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 ◆Consumer's surplus Changes in consumer's surplus 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- 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-toTrade ◆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 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
◆ 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-toTrade
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 (px+x2=m): If x=0,then x2=m If x,=1,then x2=m-p1 If x =2,then x2=m-2p1 If x =3,then x2=m-3p1
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 Reservation price for the 1st unit (r) u(0,m)=u(1,m-r) r 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) r>is the dollar equivalent of the marginal utility of the 2nd unit. Reservation price for the 3rd unit (r) u(2,m-2r3)=u(2,m-3r3)
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 )
Equivalent Utility Gains Generally,if she already has n-1 gallons of gasoline then r denotes the most she will pay for an nth gallon. rn 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
Equivalent Utility Gains r+...r will be the dollar equivalent of the total change to utility from consuming n gallons of gasoline at a price of $0
◆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
Equivalent Utility Gains ($Res. Reservation Price Curve for Gasoline Values r 234 3 4 5 6 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
Equivalent Utility Gains What is the monetary value of our consumer's gain-to-trading in the gasoline market at a price of $pe?
◆What is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $pG? $ Equivalent Utility Gains