北京大学：《微观经济学》Chapter Fourteen Consumer's Surplus 消费者剩余

Chapter Fourteen Consumer's Surplus 消费者剩余

Chapter Fourteen Consumer’s Surplus 消费者剩余

Structure Money equivalent of utility gains to trade ◆ Consumers surp|Us Changes in consumer's surplus 4 Compensating and equivalent variations ◆ Producer' s surplus

Structure ◆Money equivalent of utility gains to trade ◆Consumer’s surplus ◆Changes in consumer’s surplus ◆Compensating and equivalent variations ◆Producer’s surplus

Monetary measures of Gains-to T rade You can buy as much gasoline as you wish at $1 per gallon once you enter the gasoline market Q: What is the most you would pay to enter the market? A: You would pay up to the dollar value of the gains-to-trade you would enjoy once in the market

Monetary Measures of Gains-to￾Trade ◆You can buy as much gasoline as you wish at $1 per gallon once you enter the gasoline market. ◆Q: What is the most you would pay to enter the market? ◆A: You would pay up to the dollar value of the gains-to-trade you would enjoy once in the market

Monetary Measures of Gains-to Trade e How can such gains-to-trade be measured? e Three such measures are: Consumer's Surplus Equivalent variation(等价变换),and Compensating Variation(补偿变换) Only in one special circumstance do these three measures coincide

◆ How can such gains-to-trade be measured? ◆ Three such measures are: • Consumer’s Surplus • Equivalent Variation （等价变换）, and • Compensating Variation （补偿变换）. ◆ Only in one special circumstance do these three measures coincide. Monetary Measures of Gains-to￾Trade

Reservation price o Maximum willingness to pay for an additional unit of a good Two goods: good 1(X, and expenditure on others(x2 ;p2=1 By budget constraint (p,X,+x2=m): Ifx,=0, then x m If X,=1, then x,=m-p If X1=2, then x2 =m-2p1 If X,3, then x2=m-3p

Reservation Price ◆Maximum willingness to pay for an additional unit of a good ◆Two goods: good 1 (x1 ) and expenditure on others (x2 ); p2=1 ◆By budget constraint (p1x1+x2=m): If x1=0, then x2=m If x1=1, then x2=m-p1 If x1=2, then x2=m-2p1 If x1=3, then x2=m-3p1

Reservation price 4 Reservation price for the 1st unit (1) u(0,m)=u(1,mr1) G, is the dollar equivalent of the marginal utility of the 1st unit Reservation price for the 2nd unit (r2) u(1,m2)=u(2,m2r2) r2 is the dollar equivalent of the marginal utility of the 2nd unit Reservation price for the 3rd unit (r3) u(2,m-2r3)=u(2,m-3r)

Reservation Price ◆Reservation price for the 1st unit (r1 ) u(0, m) = u(1, m-r1 ) • r1 is the dollar equivalent of the marginal utility of the 1st unit. ◆Reservation price for the 2nd unit (r2 ) u(1, m-r2 ) = u(2, m-2r2 ) • r2 is the dollar equivalent of the marginal utility of the 2nd unit. ◆Reservation price for the 3rd unit (r3 ) u(2, m-2r3 ) = u(2, m-3r3 )

S Equivalent Utility gains Generally, if she already has n-1 gallons of gasoline then rn denotes the most she will pay for an nth gallon. is the dollar equivalent of the marginal utility of the nth gallon

◆Generally, if she already has n-1 gallons of gasoline then rn denotes the most she will pay for an nth gallon. • rn is the dollar equivalent of the marginal utility of the nth gallon. $ Equivalent Utility Gains

S Equivalent Utility gains ◆r1+…+ r will be the dollar equivalent of the total change to utility from consuming n gallons of gasoline at a price of $o

◆r1 + … + rn will be the dollar equivalent of the total change to utility from consuming n gallons of gasoline at a price of $0. $ Equivalent Utility Gains

S Equivalent Utility gains (s)Res Reservation Price Curve for gasoline Values 5 6 23456 Gasoline(gallons)

$ Equivalent Utility Gains Reservation Price Curve for Gasoline 0 2 4 6 8 10 Gasoline (gallons) ($) Res. Values 1 2 3 4 5 6 r1 r2 r3 r4 r5 r6

S Equivalent Utility gains What is the monetary value of our consumer's gain-to-trading in the gasoline market at a price of SpG?

◆What is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $pG? $ Equivalent Utility Gains