Price elasticity of demand - Revision history

Vipul: /* Interval price elasticity */

2014-09-12T14:26:06Z

Interval price elasticity

← Older revision		Revision as of 14:26, 12 September 2014
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	The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>).		The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>).

	Conceptually, the interval price elasticity can be thought of as follows~~, in terms of <math>p_1, p_2, q_1, q_2</math>~~:		Conceptually, the interval price elasticity can be thought of as follows:

	<math>\frac{\mbox{Fractional change in quantity}}{\mbox{Fractional change in price}}</math>		<math>\frac{\mbox{Fractional change in quantity}}{\mbox{Fractional change in price}}</math>

Vipul: /* Interval price elasticity */

2014-09-12T14:25:41Z

Interval price elasticity

← Older revision		Revision as of 14:25, 12 September 2014
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	The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>).		The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>).

	Conceptually, the interval price elasticity can be thought of as:		Conceptually, the interval price elasticity can be thought of as follows, in terms of <math>p_1, p_2, q_1, q_2</math>:

	<math>\frac{\mbox{Fractional change in quantity}}{\mbox{Fractional change in price}}</math>		<math>\frac{\mbox{Fractional change in quantity}}{\mbox{Fractional change in price}}</math>

Vipul: /* Interval price elasticity */

2014-09-12T14:16:50Z

Interval price elasticity

← Older revision		Revision as of 14:16, 12 September 2014
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	===Interval price elasticity===		===Interval price elasticity===

	The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>) ~~is defined in the following equivalent ways:~~		The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>).

	<math>\frac{~~(p_1 + p_2)(~~q_2 - q_1)}{(q_1 + q_2)(p_2 - p_1)} = \frac{(q_2 - q_1)/(q_2 + q_1)}{(p_2 - p_1)/(p_2 + p_1)} = \frac{(q_2 - q_1)/(p_2 - p_1)}{q_2 + q_1)/(p_2 + p_1)}</math>		Conceptually, the interval price elasticity can be thought of as:

			<math>\frac{\mbox{Fractional change in quantity}}{\mbox{Fractional change in price}}</math>

			Or equivalently, as:

			<math>\frac{\frac{\mbox{Change in quantity}}{\mbox{Average of initial and final quantity}}}{\frac{\mbox{Change in price}}{\mbox{Average of initial and final price}}}</math>

			This simplifies to:

			<math>\frac{\frac{q_2 - q_1}{(q_1 + q_2)/2}}{\frac{p_2 - p_1}{(p_1 + p_2)/2}}</math>

			The above can be simplified into any of these equivalent forms:

			<math>\frac{(q_2 - q_1)/(q_2 + q_1)}{(p_2 - p_1)/(p_2 + p_1)} = \frac{(p_1 + p_2)(q_2 - q_1)}{(q_1 + q_2)(p_2 - p_1)} = \frac{(q_2 - q_1)/(p_2 - p_1)}{(q_2 + q_1)/(p_2 + p_1)}</math>

	===Interpretation in terms of demand curve===		===Interpretation in terms of demand curve===

Vipul: /* Interpretation of various values of price elasticity */

2011-05-07T14:56:22Z

Interpretation of various values of price elasticity

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	===Interpretation of various values of price elasticity===		===Interpretation of various values of price elasticity===

	Note that we all price elasticities here are zero or negative, and to avoid unnecessary negative signs, we state results in terms of the ''magnitude'' of price elasticity.		Note that all price elasticities here are zero or negative, and to avoid unnecessary negative signs, we state results in terms of the ''magnitude'' of price elasticity.

	{\| class="sortable" border="1"		{\| class="sortable" border="1"

Vipul: /* Interval price elasticity */

2011-05-07T14:55:24Z

Interval price elasticity

← Older revision		Revision as of 14:55, 7 May 2011
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	===Interval price elasticity===		===Interval price elasticity===

	The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>) is defined ~~as follows~~:		The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>) is defined in the following equivalent ways:

	<math>\frac{(p_1 + p_2)(q_2 - q_1)}{(q_1 + q_2)(p_2 - p_1)}</math>		<math>\frac{(p_1 + p_2)(q_2 - q_1)}{(q_1 + q_2)(p_2 - p_1)} = \frac{(q_2 - q_1)/(q_2 + q_1)}{(p_2 - p_1)/(p_2 + p_1)} = \frac{(q_2 - q_1)/(p_2 - p_1)}{q_2 + q_1)/(p_2 + p_1)}</math>

	===Interpretation in terms of demand curve===		===Interpretation in terms of demand curve===

Vipul: /* Point price elasticity */

2011-05-07T14:54:00Z

Point price elasticity

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	If we want to emphasize the fact that the quantity demanded is, in fact, a function not just of the unit price but of a number of other factors, then we can use partial derivative symbols:		If we want to emphasize the fact that the quantity demanded is, in fact, a function not just of the unit price but of a number of other factors, then we can use partial derivative symbols:

	<math>\! \frac{p\partial q}{q \partial p} = \frac{(\~~partia~~ q/\partial p)}{(q/p)} = \frac{\partial q/q}{\partial p/p} = \frac{\partial(\log q)}{\partial(\log p)}</math>		<math>\! \frac{p\partial q}{q \partial p} = \frac{(\partial q/\partial p)}{(q/p)} = \frac{\partial q/q}{\partial p/p} = \frac{\partial(\log q)}{\partial(\log p)}</math>

	In other words, it is the ratio of the rate of change of quantity demand with respect to price, to the ratio of quantity to price. Note that the price elasticity of demand is a number; it has no units and is independent of the units used to measure the price or quantity demanded.		In other words, it is the ratio of the rate of change of quantity demand with respect to price, to the ratio of quantity to price. Note that the price elasticity of demand is a number; it has no units and is independent of the units used to measure the price or quantity demanded.

Vipul: /* Definition */

2011-05-07T14:53:44Z

Definition

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	<math>\! \frac{pdq}{q dp} = \frac{(dq/dp)}{(q/p)} = \frac{dq/q}{dp/p} = \frac{d(\log q)}{d(\log p)}</math>		<math>\! \frac{pdq}{q dp} = \frac{(dq/dp)}{(q/p)} = \frac{dq/q}{dp/p} = \frac{d(\log q)}{d(\log p)}</math>

			If we want to emphasize the fact that the quantity demanded is, in fact, a function not just of the unit price but of a number of other factors, then we can use partial derivative symbols:

			<math>\! \frac{p\partial q}{q \partial p} = \frac{(\partia q/\partial p)}{(q/p)} = \frac{\partial q/q}{\partial p/p} = \frac{\partial(\log q)}{\partial(\log p)}</math>

	In other words, it is the ratio of the rate of change of quantity demand with respect to price, to the ratio of quantity to price. Note that the price elasticity of demand is a number; it has no units and is independent of the units used to measure the price or quantity demanded.		In other words, it is the ratio of the rate of change of quantity demand with respect to price, to the ratio of quantity to price. Note that the price elasticity of demand is a number; it has no units and is independent of the units used to measure the price or quantity demanded.

Vipul: /* Interpretation of various values of price elasticity */

2010-09-11T21:57:38Z

Interpretation of various values of price elasticity

← Older revision		Revision as of 21:57, 11 September 2010
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Constraint on magnitude of price elasticity at a particular price <math>p_0</math> !! Interpretation in terms of demand curve !! Interpretation in terms of total money spent on the good !! Term used !!Type of good		! Constraint on magnitude of price elasticity at a particular price <math>p_0</math> !! Interpretation in terms of demand curve !! Interpretation in terms of total money spent on the good (see also [[total revenue test]])!! Term used !!Type of good
	\|-		\|-
	\| Magnitude equals <math>0</math> \|\| The demand curve is vertical (or has a vertical tangent) at the price level of <math>p_0</math> \|\| The total money spent is directly proportional to the price \|\| The demand is completely inelastic \|\| Typically, a [[necessity good]] or a basic necessity		\| Magnitude equals <math>0</math> \|\| The demand curve is vertical (or has a vertical tangent) at the price level of <math>p_0</math> \|\| The total money spent is directly proportional to the price \|\| The demand is completely inelastic \|\| Typically, a [[necessity good]] or a basic necessity

Vipul at 21:54, 11 September 2010

2010-09-11T21:54:49Z

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	==Definition==		==Definition==

			===Backdrop===

	The '''price elasticity of demand''' is defined with the following backdrop:		The '''price elasticity of demand''' is defined with the following backdrop:
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	* An economic backdrop that includes all the [[determinants of demand]] ''other than'' the unit price of that commodity.		* An economic backdrop that includes all the [[determinants of demand]] ''other than'' the unit price of that commodity.

	~~With this backdrop, the~~ price-elasticity at a price <math>p</math> is defined in any of the following four equivalent ways:		===Point price elasticity===

			The price elasticity at a price <math>p</math> is defined in any of the following four equivalent ways:

	<math>\! \frac{pdq}{q dp} = \frac{(dq/dp)}{(q/p)} = \frac{dq/q}{dp/p} = \frac{d(\log q)}{d(\log p)}</math>		<math>\! \frac{pdq}{q dp} = \frac{(dq/dp)}{(q/p)} = \frac{dq/q}{dp/p} = \frac{d(\log q)}{d(\log p)}</math>

	In other words, it is the ratio of the rate of change of quantity demand with respect to price, to the ratio of quantity to price. Note that the price elasticity of demand is a number; it has no units and is independent of the units used to measure the price or quantity demanded.		In other words, it is the ratio of the rate of change of quantity demand with respect to price, to the ratio of quantity to price. Note that the price elasticity of demand is a number; it has no units and is independent of the units used to measure the price or quantity demanded.

			===Interval price elasticity===

			The price elasticity between a price <math>p_1</math> (with corresponding quantity demanded <math>q_1</math>) and a price <math>p_2</math> (with corresponding quantity demanded <math>q_2</math>) is defined as follows:

			<math>\frac{(p_1 + p_2)(q_2 - q_1)}{(q_1 + q_2)(p_2 - p_1)}</math>

	===Interpretation in terms of demand curve===		===Interpretation in terms of demand curve===

Vipul at 21:09, 11 September 2010

2010-09-11T21:09:51Z

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	\|}		\|}

	[[File:Inverseproportionalitydemandcurve.png\|thumb\|~~500px~~\|left\|For this [[demand curve]], the quantity demanded is inversely proportional to the price, hence the price elasticity of demand is -1, or its magnitude is 1]]		[[File:Inverseproportionalitydemandcurve.png\|thumb\|250px\|left\|For this [[demand curve]], the quantity demanded is inversely proportional to the price, hence the price elasticity of demand is -1, or its magnitude is 1]]

	Note that necessity goods and luxury goods are defined in terms of their [[income elasticity of demand]]; however, the general principle remains that higher magnitudes of price elasticity of demand correlate with higher magnitudes of income elasticity of demand.		Note that necessity goods and luxury goods are defined in terms of their [[income elasticity of demand]]; however, the general principle remains that higher magnitudes of price elasticity of demand correlate with higher magnitudes of income elasticity of demand.
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	===Substitution effect and impact on price elasticity===		===Substitution effect and impact on price elasticity===

	[[File:Demandcurvewithinflection.png\|thumb\|~~500px~~\|left\|This [[demand curve]] has a very high price elasticity around a price level of 3 units; the price elasticity becomes less at higher as well as lower prices.]]		[[File:Demandcurvewithinflection.png\|thumb\|250px\|left\|This [[demand curve]] has a very high price elasticity around a price level of 3 units; the price elasticity becomes less at higher as well as lower prices.]]

	The presence of close substitutes has the following implication: at prices close to the market prices of close substitutes, the price elasticity of demand is very high. At prices much higher than the market prices of close substitutes, demand is uniformly low so the price elasticity of demand is relatively low. At prices much lower than the market prices of close substitutes, demand is high, and the price elasticity of demand is again relatively low.		The presence of close substitutes has the following implication: at prices close to the market prices of close substitutes, the price elasticity of demand is very high. At prices much higher than the market prices of close substitutes, demand is uniformly low so the price elasticity of demand is relatively low. At prices much lower than the market prices of close substitutes, demand is high, and the price elasticity of demand is again relatively low.


	==Effect of price elasticity of ~~demand~~==		==Effect of price elasticity on other things==

			===Effect on sensitivity of price to supply shifts===

			The higher the price elasticity of demand, the lower the sensitivity of [[market price]] to shifts of the supply curve.

			Thus, for [[necessity good]]s (such as staple foods and, in the case of petroleum-dependent societies, petroleum products), which have a low price elasticity of demand, the market price is much more sensitive to shifts in supply. In particular, a small [[supply shock]] can cause a significant increase in price. The main explanation for this massive shift is that, because of the relative inelasticity of demand to price, the price needs to be increased significantly to induce people to cut down on demand in order to compensate for the reduction in supply.

			In contrast, for non-essential goods, which generally have a high price elasticity of demand, supply shifts do not generally lead to significant price changes, because small (fractional) changes in price are sufficient to induce buyers to cut back on demand.