中级微观经济学英文版课件：第14章 消费者剩余

1、Chapter FourteenConsumers Surplus消费者剩余StructureMoney equivalent of utility gains to tradeConsumers surplusChanges in consumers surplusCompensating and equivalent variationsProducers surplusMonetary Measures of Gains-to-TradeYou can buy as much gasoline as you wish at $1 per gallon once you enter the

2、 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.How can such gains-to-trade be measured?Three such measures are:Consumers SurplusEquivalent Variation （等价变换）, andCompensating Varia

3、tion （补偿变换）.Only in one special circumstance do these three measures coincide.Monetary Measures of Gains-to-TradeUse r1 to denote the most a consumer would pay for a 1st gallon - reservation price （保留价格）for the 1st gallon.r1 is the dollar equivalent of the marginal utility of the 1st gallon.use r2 t

4、o denote the most she would pay for a 2nd gallon - this is her reservation price for the 2nd gallon.r2 is the dollar equivalent of the marginal utility of the 2nd gallon.$ Equivalent Utility GainsGenerally, if she already has n-1 gallons of gasoline then rn denotes the most she will pay for an nth g

5、allon.rn is the dollar equivalent of the marginal utility of the nth gallon.$ Equivalent Utility Gainsr1 + + rn will be the dollar equivalent of the total change to utility from consuming n gallons of gasoline at a price of $0.So r1 + + rn - pGn will be the dollar equivalent of the total change to u

6、tility from consuming n gallons of gasoline at a price of $pG each.$ Equivalent Utility Gains$ Equivalent Utility Gains123456r1r2r3r4r5r6What is the monetary value of our consumers gain-to-trading in the gasoline market at a price of $pG?$ Equivalent Utility GainsThe dollar equivalent net utility ga

7、in for the 1st gallon is $(r1 - pG)and is $(r2 - pG) for the 2nd gallon, and so on, so the dollar value of the gain-to-trade is$(r1 - pG) + $(r2 - pG) + for as long as rn - pG 0.$ Equivalent Utility Gains$ Equivalent Utility Gains123456r1r2r3r4r5r6pG$ Equivalent Utility Gains123456r1r2r3r4r5r6pG$ Eq

8、uivalent Utility Gains123456r1r2r3r4r5r6pG$ value of net utility gains-to-trade If gasoline can be purchased in any quantity then .$ Equivalent Utility Gains$ Equivalent Utility GainsGasoline($) Res.PricesReservation Price Curve for Gasoline$ Equivalent Utility GainsGasoline($) Res.PricespGReservati

9、on Price Curve for Gasoline$ Equivalent Utility GainsGasoline($) Res.PricespGReservation Price Curve for Gasoline$ value of net utility gains-to-tradeQuasi-Linear Utility ExampleU(x, y) = v(x) + yReservation prices for the first 3 units:r1= v(1) - v(0)r2= v(2) - v(1)r3= v(3) - v(2)r1+r2+r3=v(3)-v(0)

10、=v(3)This is the gross benefit （毛收益）of consuming 3 units of good x.Quasi-Linear Utility123456r1r2r3r4r5r6Quasi-Linear UtilityWhen x=3, y=m-3p, U(3, m-3p)= v(3) + m-3pIf consume 0 good x, then y=m U(0, m) = mThe net benefit of consuming x (gains-to-trade) U(3, m-3p) U(0, m) = v(3) - 3pIf n units of x

11、 then utility gain is v(n) pnThis is the net benefit （净收益）.Quasi-Linear Utility123456r1r2r3r4r5r6pUnfortunately, estimating a consumers reservation-price curve is difficult,so, as an approximation, we use the consumers ordinary demand curve.This approximation gives the Consumers Surplus measure of n

12、et utility gain.$ Equivalent Utility GainsA consumers reservation-price curve is not quite the same as her ordinary demand curve. Why not?A reservation-price curve describes sequentially the values of successive single units of a commodity.An ordinary demand curve describes the most that would be pa

13、id for q units of a commodity purchased simultaneously.Consumers SurplusBut, if the consumers utility function is quasilinear in income then Consumers Surplus is an exact $ measure of gains-to-trade. If income effects are small, then the approximation is good.Consumers SurplusConsumers SurplusThe co

14、nsumers utility function isquasilinear in x2.Take p2 = 1. Then the consumerschoice problem is to maximizesubject toConsumers SurplusThe consumers utility function isquasilinear in x2.Take p2 = 1. Then the consumerschoice problem is to maximizesubject toConsumers SurplusThat is, choose x1 to maximize

15、The first-order condition is That is,This is the equation of the consumersordinary demand for commodity 1.Consumers SurplusOrdinary demand curve,p1CSConsumers SurplusOrdinary demand curve,p1CSConsumers SurplusOrdinary demand curve,p1CSConsumers SurplusOrdinary demand curve,p1CSis exactly the consume

16、rs utility gain from consuming x1 units of commodity 1.Interpreting Consumers SurplusNet benefit of consuming n units of the good: Utility minus expenditureCompensation needed to give up consuming the product.The change to a consumers total utility due to a change to p1 is approximately the change i

17、n her Consumers Surplus. Change in Consumers SurplusConsumers Surplusp1p1(x1), the inverse ordinary demand curve for commodity 1Consumers Surplusp1CS beforep1(x1)Consumers Surplusp1CS afterp1(x1)Consumers Surplusp1Lost CSp1(x1), inverse ordinary demand curve for commodity 1.Consumers Surplusp1LostCS

18、x1*(p1), the consumers ordinary demand curve for commodity 1.measures the loss in Consumers 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 Variationp1 rises.Q: What

19、is the least extra income that, at the new prices, just restores the consumers original utility level?Compensating Variationp1 rises.Q: What is the least extra income that, at the new prices, just restores the consumers original utility level?A: The Compensating Variation.Compensating VariationCompe

20、nsating Variationx2x1u1p1=p1p2 is fixed.Compensating Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.Compensating Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.Compensating Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.CV = m2 - m1.p1 rises.Q: What is the least extra income that, at the original prices, just restores t

21、he consumers original utility level?A: The Equivalent Variation.Equivalent VariationEquivalent Variationx2x1u1p1=p1p2 is fixed.Equivalent Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.Equivalent Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.Equivalent Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.EV = m1 - m2.Consumers Surplus, Compensating Variation and Equivalen