《微观经济学》清华大学Tsinghua Micro Ch14

1、Chapter Fourteen,Consumers Surplus,Monetary Measures of Gains-to-Trade,You can buy as much rice as you wish at RMB1 per kilogram 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 on

2、ce in the market. How can such gains-to-trade be measured?,Monetary Measures of Gains-to-Trade,Three such measures are: Consumers Surplus Equivalent Variation, and Compensating Variation. Only in one special circumstance do these three measures coincide.,Monetary Measures of Gains-to-Trade,Suppose r

3、ice can be bought only in lumps of one kilogram. Use r1 to denote the most a single consumer would pay for a 1st kilogram - call this her reservation price for the 1st kilogram. r1 is the dollar equivalent of the marginal utility of the 1st kilogram.,$ Equivalent Utility Gains,Now that she has one k

4、ilogram, use r2 to denote the most she would pay for a 2nd kilogram - this is her reservation price for the 2nd kilogram. r2 is the dollar equivalent of the marginal utility of the 2nd gallon.,$ Equivalent Utility Gains,Generally, if she already has n-1 kilograms of rice then rn denotes the most she

5、 will pay for an nth kilogram. rn is the dollar equivalent of the marginal utility of the nth kilogram.,$ Equivalent Utility Gains,r1 + + rn will therefore be the dollar equivalent of the total change to utility from acquiring n kilograms of rice at a price of $0. So r1 + + rn - pGn will be the doll

6、ar equivalent of the total change to utility from acquiring n kilograms of rice at a price of $pG each.,$ Equivalent Utility Gains,A plot of r1, r2, , rn, against n is a reservation-price curve. This is not quite the same as the consumers demand curve for rice.,$ Equivalent Utility Gains,$ Equivalen

7、t Utility Gains,1,2,3,4,5,6,r1,r2,r3,r4,r5,r6,What is the monetary value of our consumers gain-to-trading in the rice market at a price of $pG?,$ Equivalent Utility Gains,The dollar equivalent net utility gain for the 1st kilogram is $(r1 - pG) and is $(r2 - pG) for the 2nd kilogram, and so on, so t

8、he dollar value of the gain-to-trade is $(r1 - pG) + $(r2 - pG) + for as long as rn - pG 0.,$ Equivalent Utility Gains,$ Equivalent Utility Gains,1,2,3,4,5,6,r1,r2,r3,r4,r5,r6,pG,$ Equivalent Utility Gains,1,2,3,4,5,6,r1,r2,r3,r4,r5,r6,pG,$ value of net utility gains-to-trade,Suppose rice can be pur

9、chased in any continuous quantity then .,$ Equivalent Utility Gains,$ Equivalent Utility Gains,Rice,Res. Prices,pG,Reservation Price Curve for Rice,$ value of net utility gains-to-trade,Unfortunately, estimating a consumers reservation-price curve is difficult, so, as an approximation, the reservati

10、on-price curve is replaced with the consumers ordinary demand curve.,$ Equivalent Utility Gains,A 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 o

11、rdinary demand curve describes the most that would be paid for q units of a commodity purchased simultaneously.,Consumers Surplus,Approximating the net utility gain area under the reservation-price curve by the corresponding area under the ordinary demand curve gives the Consumers Surplus measure of

12、 net utility gain.,Consumers Surplus,Consumers Surplus,Gasoline,($),Reservation price curve for gasoline,Ordinary demand curve for gasoline,Consumers Surplus,rice,Reservation price curve for rice,Ordinary demand curve for rice,pG,The difference between the consumers reservation-price and ordinary de

13、mand curves is due to income effects. But, if the consumers utility function is quasilinear in income then there are no income effects and Consumers Surplus is an exact measure of gains-to-trade.,Consumers Surplus,Consumers Surplus,The consumers utility function is quasilinear in x2.,Take p2 = 1. Th

14、en the consumers choice problem is to maximize,subject to,Consumers Surplus,That is, choose x1 to maximize,The first-order condition is,That is,This is the equation of the consumers ordinary demand for commodity 1.,Consumers Surplus,Ordinary demand curve,p1,CS,is exactly the consumers utility gain f

15、rom consuming x1 units of commodity 1.,Consumers Surplus is an exact dollar measure of utility gained from consuming commodity 1 when the consumers utility function is quasilinear in commodity 2. Otherwise Consumers Surplus is an approximation.,Consumers Surplus,The change to a consumers total utili

16、ty due to a change to p1 is approximately the change in her Consumers Surplus.,Consumers Surplus,Consumers Surplus,p1,p1(x1), the inverse ordinary demand curve for commodity 1,Consumers Surplus,p1,CS before,p1(x1),Consumers Surplus,p1,CS after,p1(x1),Consumers Surplus,p1,Lost CS,p1(x1), inverse ordi

17、nary demand curve for commodity 1.,Consumers Surplus,p1,Lost CS,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 Variatio

18、n.,Compensating Variation and Equivalent Variation,p1 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 Variation,Compensating Variation,x2,x1,u1,p1=p1,p2 is fixed.,Compensating Variation,

19、x2,x1,u1,u2,p1=p1 p1=p1”,p2 is fixed.,Compensating Variation,x2,x1,u1,u2,p1=p1 p1=p1”,p2 is fixed.,Compensating Variation,x2,x1,u1,u2,p1=p1 p1=p1”,p2 is fixed.,CV = m2 - m1.,p1 rises. Q: What is the least extra income that, at the original prices, just restores the consumers original utility level?

20、A: The Equivalent Variation.,Equivalent Variation,Equivalent Variation,x2,x1,u1,p1=p1,p2 is fixed.,Equivalent Variation,x2,x1,u1,u2,p1=p1 p1=p1”,p2 is fixed.,Equivalent Variation,x2,x1,u1,u2,p1=p1 p1=p1”,p2 is fixed.,EV = m1 - m2.,Relationship 1: When the consumers preferences are quasilinear, all t

21、hree measures are the same.,Consumers Surplus, Compensating Variation and Equivalent Variation,Consider first the change in Consumers Surplus when p1 rises from p1 to p1”.,Consumers Surplus, Compensating Variation and Equivalent Variation,Consumers Surplus, Compensating Variation and Equivalent Vari

22、ation,If,then,and so the change in CS when p1 rises from p1 to p1” is,Now consider the change in CV when p1 rises from p1 to p1”. The consumers utility for given p1 is and CV is the extra income which, at the new prices, makes the consumers utility the same as at the old prices. That is, .,Consumers

23、 Surplus, Compensating Variation and Equivalent Variation,Consumers Surplus, Compensating Variation and Equivalent Variation,So,Now consider the change in EV when p1 rises from p1 to p1”. The consumers utility for given p1 is and EV is the extra income which, at the old prices, makes the consumers utility the same as at the new prices. That is, .,Consumers Surplus, Compensating Variation and Equivalent Variation,Consumers Surplus, Compensating Variation and Equivalent Variation,That is,Consumers Surp