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1、http:/ FourteenConsumers SurplusWhat Do We Do in This Chapter?u After studying consumers choices, we now examine consumers welfareuThe key question is: How much has a consumer gained in welfare from purchasing certain units of a good?uThree such measures are:lConsumers SurpluslEquivalent Variation,
2、andlCompensating Variation.uOnly in one special circumstance do these three measures coincide.Monetary Measures of Gains-to-TradeuSuppose rice can be bought only in lumps of one kilogram.uUse r1 to denote the most a single consumer would pay for a 1st kilogram - call this her reservation price for t
3、he 1st kilogram.ur1 is the dollar equivalent of the marginal utility of the 1st kilogram.Monetary Equivalent Utility GainsuNow that she has one kilogram, use r2 to denote the most she would pay for a 2nd kilogram - this is her reservation price for the 2nd kilogram.ur2 is the dollar equivalent of th
4、e marginal utility of the 2nd gallon.Monetary Equivalent Utility GainsuGenerally, if she already has n-1 kilograms of rice then rn denotes the most she will pay for an nth kilogram.urn is the dollar equivalent of the marginal utility of the nth kilogram.Monetary Equivalent Utility Gainsur1 + + rn wi
5、ll therefore be the dollar equivalent of the total change to utility from acquiring n kilograms of rice at a price of $0.uSo r1 + + rn - pGn will be the dollar equivalent of the total change to utility from acquiring n kilograms of rice at a price of $pG each.Monetary Equivalent Utility GainsuA plot
6、 of r1, r2, , rn, against n is a reservation-price curve. This is not quite the same as the consumers demand curve for rice.Monetary Equivalent Utility GainsMonetary Equivalent Utility Gains123456r1r2r3r4r5r6uWhat is the monetary value of our consumers gain-to-trading in the rice market at a price o
7、f $pG?Monetary Equivalent Utility GainsuThe dollar equivalent net utility gain for the 1st kilogram is $(r1 - pG)uand is $(r2 - pG) for the 2nd kilogram, uand so on, so the dollar value of the gain-to-trade is$(r1 - pG) + $(r2 - pG) + for as long as rn - pG 0.Monetary Equivalent Utility GainsMonetar
8、y Equivalent Utility Gains123456r1r2r3r4r5r6pGMonetary Equivalent Utility Gains123456r1r2r3r4r5r6pG$ value of net utility gains-to-tradeSuppose rice can be purchased in any continuous quantity then .Monetary Equivalent Utility GainsMonetary Equivalent Utility GainsRiceRes.PricespGReservation Price C
9、urve for Rice$ value of net utility gains-to-tradeuUnfortunately, estimating a consumers reservation-price curve is difficult,uso, as an approximation, the reservation-price curve is replaced with the consumers ordinary demand curve.$ Equivalent Utility GainsuA reservation-price curve describes sequ
10、entially 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.The Reservation Price Curve is different from the Ordinary Demand Curve !uApproximating the net utility gain area under th
11、e reservation-price curve by the corresponding area under the ordinary demand curve gives the Consumers Surplus measure of net utility gain.Consumers SurplusConsumers SurplusGasoline($) Reservation price curve for gasolineOrdinary demand curve for gasolineConsumers SurplusriceReservation price curve
12、 for riceOrdinary demand curve for ricepGuThe difference between the consumers reservation-price and ordinary demand curves is due to income effects.uBut, 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
13、-trade. Consumers SurplusConsumers SurplusThe consumers utility function isquasilinear in x2.Take p2 = 1. Then the consumerschoice problem is to maximizesubject toConsumers SurplusThat is, choose x1 to maximizeThe first-order condition is That is,This is the equation of the consumersordinary demand
14、for commodity 1.Consumers SurplusOrdinary demand curve,p1CSis exactly the consumers utility gain from consuming x1 units of commodity 1.uConsumers Surplus is an exact dollar measure of utility gained from consuming commodity 1 when the consumers utility function is quasilinear in commodity 2. uOther
15、wise Consumers Surplus is an approximation.Consumers SurplusuThe change to a consumers total utility due to a change to p1 is approximately the change in her Consumers Surplus. Consumers SurplusConsumers Surplusp1p1(x1), the inverse ordinary demand curve for commodity 1Consumers Surplusp1CS beforep1
16、(x1)Consumers Surplusp1CS afterp1(x1)Consumers Surplusp1Lost CSp1(x1), inverse ordinary demand curve for commodity 1.Consumers Surplusp1LostCSx1*(p1), the consumers ordinary demand curve for commodity 1.measures the loss in Consumers Surplus.uTwo additional dollar measures of the total utility chang
17、e caused by a price change are Compensating Variation and Equivalent Variation.Compensating Variation and Equivalent Variationup1 rises.uQ: What is the least extra income that, at the new prices, just restores the consumers original utility level?uA: The Compensating Variation.Compensating Variation
18、Compensating 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.up1 rises.uQ: What is the level of reduction in income such that the consumer is in
19、different between the original prices with the reduced income and the new prices with the original income? uA: The Equivalent Variation.Equivalent Variationup1 rises.uQ: What is the level of income reduction such that, the consumer is indifferent between the new price with the old income and the old
20、 price with the reduced income?uA: The Equivalent Variation.Equivalent VariationEquivalent Variationx2x1u1p1=p1p2 is fixed.Equivalent Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.Equivalent Variationx2x1u1u2p1=p1p1=p1”p2 is fixed.EV = m1 - m2.uRelationship 1: When the consumers preferences are quasilinea
21、r, all three measures are the same.Consumers Surplus, Compensating Variation and Equivalent VariationuConsider first the change in Consumers Surplus when p1 rises from p1 to p1”.Consumers Surplus, Compensating Variation and Equivalent VariationConsumers Surplus, Compensating Variation and Equivalent
22、 VariationIfthenand so the change in CS when p1 risesfrom p1 to p1” isuNow consider the change in CV when p1 rises from p1 to p1”.uThe consumers utility for given p1 isand 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 VariationConsumers Surplus, Compensating Variation and Equivalent VariationSouNow consider the change in EV when p1 rises from p1 to p1”.uThe consumers utility for given p1 isand EV is the extra income which, at the old prices, makes the consumers utili
24、ty the same as at the new prices. That is, .Consumers Surplus, Compensating Variation and Equivalent VariationConsumers Surplus, Compensating Variation and Equivalent VariationThat is,Consumers Surplus, Compensating Variation and Equivalent VariationSo when the consumer has quasilinearutility,CV = E
25、V = D DCS.But, otherwise, we have:Relationship 2: In size, EV D DCS CV.uChanges in a firms welfare can be measured in dollars much as for a consumer.Producers SurplusProducers Surplusy(output units)Output price (p)Marginal CostProducers Surplusy(output units)Output price (p)Marginal CostProducers Su
26、rplusy(output units)Output price (p)Marginal CostRevenue= Producers Surplusy(output units)Output price (p)Marginal CostVariable Cost of producingy units is the sum of themarginal costsProducers Surplusy(output units)Output price (p)Marginal CostVariable Cost of producingy units is the sum of themarginal costsRevenue less VCis the ProducersSurplus.Summaryu Key concepts: lConsumer surplus;lCompensation variation;lEquivalent variation.
