lect06__CV_and_EV - Compensating and Equivalent Variation...

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62 Compensating and Equivalent Variation For any change in a consumer's budget constraint, we can determine a dollar measure of the value of this change. We call Compensating Variation the change in income necessary to just compensate a consumer for a change in their budget set (at the new prices). We call Equivalent Variation the change in income that would generate an equivalent change in utility as the change in the budget set (at the original prices). Example 1: I=$100, P 1 =$1, and P 2 =$1. Illustrate the compensating variation of an increase in P 1 to $2. If the P 1 increases from $1 to $2, utility falls from U 1 to U 0 . At the new prices if this consumer were given CV more dollars of income, utility would increase back to U 1 . Notice that this is just the income effect of the price change. X 2 X 1 U 1 U 0 CV 50 100
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63 Example 2: I=$200, P 1 =$2, and P 2 =$2. Illustrate the equivalent variation of an increase in P 2 to $4. If P 2 were to increase to $4, the consumer's utility would fall to U 0 . At the old prices the consumer would receive an equivalent loss in utility if he were to lose EV dollars of income. X 2 X 1 U 1 U 0 50 100 100 50 EV
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Example 3: A consumer with I=$100, P1=$2 and P2=$1 is given $80 in coupons that can only be used on good 1. After receiving these coupons, the consumer spends only the $80 in coupons on good 1, and in fact would like to trade coupons for money to spend on good 2, if that were allowed. Illustrate this consumer's optimal choice. Show the equivalent variation of the $80 of coupons. Coupons for X 1 allow the consumer to reach utility level U 2 . (Although the consumer would like to move up the dotted part of the budget line if possible by selling coupons in the black market). The consumer could also reach utility level U
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lect06__CV_and_EV - Compensating and Equivalent Variation...

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