2Monetary 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.How can such gains-to-trade be measured?
3Monetary Measures of Gains-to-Trade Three such measures are:Consumer’s SurplusEquivalent Variation, andCompensating Variation.Only in one special circumstance do these three measures coincide.
4Equivalent Utility Gains Suppose gasoline can be bought only in lumps of one gallon.Use r1 to denote the most a consumer would pay for a 1st gallon -- call this her reservation price for the 1st gallon.r1 is the dollar equivalent of the marginal utility of the 1st gallon.
5Equivalent Utility Gains Now that she has one gallon, use r2 to 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.
6Equivalent Utility Gains 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.
7Equivalent Utility Gains r1 + … + rn will therefore be the dollar equivalent of the total change to utility from acquiring n gallons of gasoline at a price of $0.So r1 + … + rn - pGn will be the dollar equivalent of the total change to utility from acquiring n gallons of gasoline at a price of $pG each.
9Equivalent Utility Gains What is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $pG?
10Equivalent Utility Gains The dollar equivalent net utility gain 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.
11Equivalent Utility Gains $ value of net utility gains-to-trader1Consumer’s surplus orNet consumer’s surplusr2r3r4pGr5r6123456
12Equivalent Utility Gains If gasoline can be purchased in any quantity then ...
13Equivalent Utility Gains ($) Res. PricesReservation Price Curve for Gasoline$ value of net utility gains-to-tradepGGasoline
14Equivalent Utility Gains Unfortunately, estimating a consumer’s reservation-price curve is difficult,so, as an approximation, the reservation-price curve is replaced with the consumer’s ordinary demand curve.This approximation gives the Consumer’s Surplus measure of net utility gain.
15Quasi-Linear Utility One special case would be quasi-linear utility. With quasi-linear utility, calculating CS using the reservation-price curve will result in the same value with that using the ordinary demand curve.
16CS for Quasi-linear Utility p1Ordinary demand curve,is exactly the consumer’s utility gain from consuming x1’ units of commodity 1.CS
17Change in CS Now, what if there is a change in one of the prices? How would a price change affect the consumer’s surplus?
18Consumer’s Surplusp1p1(x1), the inverse ordinary demand curve for commodity 1
26Compensating Variation x2p1=p1’ p1=p1”p2 is fixed.u1u2x1
27Compensating Variation x2p1=p1’ p1=p1”p2 is fixed.u1u2x1
28Compensating Variation p1=p1’ p1=p1”p2 is fixed.x2u1CV = m2 - m1.u2x1
29Equivalent Variation p1 rises. Q: How much money would have to be taken away from the consumer before the price change to leave him just as well off as he would be after the price change?A: The Equivalent Variation.
31Equivalent Variationp1=p1’ p1=p1”p2 is fixed.x2u1u2x1
32Equivalent Variationp1=p1’ p1=p1”p2 is fixed.x2u1u2x1
33Equivalent Variation EV = m1 - m2. p1=p1’ p1=p1” p2 is fixed. x2 u1 u2
34CV and EVBoth CV and EV measure “how far apart” two indifference curves are.Depend on the slope of the tangent line.CV does not equal EV in most cases.Only in quasilinear utility. Why?The distance of two indifference curves is the same no matter where it is measured.CV = EV = △ CS
35Producer’s SurplusChanges in a firm’s welfare can be measured in dollars much as for a consumer.