【正文】 curve for gasoline 2021/11/11 32 Intermediate Micro: Consumer Surplus Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG ($) 2021/11/11 33 Intermediate Micro: Consumer Surplus Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG $ value of utility gainstotrade ($) 2021/11/11 34 Intermediate Micro: Consumer Surplus Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG $ value of utility gainstotrade Consumer’s Surplus ($) 2021/11/11 35 Intermediate Micro: Consumer Surplus Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG $ value of utility gainstotrade Consumer’s Surplus ($) 2021/11/11 36 Intermediate Micro: Consumer Surplus ? The difference between the consumer’s reservationprice and ordinary demand curves is due to ine effects. ? But, if the consumer’s utility function is quasilinear in ine then there are no ine effects and Consumer’s Surplus is an exact $ measure of gainstotrade. Consumer’s Surplus 2021/11/11 37 Intermediate Micro: Consumer Surplus Consumer’s Surplus U x x v x x( , ) ( )1 2 1 2? ?The consumer’s utility function is quasilinear in x2. Take p2 = 1. Then the consumer’s choice problem is to maximize U x x v x x( , ) ( )1 2 1 2? ?subject to p x x m1 1 2? ? .2021/11/11 38 Intermediate Micro: Consumer Surplus Consumer’s Surplus U x x v x x( , ) ( )1 2 1 2? ?The consumer’s utility function is quasilinear in x2. Take p2 = 1. Then the consumer’s choice problem is to maximize U x x v x x( , ) ( )1 2 1 2? ?subject to p x x m1 1 2? ? .2021/11/11 39 Intermediate Micro: Consumer Surplus Consumer’s Surplus That is, choose x1 to maximize v x m p x( ) .1 1 1? ?The firstorder condition is v x p39。 ( )x1*x139。CS CS v x dx p xx? ?? 39。 1 1 1 10 1p139。 ( ) 39。 39。 ( )x1*x139。 39。 39。CS before p1(x1) p139。x1Lost CS p1(x1), inverse ordinary demand curve for modity 1. p1p139。measures the loss in Consumer’s Surplus. 2021/11/11 51 Intermediate Micro: Consumer Surplus ? Two additional dollar measures of the total utility change caused by a price change are Compensating Variation and Equivalent Variation. Compensating Variation and Equivalent Variation 2021/11/11 52 Intermediate Micro: Consumer Surplus ? p1 rises. ? Q: What is the least extra ine that, at the new prices, just restores the consumer’s original utility level? Compensating Variation 2021/11/11 53 Intermediate Micro: Consumer Surplus ? p1 rises. ? Q: What is the least extra ine that, at the new prices, just restores the consumer’s original utility level? ? A: The Compensating Variation. Compensating Variation 2021/11/11 54 Intermediate Micro: Consumer Surplus Compensating Variation x2 x1 x139。 39。 39。x239。 39。u1 u2 x1x2x239。 39。112 xpxpm ??CV = m2 m1. 2021/11/11 58 Intermediate Micro: Consumer Surplus ? p1 rises. ? Q: What is the least extra ine that, at the original prices, just restores the consumer’s original utility level? ? A: The Equivalent Variation. Equivalent Variation 2021/11/11 59 Intermediate Micro: Consumer Surplus Equivalent Variation x2 x1 x139。 39。 39。x239。 39。2021/11/11 62 Intermediate Micro: Consumer Surplus Equivalent Variation x2 x1 x139。p1=p1? p1=p1?? p2 is fixed. m p x p x1 1 1 2 2? ?39。 39。 39。 39。 39。 1 1? ?? ? ? ? ? ?v x v p x v x v p x( ) ( ) ( ) ( )39。 39。 1 1? ?? ? ? ? ? ?v x v p x v x v p x( ) ( ) ( ) ( )39。 39。 39。1 1 1? ?? ? ? ?v x m CV p x( ) . 1 1 1So CV v x v x p x p x? ? ? ?( ) ( ) ( )39。 39。 39。1 1 1? ?? ? ? ?v x m EV p x( ) . 1 1 12021/11/11 75 Intermediate Micro: Consumer Surplus Consumer’s Surplus, Compensating Variation and Equivalent Variation So when the consumer has quasilinear utility, CV = EV = ?CS. But, otherwise, we have: Relationship 2: In size, EV ?CS CV. 2021/11/11 76 Intermediate Micro: Consumer Surplus Compensating and Equivalent Variation ? this presentation takes you through the calculation of pensating and equivalent variation using the CobbDouglas utility function as an example. ? First we calculate the demands for x and y before and after the price change and then the two welfare measures 2021/11/11 77 Intermediate Micro: Consumer Surplus The demand functions when utility is CobbDouglas We know that for CobbDouglas Utility functions with U = xayb that the demand function are: xaa bMPDx??yba bMPDy??2021/11/11 78 Intermediate Micro: Consumer Surplus Suppose we assume that M = 100, p1=1 amp。y39。