INTMIC9.jpg Chapter 14 Consumer’s Surplus Monetary Measures of Gains-to-Trade uYou 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? Monetary Measures of Gains-to-Trade uA: You would pay up to the dollar value of the gains-to-trade you would enjoy once in the market. uHow can such gains-to-trade be measured? Monetary Measures of Gains-to-Trade uThree such measures are: –Consumer’s Surplus –Equivalent Variation, and –Compensating Variation. uOnly in one special circumstance do these three measures coincide. $ Equivalent Utility Gains uSuppose gasoline can be bought only in lumps of one gallon. uUse r1 to denote the most a single consumer would pay for a 1st gallon -- call this her reservation price for the 1st gallon. ur1 is the dollar equivalent of the marginal utility of the 1st gallon. $ Equivalent Utility Gains uNow 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. ur2 is the dollar equivalent of the marginal utility of the 2nd gallon. $ Equivalent Utility Gains uGenerally, if she already has n-1 gallons of gasoline then rn denotes the most she will pay for an nth gallon. urn is the dollar equivalent of the marginal utility of the nth gallon. $ Equivalent Utility Gains ur1 + … + rn will therefore be the dollar equivalent of the total change to utility from acquiring n gallons of gasoline at a price of $0. uSo 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. $ Equivalent Utility Gains uA plot of r1, r2, … , rn, … against n is a reservation-price curve. This is not quite the same as the consumer’s demand curve for gasoline. $ Equivalent Utility Gains 1 2 3 4 5 6 r1 r2 r3 r4 r5 r6 $ Equivalent Utility Gains uWhat is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $pG? $ Equivalent Utility Gains 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 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 $ Equivalent Utility Gains 1 2 3 4 5 6 r1 r2 r3 r4 r5 r6 pG $ value of net utility gains-to-trade $ Equivalent Utility Gains uNow suppose that gasoline is sold in half-gallon units. ur1, r2, … , rn, … denote the consumer’s reservation prices for successive half-gallons of gasoline. uOur consumer’s new reservation price curve is $ Equivalent Utility Gains 1 2 3 4 5 6 r1 r3 r5 r7 r9 r11 7 8 9 10 11 $ Equivalent Utility Gains 1 2 3 4 5 6 r1 r3 r5 r7 r9 r11 7 8 9 10 11 pG $ Equivalent Utility Gains 1 2 3 4 5 6 r1 r3 r5 r7 r9 r11 7 8 9 10 11 pG $ value of net utility gains-to-trade $ Equivalent Utility Gains uAnd if gasoline is available in one-quarter gallon units ... $ Equivalent Utility Gains 1 2 3 4 5 6 7 8 9 10 11 $ Equivalent Utility Gains 1 2 3 4 5 6 7 8 9 10 11 pG $ Equivalent Utility Gains pG $ value of net utility gains-to-trade $ Equivalent Utility Gains uFinally, if gasoline can be purchased in any quantity then ... $ Equivalent Utility Gains Gasoline ($) Res. Prices Reservation Price Curve for Gasoline $ Equivalent Utility Gains Gasoline ($) Res. Prices pG Reservation Price Curve for Gasoline $ Equivalent Utility Gains Gasoline ($) Res. Prices pG Reservation Price Curve for Gasoline $ value of net utility gains-to-trade $ Equivalent Utility Gains uUnfortunately, estimating a consumer’s reservation-price curve is difficult, uso, as an approximation, the reservation-price curve is replaced with the consumer’s ordinary demand curve. Consumer’s Surplus 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 Surplus uApproximating the net utility gain area under the reservation-price curve by the corresponding area under the ordinary demand curve gives the Consumer’s Surplus measure of net utility gain. Consumer’s Surplus Gasoline ($) Reservation price curve for gasoline Ordinary demand curve for gasoline Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG ($) Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG $ value of net utility gains-to-trade ($) Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG $ value of net utility gains-to-trade Consumer’s Surplus ($) Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pG $ value of net utility gains-to-trade Consumer’s Surplus ($) Consumer’s Surplus uThe difference between the consumer’s reservation-price and ordinary demand curves is due to income effects. uBut, if the consumer’s utility function is quasilinear in income then there are no income effects and Consumer’s Surplus is an exact $ measure of gains-to-trade. Consumer’s Surplus The consumer’s utility function is quasilinear in x2. Take p2 = 1. Then the consumer’s choice problem is to maximize subject to Consumer’s Surplus The consumer’s utility function is quasilinear in x2. Take p2 = 1. Then the consumer’s choice problem is to maximize subject to Consumer’s Surplus That is, choose x1 to maximize The first-order condition is That is, This is the equation of the consumer’s ordinary demand for commodity 1. Consumer’s Surplus Ordinary demand curve, p1 CS Consumer’s Surplus Ordinary demand curve, p1 CS Consumer’s Surplus Ordinary demand curve, p1 CS Consumer’s Surplus Ordinary demand curve, p1 CS is exactly the consumer’s utility gain from consuming x1’ units of commodity 1. Consumer’s Surplus uConsumer’s Surplus is an exact dollar measure of utility gained from consuming commodity 1 when the consumer’s utility function is quasilinear in commodity 2. uOtherwise Consumer’s Surplus is an approximation. Consumer’s Surplus uThe change to a consumer’s total utility due to a change to p1 is approximately the change in her Consumer’s Surplus. Consumer’s Surplus p1 p1(x1), the inverse ordinary demand curve for commodity 1 Consumer’s Surplus p1 CS before p1(x1) Consumer’s Surplus p1 CS after p1(x1) Consumer’s Surplus p1 Lost CS p1(x1), inverse ordinary demand curve for commodity 1. Consumer’s Surplus p1 Lost CS x1*(p1), the consumer’s ordinary demand curve for commodity 1. measures the loss in Consumer’s Surplus. Compensating Variation and Equivalent Variation uTwo additional dollar measures of the total utility change caused by a price change are Compensating Variation and Equivalent Variation. Compensating Variation up1 rises. uQ: What is the least extra income that, at the new prices, just restores the consumer’s original utility level? Compensating Variation up1 rises. uQ: What is the least extra income that, at the new prices, just restores the consumer’s original utility level? uA: The Compensating Variation. Compensating Variation x2 x1 u1 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. Compensating Variation x2 x1 u1 u2 p1=p1’ p1=p1” p2 is fixed. CV = m2 - m1. Equivalent Variation up1 rises. uQ: What is the least extra income that, at the original prices, just restores the consumer’s original utility level? uA: The 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. Equivalent Variation x2 x1 u1 u2 p1=p1’ p1=p1” p2 is fixed. EV = m1 - m2. Consumer’s Surplus, Compensating Variation and Equivalent Variation uRelationship 1: When the consumer’s preferences are quasilinear, all three measures are the same. Consumer’s Surplus, Compensating Variation and Equivalent Variation uConsider first the change in Consumer’s Surplus when p1 rises from p1’ to p1”. Consumer’s Surplus, Compensating Variation and Equivalent Variation If then Consumer’s Surplus, Compensating Variation and Equivalent Variation If then and so the change in CS when p1 rises from p1’ to p1” is Consumer’s Surplus, Compensating Variation and Equivalent Variation If then and so the change in CS when p1 rises from p1’ to p1” is Consumer’s Surplus, Compensating Variation and Equivalent Variation If then and so the change in CS when p1 rises from p1’ to p1” is Consumer’s Surplus, Compensating Variation and Equivalent Variation uNow consider the change in CV when p1 rises from p1’ to p1”. uThe consumer’s utility for given p1 is and CV is the extra income which, at the new prices, makes the consumer’s utility the same as at the old prices. That is, ... Consumer’s Surplus, Compensating Variation and Equivalent Variation Consumer’s Surplus, Compensating Variation and Equivalent Variation So Consumer’s Surplus, Compensating Variation and Equivalent Variation uNow consider the change in EV when p1 rises from p1’ to p1”. uThe consumer’s utility for given p1 is and EV is the extra income which, at the old prices, makes the consumer’s utility the same as at the new prices. That is, ... Consumer’s Surplus, Compensating Variation and Equivalent Variation Consumer’s Surplus, Compensating Variation and Equivalent Variation That is, Consumer’s Surplus, Compensating Variation and Equivalent Variation So when the consumer has quasilinear utility, CV = EV = DCS. But, otherwise, we have: Relationship 2: In size, EV < DCS < CV. Producer’s Surplus uChanges in a firm’s welfare can be measured in dollars much as for a consumer. Producer’s Surplus y (output units) Output price (p) Marginal Cost Producer’s Surplus y (output units) Output price (p) Marginal Cost Producer’s Surplus y (output units) Output price (p) Marginal Cost Revenue = Producer’s Surplus y (output units) Output price (p) Marginal Cost Variable Cost of producing y’ units is the sum of the marginal costs Producer’s Surplus y (output units) Output price (p) Marginal Cost Variable Cost of producing y’ units is the sum of the marginal costs Revenue less VC is the Producer’s Surplus. Benefit-Cost Analysis uCan we measure in money units the net gain, or loss, caused by a market intervention; e.g., the imposition or the removal of a market regulation? uYes, by using measures such as the Consumer’s Surplus and the Producer’s Surplus. Benefit-Cost Analysis QD, QS (output units) Price Supply Demand p0 q0 The free-market equilibrium CS Benefit-Cost Analysis QD, QS (output units) Price Supply Demand p0 q0 The free-market equilibrium and the gains from trade generated by it. PS CS Benefit-Cost Analysis QD, QS (output units) Price Supply Demand p0 q0 PS q1 Consumer’s gain Producer’s gain The gain from freely trading the q1th unit. CS Benefit-Cost Analysis QD, QS (output units) Price Supply Demand p0 q0 The gains from freely trading the units from q1 to q0. PS q1 Consumer’s gains Producer’s gains CS Benefit-Cost Analysis QD, QS (output units) Price Supply Demand p0 q0 The gains from freely trading the units from q1 to q0. PS q1 Consumer’s gains Producer’s gains CS Benefit-Cost Analysis QD, QS (output units) Price p0 q0 PS q1 Consumer’s gains Producer’s gains Any regulation that causes the units from q1 to q0 to be not traded destroys these gains. This loss is the net cost of the regulation. Tax Revenue Benefit-Cost Analysis QD, QS (output units) Price q0 PS q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. ps pb t CS Deadweight Loss Benefit-Cost Analysis QD, QS (output units) Price q0 q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. pf CS Deadweight Loss So does a floor price set at pf PS Benefit-Cost Analysis QD, QS (output units) Price q0 q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. pc Deadweight Loss So does a floor price set at pf, a ceiling price set at pc PS CS Benefit-Cost Analysis QD, QS (output units) Price q0 q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. pc Deadweight Loss So does a floor price set at pf, a ceiling price set at pc, and a ration scheme that allows only q1 units to be traded. PS pe CS Revenue received by holders of ration coupons.