【正文】 100, p1=1 amp。 p2=1 then with U(x,y) = x1/2 y1/2, that is a=b=1/2 xaa bMPDx??yba bMPDy??? ?xD ??? ?1 21 2 1 2100112100150// /and s im ila r ly y D ? 502021/11/11 79 Intermediate Micro: Consumer Surplus So the initial demands for x and y with the price of x =1 ,price of y=1 and M= 100 are: xd = 50 and yD = 50 2021/11/11 80 Intermediate Micro: Consumer Surplus 50 50 x y The CobbDouglas Utility Function with M=100 and px=py=1 2021/11/11 81 Intermediate Micro: Consumer Surplus ? Suppose we increase the price of x, what will the demand for x and y be now? 2021/11/11 82 Intermediate Micro: Consumer Surplus xMPDx?12Using our CobbDouglas demand functions we can calculate the new demand for x (and y) If px rises to 2 then x = 25 and y = 50 yMPDy?122021/11/11 83 Intermediate Micro: Consumer Surplus Successive clicks of the mouse reveals the effect of increasing the price of x. x 50 50 y 25 2021/11/11 84 Intermediate Micro: Consumer Surplus Compensating Variation ? To calculate this we need to calculate the ine required to ensure that we can reach the original utility at the new set of prices. ? The original utility was U(50,50)=501/2 501/2 ? U(50,50)=()1/2 (50 2 )1/2 = 50 2021/11/11 85 Intermediate Micro: Consumer Surplus 50 50 y 25 CV { Next we need to find the ine that must be given back to a consumer to pensate him or her for the rise in prices. This is the pensating variation, and it can be seen by clicking on the mouse. 2021/11/11 86 Intermediate Micro: Consumer Surplus What level of Ine gives Utility =50 at the new prices? ? To find this out we can use the demand functions we have derived for x and y. ? Next we substitute these demands (using the new prices (2,1) directly into the utility function and set it equal to U0 U x y UMpMpx y( , ) ,????????? ?1212501 02021/11/11 87 Intermediate Micro: Consumer Surplus Applying the specific CobbDouglas utility function we get: ??????????????? ? ???????????? ?121212 212 15011 201 2 1 2 1 2MpMpM Mx y/ / / /??????? ??????? ??????? ?12 212 11818501 221 2 1 2M MM M/ / /2021/11/11 88 Intermediate Micro: Consumer Surplus Compensating Variation ??????? ??????? ??????? ?12 212 11818501 221 2 1 2M MM M/ / /M ? ?50 2 2 100 2( ) .? 1412021/11/11 89 Intermediate Micro: Consumer Surplus Equivalent Variation WE find this in a similar manner to pensating variation except that now we want to find the ine required to ensure that we are at the new level of utility but with the old set of prices. The new level of utility is: U(25,50) = 251/2501/2 25 25 2 5 5 2 25 2 35 35? ? ?. . . .2021/11/11 90 Intermediate Micro: Consumer Surplus 50 50 y 25 EV{ Clicking the mouse shows the amount of ine we need to take away from the consumer at the old set of prices to bring them to the new utility level. Uo= U1=50 2021/11/11 91 Intermediate Micro: Consumer Surplus Equivalent Variation Once again we find the Ine which will give us this Utility at the old prices. U x yM M( , ) ./ /? ??? ??? ??? ??? ?12 112 135 351 2 1 2????????????? ? ?12 112 135 351 2 2M M/.? ? ?M 2 35 35 70 7( . ) .2021/11/11 92 Intermediate Micro: Consumer Surplus Result ?Compensating Variation = 141 ?Equivalent Variation = ?and since price has risen CVEV as we saw in lectures 2021/11/11 93 Intermediate Micro: Consumer Surplus ? Changes in a firm’s welfare can be measured in dollars much as for a consumer. Producer’s Surplus 2021/11/11 94 Intermediate Micro: Consumer Surplus Producer’s Surplus y (output units) Output price (p) Marginal Cost 2021/11/11 95 Intermediate Micro: Consumer Surplus Producer’s Surplus y (output units) Output price (p) Marginal Cost p39。y39。2021/11/11 96 Intermediate Micro: Consumer Surplus Producer’s Surplus y (output units) Output price (p) Marginal Cost p39。y39。Revenue = py39。 39。2021/11/11 97 Intermediate Micro: Consumer Surplus Producer’s Surplus y (output units) Output price (p) Marginal Cost p39。y39。Variable Cost of producing y? units is the sum of the marginal costs 2021/11/11 98 Intermediate Micro: Consumer Surplus Producer’s Surplus y (output units) Output price (p) Marginal Cost p39。y39。Variable Cost of producing y? units is the sum of the marginal costs Revenue less VC is the Producer’s Surplus