Chapter Fourteen Consumer’s Surplus

Monetary Measures of Gains-to- Trade  Suppose you know you can buy as much gasoline as you choose at a given price of $1 per gallon once you have entered the gasoline market.  Q: What is the most you would pay to be able to enter the market for gasoline?

 A: You would pay a sum up to, but not exceeding, the dollar value to you of the gains-to-trade you would enjoy once inside the market.  How can we measure the monetary values of such gains-to-trade? Monetary Measures of Gains-to- Trade

 We will consider three such measures Consumer’s Surplus Equivalent Variation, and Compensating Variation.  Only in one special circumstance do these three measures coincide. Monetary Measures of Gains-to- Trade

 Suppose gasoline is purchasable only in lumps of one gallon and consider a single consumer.  Ask “What is the most she would pay for a 1st gallon?”. Call this r 1, her reservation price for the 1st gallon.  r 1 is the dollar equivalent of the marginal utility of the 1st gallon. $ Equivalent Utility Gains

 Now that she has one gallon, ask “What is the most she would pay for a 2nd gallon?”. Call this r 2, her reservation price for the 2nd gallon.  r 2 is the dollar equivalent of the marginal utility of the 2nd gallon. $ Equivalent Utility Gains

 More generally, if she already has n-1 gallons of gasoline then let r n be the most she will pay for an nth gallon.  r n is the dollar equivalent of the marginal utility of the nth gallon. $ Equivalent Utility Gains

 The sum r 1 + … + r n will therefore be the dollar equivalent of the total change to utility from acquiring n gallons of gasoline at a price of $0.  So r 1 + … + r n - p G n will be the dollar equivalent of the total change to utility from acquiring n gallons of gasoline at a price of $p G each. $ Equivalent Utility Gains

 A plot of r 1, r 2, …, r n, … against n is a reservation-price curve. This is not quite the same as the consumer’s demand curve for gasoline. $ Equivalent Utility Gains

r1r1 r2r2 r3r3 r4r4 r5r5 r6r6

 What is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $p G ? $ Equivalent Utility Gains

 For the 1st gallon the dollar equivalent of the net utility gain is $(r 1 - p G ).  For the 2nd gallon the dollar equivalent of the net utility gain is $(r 2 - p G ).  And so on, so the monetary value of the gain-to-trade is $(r 1 - p G ) + $(r 2 - p G ) + … for as long as r n - p G > 0. $ Equivalent Utility Gains

r1r1 r2r2 r3r3 r4r4 r5r5 r6r6 pGpG

r1r1 r2r2 r3r3 r4r4 r5r5 r6r6 pGpG $ value of net utility gains-to-trade

 Now suppose that gasoline is sold in half-gallon units.  Now let r 1, r 2, …, r n, … denote the consumer’s reservation prices for successive half-gallons of gasoline.  Our consumer’s new reservation price curve is $ Equivalent Utility Gains

r1r1 r3r3 r5r5 r7r7 r9r9 r

$ Equivalent Utility Gains r1r1 r3r3 r5r5 r7r7 r9r9 r pGpG

$ Equivalent Utility Gains r1r1 r3r3 r5r5 r7r7 r9r9 r pGpG $ value of net utility gains-to-trade

 Suppose gasoline can be purchased in any quantity.  Then our consumer’s reservation price curve is $ Equivalent Utility Gains

Gasoline ($) Res. Prices pGpG Reservation Price Curve for Gasoline $ value of net utility gains-to-trade

 If we approximate the net utility gain area under the reservation-price curve by the corresponding area under the ordinary demand curve then we get the Consumer’s Surplus approximate measure of net utility gain from buying gasoline at a price of $p G. Consumer’s Surplus

 Consumer’s Surplus is an exact dollar measure of total utility gains from consumption of commodity 1 when the consumer’s utility function is quasilinear in commodity 2.  Otherwise Consumer’s Surplus is an approximation. Consumer’s Surplus

 The change to a consumer’s total utility due to a change to p 1 is approximately measured by the change in her Consumer’s Surplus. Consumer’s Surplus

p1p1 For quasi-linear preferences, p 1 (x 1 ) is the inverse ordinary demand curve for commodity 1

Consumer’s Surplus p1p1 CS before p 1 (x 1 )

Consumer’s Surplus p1p1 CS after p 1 (x 1 )

Consumer’s Surplus p1p1 Lost CS p 1 (x 1 ), inverse ordinary demand curve for commodity 1.

 Two additional monetary measures of the total utility change caused by a price change are Compensating Variation and Equivalent Variation. Compensating Variation and Equivalent Variation

 Suppose the price of commodity 1 rises.  Q: What is the smallest amount of additional income which, at the new prices, would just restore the consumer’s original utility level?  A: The Compensating Variation. Compensating Variation

x2x2 x1x1 u1u1 p1=p1’p1=p1’p 2 is fixed.

Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. CV = m 2 - m 1.

 Suppose the price of commodity 1 rises.  Q: What is the smallest amount of additional income which, at the original prices, would just restore the consumer’s original utility level?  A: The Equivalent Variation. Equivalent Variation

x2x2 x1x1 u1u1 p1=p1’p1=p1’p 2 is fixed.

Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. EV = m 1 - m 2.

 What relationships exist between the three monetary measures of utility changes due to price changes?  Relationship 1: When the consumer’s preferences are quasilinear, all three measures are the same. Consumer’s Surplus, Compensating Variation and Equivalent Variation

 Changes in the welfare of a firm can be measured in monetary units in much the same way 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 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.