北大微观经济学课件(英文版)ch14 Consumer’s Surplus.ppt

Chapter FourteenConsumer’s Surplus 消费者剩余*中级微观经济学StructureuMoney equivalent of utility gains to tradeuConsumer’s surplusuChanges in consumer’s surplusuCompensating and equivalent variationsuProducer’s surplusDate中级微观经济学Monetary Measures of Gains-to- TradeuYou can buy as much gasoline as you wish at $1 per gallon once you enter the gasoline market. uQ: What is the most you would pay to enter the market?uA: You would pay up to the dollar value of the gains-to-trade you would enjoy once in the market.Date中级微观经济学uHow can such gains-to-trade be measured?uThree such measures are: • Consumer’s Surplus • Equivalent Variation （等价变换）, and • Compensating Variation （补偿变换）.uOnly in one special circumstance do these three measures coincide.Monetary Measures of Gains-to- TradeDate中级微观经济学Reservation PriceuMaximum willingness to pay for an additional unit of a gooduTwo goods: good 1 (x1) and expenditure on others (x2); p2=1uBy budget constraint (p1x1+x2=m): If x1=0, then x2=m If x1=1, then x2=m-p1 If x1=2, then x2=m-2p1 If x1=3, then x2=m-3p1Date中级微观经济学Reservation PriceuReservation price for the 1st unit (r1) u(0, m) = u(1, m-r1)•r1 is the dollar equivalent of the marginal utility of the 1st unit.uReservation price for the 2nd unit (r2) u(1, m-r2) = u(2, m-2r2)•r2 is the dollar equivalent of the marginal utility of the 2nd unit.uReservation price for the 3rd unit (r3) u(2, m-2r3) = u(2, m-3r3) Date中级微观经济学uGenerally, if she already has n-1 gallons of gasoline then rn denotes the most she will pay for an nth gallon. • rn is the dollar equivalent of the marginal utility of the nth gallon.$ Equivalent Utility GainsDate中级微观经济学ur1 + … + 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 GainsDate中级微观经济学$ Equivalent Utility Gains123456r1 r2 r3 r4 r5 r6Date中级微观经济学uWhat is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $pG?$ Equivalent Utility GainsDate中级微观经济学uThe dollar equivalent net utility gain for the 1st gallon is $(r1 - pG)uand is $(r2 - pG) for the 2nd gallon, uand 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 GainsDate中级微观经济学uSo r1 + … + rn - pGn will be the dollar equivalent of the total change to utility from consuming n gallons of gasoline at a price of $pG each.$ Equivalent Utility GainsDate中级微观经济学$ Equivalent Utility Gains123456r1 r2 r3 r4 r5 r6pGDate中级微观经济学$ Equivalent Utility Gains123456r1 r2 r3 r4 r5 r6pGDate中级微观经济学$ Equivalent Utility Gains123456r1 r2 r3 r4 r5 r6pG$ value of net utility gains-to-tradeDate中级微观经济学uIf gasoline can be purchased in any quantity then ...$ Equivalent Utility GainsDate中级微观经济学$ Equivalent Utility GainsGasoline($) Res. PricesReservation Price Curve for GasolineDate中级微观经济学$ Equivalent Utility GainsGasoline($) Res. PricespGReservation Price Curve for GasolineDate中级微观经济学$ Equivalent Utility GainsGasoline($) Res. PricespGReservation Price Curve for Gasoline$ value of net utility gains-to-tradeDate中级微观经济学Quasi-Linear UtilityuU(x, y) = v(x) + yuReservation prices for the first 3 units: v(0)+m=v(1)+m- r1  r1= v(1) - v(0) v(1)+m- r2=v(2)+m- 2r2  r2= v(2) - v(1) v(2)+m- 2r3=v(3)+m- 3r3  r3= v(3) - v(2)ur1+r2+r3=v(3)-v(0)=v(3)uThis is the gross benefit （毛收益）of consuming 3 units of good x.Date中级微观经济学Quasi-Linear Utility123456r1 r2 r3 r4 r5 r6Date中级微观经济学Quasi-Linear UtilityuWhen x=3, y=m-3p, U(3, m-3p)= v(3) + m-3puIf consume 0 good x, then y=mU(0, m) = muThe net benefit of consuming x (gains-to- trade)U(3, m-3p) – U(0, m) = v(3) - 3puIf n units of x then utility gain isv(n) – pnuThis is the net benefit （净收益）.Date中级微观经济学Quasi-Linear Utility123456r1 r2 r3 r4 r5 r6pDate中级微观经济学uUnfortunately, estimating a consumer’s reservation-price curve is difficult,uso, as an approximation, we use the consumer’s ordinary demand curve.uThis approximation gives the Consumer’s Surplus measure of net utility gain.$ Equivalent Utility GainsDate中级微观经济学uA consumer’s reservation-price curve is not quite the same as her ordinary demand curve. Why not?uA reservation-price curve describes sequentially the values of successive single units of a commodity.uAn ordinary demand curve describes the most that would be paid for q units of a commodity purchased simultaneously.Consumer’s SurplusDate中级微观经济学uBut, if the consumer’s utility function is quasilinear in income then • The reservation price curve is exactly the demand curve • Consumer’s Surplus is an exact $ measure of gains-to-trade. uIf income effects are small, then the approximation is good.Consumer’s SurplusDate中级微观经济学Consumer’s SurplusThe consumer’s utility function is quasilinear in x2.Take p2 = 1. Then the consumer’s choice problem is to maximizesubject toDate中级微观经济学Consumer’s SurplusThe consumer’s utility function is quasilinear in x2.Take p2 = 1. Then the consumer’s choice problem is to maximizesubject t。