Cross-price elasticity of demand - Revision history

Vipul: /* Properties */

2010-08-14T23:56:26Z

Properties

← Older revision		Revision as of 23:56, 14 August 2010
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	! Effect !! Condition on relationship between goods !! Explanation of effect !! How it affects cross-price elasticity of demand		! Effect !! Condition on relationship between goods !! Explanation of effect !! How it affects cross-price elasticity of demand
	\|-		\|-
	\| [[income effect]] \|\| none \|\| A finite income imposes a [[budget constraint]]. An increase in the price of <math>B</math> changes the quantity consumed and hence the total money spent on <math>B</math>. This in turn changes the effective available income for other purposes, including the consumption of <math>A</math>. \|\| This depends on the (own)-[[price elasticity of demand]] of <math>B</math>. If its magnitude is greater than <math>1</math> ~~(the [[luxury good]] case)~~ the total money spent on <math>B</math> ''declines'' with an increase in price, leaving more money free for consuming <math>A</math> -- thus it tends to make the cross-price elasticity of demand more positive. If the magnitude of own-price elasticity of demand of <math>B</math> is less than <math>1</math> ~~(the [[essential good]] case)~~ the total money spent on <math>B</math> increases as price increases, leaving less money for <math>A</math>, thus it tends to make the cross-price elasticity of demand more negative.		\| [[income effect]] \|\| none \|\| A finite income imposes a [[budget constraint]]. An increase in the price of <math>B</math> changes the quantity consumed and hence the total money spent on <math>B</math>. This in turn changes the effective available income for other purposes, including the consumption of <math>A</math>. \|\| This depends on the (own)-[[price elasticity of demand]] of <math>B</math>. If its magnitude is greater than <math>1</math>, the total money spent on <math>B</math> ''declines'' with an increase in price, leaving more money free for consuming <math>A</math> -- thus it tends to make the cross-price elasticity of demand more positive. If the magnitude of own-price elasticity of demand of <math>B</math> is less than <math>1</math>, the total money spent on <math>B</math> increases as price increases, leaving less money for <math>A</math>, thus it tends to make the cross-price elasticity of demand more negative.
	\|-		\|-
	\| [[substitution effect]] \|\| <math>A</math> and <math>B</math> are [[substitute goods]]: they substitute (partially or wholly) for each other -- i.e., having more of <math>A</math> reduces the marginal utility of obtaining <math>B</math>, and vice versa \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more positive, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> increase in utility of consuming <math>A</math> <math>\to</math> increase in quantity of <math>A</math> demanded at a given price		\| [[substitution effect]] \|\| <math>A</math> and <math>B</math> are [[substitute goods]]: they substitute (partially or wholly) for each other -- i.e., having more of <math>A</math> reduces the marginal utility of obtaining <math>B</math>, and vice versa \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more positive, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> increase in utility of consuming <math>A</math> <math>\to</math> increase in quantity of <math>A</math> demanded at a given price
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	! Is the magnitude of own-price elasticity of demand of <math>B</math> greater than or less than <math>1</math>? !! Do <math>A</math> and <math>B</math> complement or substitute for each other? !! Conclusion about sign of cross-price elasticity		! Is the magnitude of own-price elasticity of demand of <math>B</math> greater than or less than <math>1</math>? !! Do <math>A</math> and <math>B</math> complement or substitute for each other? !! Conclusion about sign of cross-price elasticity
	\|-		\|-
	\| less than <math>1</math> ~~([[essential good]])~~ \|\| complement \|\| negative		\| less than <math>1</math>\|\| complement \|\| negative
	\|-		\|-
	\| less than <math>1</math> ~~([[essential good]])~~ \|\| substitute \|\| ambiguous but typically positive; positive if [[substitution effect]] dominates, which would be the case for close substitutes.		\| less than <math>1</math>\|\| substitute \|\| ambiguous but typically positive; positive if [[substitution effect]] dominates, which would be the case for close substitutes.
	\|-		\|-
	\| greater than <math>1</math> ~~([[luxury good]])~~ \|\| complement \|\| ambiguous; sign depends on whether the complementary effect or income effect is stronger.		\| greater than <math>1</math>\|\| complement \|\| ambiguous; sign depends on whether the complementary effect or income effect is stronger.
	\|-		\|-
	\| greater than <math>1</math> ~~([[luxury good]])~~ \|\| substitute \|\| positive		\| greater than <math>1</math>\|\| substitute \|\| positive
	\|}		\|}

Vipul: /* Properties */

2010-08-14T23:52:17Z

Properties

← Older revision		Revision as of 23:52, 14 August 2010
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	==Properties==		==Properties==

			For the entire discussion, we assume that both <math>A</math> and <math>B</math> are [[ordinary good]]s (quantity demanded decreases with increase in price) and [[normal good]]s (quantity demanded increases with increase in disposable income). In the absence of these assumptions, more interesting and complicated variations of the possibilities below can occur.

	===Factors affecting cross-price elasticity of demand===		===Factors affecting cross-price elasticity of demand===
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	! Effect !! Condition on relationship between goods !! Explanation of effect !! How it affects cross-price elasticity of demand		! Effect !! Condition on relationship between goods !! Explanation of effect !! How it affects cross-price elasticity of demand
	\|-		\|-
	\| [[income effect]] \|\| none \|\| A finite income imposes a [[budget constraint]]. An increase in the price of <math>B</math> changes the quantity consumed and hence the total money spent on <math>B</math>. This in turn changes the effective available income for other purposes, including the consumption of <math>A</math>. \|\| This depends on the (own)-[[price elasticity of demand]] of <math>B</math>. If ~~this~~ is greater than <math>1</math> (the [[luxury good]] case) the total money spent on <math>B</math> ''declines'' with an increase in price, leaving more money free for consuming <math>A</math> -- thus it tends to make the cross-price elasticity of demand more positive. If the own-price elasticity of demand of <math>B</math> is less than <math>1</math> (the [[essential good]] case) the total money spent on <math>B</math> increases as price increases, leaving less money for <math>A</math>, thus it tends to make the cross-price elasticity of demand more negative.		\| [[income effect]] \|\| none \|\| A finite income imposes a [[budget constraint]]. An increase in the price of <math>B</math> changes the quantity consumed and hence the total money spent on <math>B</math>. This in turn changes the effective available income for other purposes, including the consumption of <math>A</math>. \|\| This depends on the (own)-[[price elasticity of demand]] of <math>B</math>. If its magnitude is greater than <math>1</math> (the [[luxury good]] case) the total money spent on <math>B</math> ''declines'' with an increase in price, leaving more money free for consuming <math>A</math> -- thus it tends to make the cross-price elasticity of demand more positive. If the magnitude of own-price elasticity of demand of <math>B</math> is less than <math>1</math> (the [[essential good]] case) the total money spent on <math>B</math> increases as price increases, leaving less money for <math>A</math>, thus it tends to make the cross-price elasticity of demand more negative.
	\|-		\|-
	\| [[substitution effect]] \|\| <math>A</math> and <math>B</math> are [[substitute goods]]: they substitute (partially or wholly) for each other -- i.e., having more of <math>A</math> reduces the marginal utility of obtaining <math>B</math>, and vice versa \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more positive, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> increase in utility of consuming <math>A</math> <math>\to</math> increase in quantity of <math>A</math> demanded at a given price		\| [[substitution effect]] \|\| <math>A</math> and <math>B</math> are [[substitute goods]]: they substitute (partially or wholly) for each other -- i.e., having more of <math>A</math> reduces the marginal utility of obtaining <math>B</math>, and vice versa \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more positive, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> increase in utility of consuming <math>A</math> <math>\to</math> increase in quantity of <math>A</math> demanded at a given price
	\|-		\|-
	\| complementary effects \|\| <math>A</math> and <math>B</math> are [[complementary goods]]: having more of <math>A</math> increases the marginal utility of <math>B</math> and vice versa. \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more negative, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> decrease in utility of consuming <math>A</math> <math>\to</math> decrease in quantity of <math>A</math> demanded at a given price		\| complementary effects \|\| <math>A</math> and <math>B</math> are [[complementary goods]]: having more of <math>A</math> increases the marginal utility of <math>B</math> and vice versa. \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more negative, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> decrease in utility of consuming <math>A</math> <math>\to</math> decrease in quantity of <math>A</math> demanded at a given price
			\|}

			===Sign===

			The sign of the cross-price elasticity of demand depends on the relative extent of operation of the various factors that influence the cross-price elasticity of demand noted above. In some cases, the sign is unambiguous, while in others, it is ambiguous.

			{\| class="sortable" border="1"
			! Is the magnitude of own-price elasticity of demand of <math>B</math> greater than or less than <math>1</math>? !! Do <math>A</math> and <math>B</math> complement or substitute for each other? !! Conclusion about sign of cross-price elasticity
			\|-
			\| less than <math>1</math> ([[essential good]]) \|\| complement \|\| negative
			\|-
			\| less than <math>1</math> ([[essential good]]) \|\| substitute \|\| ambiguous but typically positive; positive if [[substitution effect]] dominates, which would be the case for close substitutes.
			\|-
			\| greater than <math>1</math> ([[luxury good]]) \|\| complement \|\| ambiguous; sign depends on whether the complementary effect or income effect is stronger.
			\|-
			\| greater than <math>1</math> ([[luxury good]]) \|\| substitute \|\| positive
	\|}		\|}

Vipul at 23:43, 14 August 2010

2010-08-14T23:43:22Z

← Older revision		Revision as of 23:43, 14 August 2010
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	Note that although only <math>q_A</math> and <math>p_B</math> appear in the expression for cross-price elasticity, the value <math>p_A</math> could also affect the value of cross-price elasticity. More specifically, the formula makes sense against a backdrop of the value of <math>p_A</math> and all the other [[determinants of demand]].		Note that although only <math>q_A</math> and <math>p_B</math> appear in the expression for cross-price elasticity, the value <math>p_A</math> could also affect the value of cross-price elasticity. More specifically, the formula makes sense against a backdrop of the value of <math>p_A</math> and all the other [[determinants of demand]].

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

			The cross-price elasticity of demand cannot be computed by looking at any single instance of the usual [[demand curve]] or [[logarithmic demand curve]] for either <math>A</math> or <math>B</math>. Rather, it measures the ''speed of expansion/contraction'' of the demand curve for <math>A</math> with respect to a price change in <math>B</math>.

			The price of <math>B</math> is possibly one of the [[determinants of demand]] for the quantity demanded of <math>A</math>. The price of <math>B</math> is thus one of the [[exogenous parameter]]s to the demand curve of <math>A</math>. A change in this parameter leads to a shift (expansion or contraction) in the demand curve for <math>A</math> and the magnitude of this shift at the price level <math>p_A</math> is what the cross-price elasticity measures.

			==Properties==

			===Factors affecting cross-price elasticity of demand===

			There are three kinds of factors affecting cross-price elasticity of demand. As above, <math>B</math> is the good whose price is changed and we measure the effect of this change on the quantity of <math>A</math> demanded.

			{\| class="sortable" border="1"
			! Effect !! Condition on relationship between goods !! Explanation of effect !! How it affects cross-price elasticity of demand
			\|-
			\| [[income effect]] \|\| none \|\| A finite income imposes a [[budget constraint]]. An increase in the price of <math>B</math> changes the quantity consumed and hence the total money spent on <math>B</math>. This in turn changes the effective available income for other purposes, including the consumption of <math>A</math>. \|\| This depends on the (own)-[[price elasticity of demand]] of <math>B</math>. If this is greater than <math>1</math> (the [[luxury good]] case) the total money spent on <math>B</math> ''declines'' with an increase in price, leaving more money free for consuming <math>A</math> -- thus it tends to make the cross-price elasticity of demand more positive. If the own-price elasticity of demand of <math>B</math> is less than <math>1</math> (the [[essential good]] case) the total money spent on <math>B</math> increases as price increases, leaving less money for <math>A</math>, thus it tends to make the cross-price elasticity of demand more negative.
			\|-
			\| [[substitution effect]] \|\| <math>A</math> and <math>B</math> are [[substitute goods]]: they substitute (partially or wholly) for each other -- i.e., having more of <math>A</math> reduces the marginal utility of obtaining <math>B</math>, and vice versa \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more positive, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> increase in utility of consuming <math>A</math> <math>\to</math> increase in quantity of <math>A</math> demanded at a given price
			\|-
			\| complementary effects \|\| <math>A</math> and <math>B</math> are [[complementary goods]]: having more of <math>A</math> increases the marginal utility of <math>B</math> and vice versa. \|\| A change in the price of <math>B</math> affects the quantity of <math>B</math> demanded. By the [[law of demand]], the quantity demanded decreases with an increase in price. This in turn affects the utility function of <math>A</math>, and hence, the quantity demanded at a given price. \|\| This tends to make the cross-price elasticity of demand more negative, because increasing price of <math>B</math> <math>\to</math> lower quantity of <math>B</math> <math>\to</math> decrease in utility of consuming <math>A</math> <math>\to</math> decrease in quantity of <math>A</math> demanded at a given price
			\|}

Vipul: Created page with "==Definition== Suppose $A$ and $B$ are two commodities. The '''cross-price elasticity of demand''' of $A$ with respect to $B$ measure..."

2010-08-14T23:25:39Z

Created page with "==Definition== Suppose <math>A</math> and <math>B</math> are two commodities. The '''cross-price elasticity of demand''' of <math>A</math> with respect to <math>B</math> measure..."

New page

==Definition==

Suppose <math>A</math> and <math>B</math> are two commodities. The '''cross-price elasticity of demand''' of <math>A</math> with respect to <math>B</math> measures the fractional change in the demand of <math>A</math> in response to a fractional change in the unit price of <math>B</math>. Note that the price of <math>A</math> is not changed in the process.

Formally, if <math>p_A</math> and <math>p_B</math> denote the unit prices of <math>p_A</math> and <math>p_B</math> and <math>q_A</math> and <math>q_B</math> denote the quantities demanded for <math>A</math> and <math>B</math>, the cross-price elasticity is given by any of the following four equivalent formulations:

<math>\! \frac{p_B dq_A}{q_A dp_B} = \frac{dq_A/q_A}{dp_B/p_B} = \frac{dq_A/dp_B}{q_A/p_B} = \frac{d(\log (q_A))}{d(\log (p_B))}</math>

Note that although only <math>q_A</math> and <math>p_B</math> appear in the expression for cross-price elasticity, the value <math>p_A</math> could also affect the value of cross-price elasticity. More specifically, the formula makes sense against a backdrop of the value of <math>p_A</math> and all the other [[determinants of demand]].

Cross-price elasticity of demand - Revision history

Vipul: /* Properties */

Vipul: /* Properties */

Vipul at 23:43, 14 August 2010

Vipul: Created page with "==Definition== Suppose A and B are two commodities. The '''cross-price elasticity of demand''' of A with respect to B measure..."

Vipul: Created page with "==Definition== Suppose $A$ and $B$ are two commodities. The '''cross-price elasticity of demand''' of $A$ with respect to $B$ measure..."