===Other effects of sales tax===

* [[Effect of sales tax on social 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 social surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on social surplus]]
* [[Effect of price floor on social surplus]]
* [[Effect of quantity ceiling on social 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 price-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 price-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==

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.

Unlike in the previous section, here we assume that the market for the single good is supplied solely by one firm which is seeking to maximize its profits. Here, the demand curve the firm faces for its product is the same as the demand curve for the industry as a whole, so the price they receive for their goods declines as the quantity sold increases (assuming the law of demand holds). This means that the marginal revenue from selling a unit is lower than the price of that unit. Since maximizing profits involves setting marginal cost equal to marginal revenue, the monopolist will produce goods at a level where price exceeds the marginal cost of producing a good.

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 Product Rule of calculus, 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.

Furthermore, we avoid referring to a "supply curve" for a monopolist and instead refer to its "marginal cost curve". The latter refers to the relationship between the quantity of the good the monopolist produces and the marginal cost of producing each unit. The reason we do not call this the supply curve is that at the level of quantity traded, price exceeds marginal cost, and so the demand curve does not intersect the marginal cost curve at this point. Calling the marginal cost curve the "supply curve" would imply that it should, as supply and demand curves are normally expected to intersect when the market is in equilibrium.

===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 marginal cost, marginal revenue, 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 marginal cost, marginal revenue, and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply, marginal revenue, 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 marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''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.

'''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 price-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]]
|}

'''Marginal revenue curve''': The marginal revenue curve changes. In general, it moves downward in the case of a quantity-proportional sales tax, and closer to zero in the case of a price-proportional sales tax. (This means that in the case of a price-proportional sales tax, if marginal revenue is negative at a given quantity sold, marginal revenue will actually increase at that point, as it will be less negative.) Assuming the law of demand, the marginal revenue curve slopes downwards, so that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new marginal revenue curve is related to the old marginal revenue curve as follows:
{| class="sortable" border="1"
! Case !! What happens to the marginal revenue curve algebraically !! Pictorial depiction
|-
| price-propotional sales tax || For a price-proportional sales tax with a factor of <math>x</math>, the new marginal revenue function equals <math>(1/(1+x))*(Q*(dP/dQ) + P)</math>. The reason is that the demand curve is multiplied by 1/(1+x), so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d(PQ/(1+x))/dQ</math>. || An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. INSERT IMAGE
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new marginal revenue function equals <math>Q*(dP/dQ) + P - b</math>. The reason is that the demand curve shifts downward by b, so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d((P-b)Q)/dQ</math>.|| An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue 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. INSERT IMAGE
|}

The upshot is that the marginal cost curve remains the same and the demand and marginal revenue curves move inward. We can therefore determine that the equilibrium quantity traded falls. However, we cannot necessarily determine whether the pre-tax price will rise or fall. In most cases, we would expect the pre-tax price to fall, as demand falls. However, it is possible for the pre-tax price to rise if the monopolist switches from one potential equilibrium to another.

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.

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

To analyze the imposition of a sales tax on a monopolistic market, it is easiest to take the analysis for pre-tax prices and simply apply the sales tax on top of those prices. The net effect of the tax on the equilibrium quantity traded is negative. The net effect of the tax on the post-tax price is zero or positive. (Even in the case where the pre-tax price falls, it cannot fall by more than the level of the tax imposed. At maximum, the pre-tax price will fall by the full amount of the tax; this happens in the case where the marginal cost curve is completely inelastic.)

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price may be lower or 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 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)
* The sales tax effectively adds additional deadweight loss on top of the existing deadweight loss caused by the monopoly

===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 marginal cost]] !! 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]]) || indeterminate || rises || falls
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || indeterminate || 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]]) || indeterminate || 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. || indeterminate || rises || falls
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic || indeterminate || 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 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes up and the post-tax price goes up too, while the equilibrium quantity traded rises.
* The combined effect on the pre-tax price is ambiguous (in the first approximation, it goes down, but the substitution effect pushes it back up, and it is unclear which effect dominates). The combined effect on the equilibrium quantity traded is also ambiguous. However, the combined effect on the post-tax price is unambiguous: both reasons cause it to go up.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the post-tax price goes up. However, it does not clearly show the conclusions mentioned about pre-tax price and quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods, similar to that done for substitution effects.

* In the first approximation, ignore the complementarity effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes down and the post-tax price goes down too, while the equilibrium quantity traded falls.
* The combined effect on the post-tax price is ambiguous (in the first approximation, it goes up, but the complementarity effect pushes it back down, and it is unclear which effect dominates). The combined effects on the pre-tax price and equilibrium quantity traded are unambiguous, however: both reasons cause them to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price and quantity traded both go down. However, it does not clearly show the conclusions mentioned about the post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

Effect of sales tax on market price and quantity traded

2016-06-26T19:15:05Z

MiloKing: adding a section on monopolist-provided goods

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 ''price-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.

==Relationship with other analyses==

===Other effects of sales tax===

* [[Effect of sales tax on social 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 social surplus are often in the same direction as that of taxes: negative.

===Effects of related interventions===

* [[Effect of price ceiling on social surplus]]
* [[Effect of price floor on social surplus]]
* [[Effect of quantity ceiling on social 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 price-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 price-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==

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.

Unlike in the previous section, here we assume that the market for the single good is supplied solely by one firm which is seeking to maximize its profits. Here, the demand curve the firm faces for its product is the same as the demand curve for the industry as a whole, so the price they receive for their goods declines as the quantity sold increases (assuming the law of demand holds). This means that the marginal revenue from selling a unit is lower than the price of that unit. Since maximizing profits involves setting marginal cost equal to marginal revenue, the monopolist will produce goods at a level where price exceeds the marginal cost of producing a good.

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 Product Rule of calculus, 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.

Furthermore, we avoid referring to a "supply curve" for a monopolist and instead refer to its "marginal cost curve". The latter refers to the relationship between the quantity of the good the monopolist produces and the marginal cost of producing each unit. The reason we do not call this the supply curve is that at the level of quantity traded, price exceeds marginal cost, and so the demand curve does not intersect the marginal cost curve at this point. Calling the marginal cost curve the "supply curve" would imply that it should, as supply and demand curves are normally expected to intersect when the market is in equilibrium.

===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 marginal cost, marginal revenue, 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 marginal cost, marginal revenue, and demand curves drawn with respect to ''pre-tax'' prices.
# Consider the world with sales tax. In this world, consider supply, marginal revenue, 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 marginal cost, demand, and marginal revenue curves for the latter in terms of the pre-tax prices.

'''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.

'''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 price-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]]
|}

'''Marginal revenue curve''': The marginal revenue curve changes. In general, it moves downward in the case of a quantity-proportional sales tax, and closer to zero in the case of a price-proportional sales tax. (This means that in the case of a price-proportional sales tax, if marginal revenue is negative at a given quantity sold, marginal revenue will actually increase at that point, as it will be less negative.) Assuming the law of demand, the marginal revenue curve slopes downwards, so that is the same as moving inward, i.e., a ''contraction'' of the demand curve. Arithmetically, the new marginal revenue curve is related to the old marginal revenue curve as follows:
{| class="sortable" border="1"
! Case !! What happens to the marginal revenue curve algebraically !! Pictorial depiction
|-
| price-propotional sales tax || For a price-proportional sales tax with a factor of <math>x</math>, the new marginal revenue function equals <math>(1/(1+x))*(Q*(dP/dQ) + P)</math>. The reason is that the demand curve is multiplied by 1/(1+x), so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d(PQ/(1+x))/dQ</math>. || An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue curve for a 50% sales tax (dashed purple). The original curve shrinks downward to 2/3 of its original level. INSERT IMAGE
|-
| quantity-proportional sales tax || For a quantity-proportional sales tax with a tax of <math>b</math> per unit quantity, the new marginal revenue function equals <math>Q*(dP/dQ) + P - b</math>. The reason is that the demand curve shifts downward by b, so instead of marginal revenue equaling <math>d(PQ)/dQ</math>, it now equals <math>d((P-b)Q)/dQ</math>.|| An example picture is below, comparing the no-tax marginal revenue curve (solid blue) with the pre-tax marginal revenue 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. INSERT IMAGE
|}

The upshot is that the marginal cost curve remains the same and the demand and marginal revenue curves move inward. We can therefore determine that the equilibrium quantity traded falls. However, we cannot necessarily determine whether the pre-tax price will rise or fall. In most cases, we would expect the pre-tax price to fall, as demand falls. However, it is possible for the pre-tax price to rise if the monopolist switches from one potential equilibrium to another.

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.

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

To analyze the imposition of a sales tax on a monopolistic market, it is easiest to take the analysis for pre-tax prices and simply apply the sales tax on top of those prices. The net effect of the tax on the equilibrium quantity traded is negative. The net effect of the tax on the post-tax price is zero or positive. (Even in the case where the pre-tax price falls, it cannot fall by more than the level of the tax imposed. At maximum, the pre-tax price will fall by the full amount of the tax; this happens in the case where the marginal cost curve is completely inelastic.)

===Combined analysis and conclusions===

Combining both these analyses, we obtain the three conclusions:

* The pre-tax market price may be lower or 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 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)
* The sales tax effectively adds additional deadweight loss on top of the existing deadweight loss caused by the monopoly

===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 marginal cost]] !! 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]]) || indeterminate || rises || falls
|-
| infinite, i.e., a horizontal demand curve (e.g., when the good has a perfect substitute) || positive (satisfies the [[law of supply]]) || indeterminate || 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]]) || indeterminate || 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. || indeterminate || rises || falls
|-
| negative (satisfies the [[law of demand]]) || zero, i.e., a vertical supply curve. We say that the supply is perfectly price-inelastic || indeterminate || 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 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes up and the post-tax price goes up too, while the equilibrium quantity traded rises.
* The combined effect on the pre-tax price is ambiguous (in the first approximation, it goes down, but the substitution effect pushes it back up, and it is unclear which effect dominates). The combined effect on the equilibrium quantity traded is also ambiguous. However, the combined effect on the post-tax price is unambiguous: both reasons cause it to go up.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the post-tax price goes up. However, it does not clearly show the conclusions mentioned about pre-tax price and quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods, similar to that done for substitution effects.

* In the first approximation, ignore the complementarity effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes down and the post-tax price goes down too, while the equilibrium quantity traded falls.
* The combined effect on the post-tax price is ambiguous (in the first approximation, it goes up, but the complementarity effect pushes it back down, and it is unclear which effect dominates). The combined effects on the pre-tax price and equilibrium quantity traded are unambiguous, however: both reasons cause them to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price and quantity traded both go down. However, it does not clearly show the conclusions mentioned about the post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

User:MiloKing/SalesTaxEdit CompSubEdit

2016-06-14T18:39:39Z

MiloKing: /* Sales tax on two mutually substitute goods with one supplied by a monopolist */ another change

==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 in perfect competition===

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. Finally, we assume that the markets for both <math>A</math> and <math>B</math> are perfectly competitive. 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes up and the post-tax price goes up too, while the equilibrium quantity traded rises.
* The combined effect on the pre-tax price of <math>A</math> is ambiguous (in the first approximation, it goes down, but the substitution effect pushes it back up, and it is unclear which effect dominates). The combined effect on the equilibrium quantity traded is also ambiguous. However, the combined effect on the post-tax price is unambiguous: both reasons cause it to go up.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the post-tax price goes up. However, it does not clearly show the conclusions mentioned about pre-tax price and quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===Sales tax on two mutually complementary goods in perfect competition===

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. Finally, we assume that the markets for both <math>A</math> and <math>B</math> are perfectly competitive. 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods, similar to that done for substitution effects.

* In the first approximation, ignore the complementarity effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes down and the post-tax price goes down too, while the equilibrium quantity traded falls.
* The combined effect on the post-tax price of <math>A</math> is ambiguous (in the first approximation, it goes up, but the complementarity effect pushes it back down, and it is unclear which effect dominates). The combined effects on the pre-tax price and equilibrium quantity traded are unambiguous, however: both reasons cause them to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price and quantity traded both go down. However, it does not clearly show the conclusions mentioned about the post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===Sales tax on two mutually substitute goods with one supplied by a monopolist===

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. Also assume that the market for good A is supplied by only one firm which seeks to maximize its profits. The market for good B is perfectly competitive.

We can draw the following conclusions:

# The ''post-tax'' market prices for <math>A</math> and <math>B</math> change ambiguously.
# The ''pre-tax'' market prices of <math>A</math> and <math>B</math> change ambiguously; they can either rise or fall for each good. This is different from the perfectly competitive case, in which it is impossible for the pre-tax price to rise for both goods.
# 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, the post-tax price is higher than the original market price and the equilibrium quantity traded is lower than the original. As for the pre-tax price, for <math>B</math> we expect it will fall, but for <math>A</math> it may not fall for reasons described in the section on sales tax in a monopoly.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. However, as we pointed out in the section on monopoly for a single good, it is possible for an increase in demand to actually reduce the price of a good supplied by a monopolist (by encouraging the monopolist to sell the good to a much larger market). So while we might normally expect that the expansion in the demand curve for <math>A</math> would cause an increase in the pre-tax and post-tax prices (relative to the baseline established after the previous bullet point), it could actually cause a decrease in the pre-tax price, or even the post-tax price as well.
* The combined effect on the pre-tax price is ambiguous (in the first approximation, it may either go down or up, and the substitution effect also has an ambiguous effect). The combined effect on the equilibrium quantity traded is also ambiguous. Finally, the effect on the post-tax price is ambiguous for the same reason listed in the second bullet point.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. (In particular, an observation made above is that the post-tax price of <math>B</math> might not rise. We could justify this if the post-tax price of <math>A</math> fell in the stage described in the second bullet point. If the price of <math>A</math> falls, this will reduce demand for <math>B</math> to the point where the eventual post-tax price of <math>B</math> might be lower.) The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax and post-tax prices change ambiguously for both goods. However, it does not clearly demonstrate the effects on equilibrium quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===Sales tax on two mutually complementary goods with one supplied by a monopolist===

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. Also assume that the market for good A is supplied by only one firm which seeks to maximize its profits. The market for good B is perfectly competitive.

We can draw the following conclusions:

# The ''pre-tax'' market price for <math>A</math> is ambiguous; it can either rise or fall. The ''pre-tax'' market price for <math>B</math> falls.
# 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the complementarity effects entirely. We expect that for both <math>A</math> and <math>B</math>, in the first approximation, the post-tax price is higher than the original market price and the equilibrium quantity traded is lower than the original. For <math>B</math>, we expect that the pre-tax price is lower than the original market price, but for <math>A</math>, the pre-tax price may be higher or lower than the original market price for reasons described in the section on sales tax in a monopoly.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The equilibrium quantity traded of <math>A</math> falls, but the pre-tax and post-tax prices could either rise or fall. Normally, they would be expected to fall, but as explained in the section on sales taxes on a monopolist, they could rise if the monopolist decides to shrink the market and only sell the good to higher-end consumers. So the effects on the pre-tax and post-tax prices are ambiguous.
* The combined effect on the post-tax price of <math>A</math> is ambiguous (in the first approximation, it goes up, and the complementarity effects are ambiguous). The combined effect on the pre-tax price of <math>A</math> is ambiguous (in the first approximation, it is ambiguous, and the complementarity effect is also ambiguous). The combined effect on equilibrium quantity traded are unambiguous, however: both reasons cause it to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price of <math>B</math> falls, and that the quantity traded for both goods falls. However, it does not clearly show the conclusions mentioned about post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

User:MiloKing/SalesTaxEdit CompSubEdit

2016-06-14T17:44:26Z

MiloKing: /* Sales tax on two mutually substitute goods with one supplied by a monopolist */ Pretty sure I made a mistake

==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 in perfect competition===

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. Finally, we assume that the markets for both <math>A</math> and <math>B</math> are perfectly competitive. 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, that the pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes up and the post-tax price goes up too, while the equilibrium quantity traded rises.
* The combined effect on the pre-tax price of <math>A</math> is ambiguous (in the first approximation, it goes down, but the substitution effect pushes it back up, and it is unclear which effect dominates). The combined effect on the equilibrium quantity traded is also ambiguous. However, the combined effect on the post-tax price is unambiguous: both reasons cause it to go up.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the post-tax price goes up. However, it does not clearly show the conclusions mentioned about pre-tax price and quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===Sales tax on two mutually complementary goods in perfect competition===

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. Finally, we assume that the markets for both <math>A</math> and <math>B</math> are perfectly competitive. 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods, similar to that done for substitution effects.

* In the first approximation, ignore the complementarity effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, pre-tax price is lower than the original market price, the post-tax price is higher than the original market price, and the equilibrium quantity traded is lower than the original.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The upshot is that the pre-tax price goes down and the post-tax price goes down too, while the equilibrium quantity traded falls.
* The combined effect on the post-tax price of <math>A</math> is ambiguous (in the first approximation, it goes up, but the complementarity effect pushes it back down, and it is unclear which effect dominates). The combined effects on the pre-tax price and equilibrium quantity traded are unambiguous, however: both reasons cause them to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price and quantity traded both go down. However, it does not clearly show the conclusions mentioned about the post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===Sales tax on two mutually substitute goods with one supplied by a monopolist===

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. Also assume that the market for good A is supplied by only one firm which seeks to maximize its profits. The market for good B is perfectly competitive.

We can draw the following conclusions:

# The ''post-tax'' market price for <math>B</math> is higher than the market price in a world without taxes. The ''post-tax'' market price for <math>A</math> changes ambiguously.
# The ''pre-tax'' market prices of <math>A</math> and <math>B</math> change ambiguously; they can either rise or fall for each good. This is different from the perfectly competitive case, in which it is impossible for the pre-tax price to rise for both goods.
# 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the substitution effects entirely. Then, the analysis proceeds as in the preceding section, so we expect that for both <math>A</math> and <math>B</math>, in the first approximation, the post-tax price is higher than the original market price and the equilibrium quantity traded is lower than the original. As for the pre-tax price, for <math>B</math> we expect it will fall, but for <math>A</math> it may not fall for reasons described in the section on sales tax in a monopoly.
* We now consider the substitution effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''expansion'' in the demand curve for <math>A</math>. This expansion applies to both the pre-tax and post-tax demand curves. However, as we pointed out in the section on monopoly for a single good, it is possible for an increase in demand to actually reduce the price of a good supplied by a monopolist (by encouraging the monopolist to sell the good to a much larger market). So while we might normally expect that the expansion in the demand curve for <math>A</math> would cause an increase in the pre-tax and post-tax prices (relative to the baseline established after the previous bullet point), it could actually cause a decrease in the pre-tax price, or even the post-tax price as well.
* The combined effect on the pre-tax price is ambiguous (in the first approximation, it may either go down or up, and the substitution effect also has an ambiguous effect). The combined effect on the equilibrium quantity traded is also ambiguous. Finally, the effect on the post-tax price is ambiguous for the same reason listed in the second bullet point.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the substitution effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the post-tax price goes up for <math>A</math>, and that the effects pre-tax prices change ambiguously for both goods. However, it does not clearly demonstrate the effects on equilibrium quantity traded. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.

===Sales tax on two mutually complementary goods with one supplied by a monopolist===

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. Also assume that the market for good A is supplied by only one firm which seeks to maximize its profits. The market for good B is perfectly competitive.

We can draw the following conclusions:

# The ''pre-tax'' market price for <math>A</math> is ambiguous; it can either rise or fall. The ''pre-tax'' market price for <math>B</math> falls.
# 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.

The justification of these using a combined partial equilibrium analysis is hard, but we can try to do a ''seriatim'' analysis of the two goods:

* In the first approximation, ignore the complementarity effects entirely. We expect that for both <math>A</math> and <math>B</math>, in the first approximation, the post-tax price is higher than the original market price and the equilibrium quantity traded is lower than the original. For <math>B</math>, we expect that the pre-tax price is lower than the original market price, but for <math>A</math>, the pre-tax price may be higher or lower than the original market price for reasons described in the section on sales tax in a monopoly.
* We now consider the complementarity effects. Since the post-tax price for <math>B</math> has risen, this is a change to one of the [[determinants of demand]] for <math>A</math>, and the effect of the change is an ''contraction'' in the demand curve for <math>A</math>. This contraction applies to both the pre-tax and post-tax demand curves. The equilibrium quantity traded of <math>A</math> falls, but the pre-tax and post-tax prices could either rise or fall. Normally, they would be expected to fall, but as explained in the section on sales taxes on a monopolist, they could rise if the monopolist decides to shrink the market and only sell the good to higher-end consumers. So the effects on the pre-tax and post-tax prices are ambiguous.
* The combined effect on the post-tax price of <math>A</math> is ambiguous (in the first approximation, it goes up, and the complementarity effects are ambiguous). The combined effect on the pre-tax price of <math>A</math> is ambiguous (in the first approximation, it is ambiguous, and the complementarity effect is also ambiguous). The combined effect on equilibrium quantity traded are unambiguous, however: both reasons cause it to go down.
* Of course, these are just two approximations. We can continue the process ad infinitum -- we can use the changes to the price of <math>A</math> to shift the demand curve for <math>B</math> via the complementarity effect, and then again back to <math>A</math>, and so on. The hope is that the process will eventually converge. To avoid this kind of infinite process, a combined partial equilibrium analysis is useful.

The crude seriatim analysis ''does'' show that the pre-tax price of <math>B</math> falls, and that the quantity traded for both goods falls. However, it does not clearly show the conclusions mentioned about post-tax price. Those conclusions can be better derived by thinking of the ''combined market'' for both goods and applying a single analysis to that.