Consumer Surplus

Monetary Measures of Gains-to- Trade  Basic idea of consumer surplus: We want a measure of how much a person is willing to pay for something.  Price measures marginal willingness to pay, so add up over all different outputs to get total willingness to pay.

Monetary Measures of Gains-to- Trade  You can buy as much gasoline as you wish at €p per liter once you enter the gasoline market.  How can the gains-to-trade be measured?

 Suppose gasoline can be bought only in lumps of one liter.  Use r 1 to denote the most a single consumer would pay for a 1st liter -- call this her reservation price for the 1st liter.  r 1 is the euro equivalent of the marginal utility of the 1st liter. € Equivalent Utility Gains

 Now that she has one liter, use r 2 to denote the most she would pay for a 2nd liter -- this is her reservation price for the 2nd liter.  r 2 is the euro equivalent of the marginal utility of the 2nd liter. € Equivalent Utility Gains

 Generally, if she already has n-1 liters of gasoline then r n denotes the most she will pay for an n-th liter.  r n is the euro equivalent of the marginal utility of the n-th liter. € Equivalent Utility Gains

 So r 1 + … + r n - pn will be the euro equivalent of the total change to utility from acquiring n liters of gasoline at a price of €p each. € Equivalent Utility Gains

r1r1 r2r2 r3r3 r4r4 r5r5 r6r6 p € value of net utility gains-to-trade

 Now suppose that gasoline is sold in half-liter units.  r 1, r 2, …, r n, … denote the consumer’s reservation prices for successive half-liters of gasoline. € Equivalent Utility Gains

r1r1 r3r3 r5r5 r7r7 r9r9 r p € value of net utility gains-to-trade

 And if gasoline is available in one- quarter liter units... € Equivalent Utility Gains

p € value of net utility gains-to-trade

 Finally, if gasoline can be purchased in any quantity then... € Equivalent Utility Gains

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

 Unfortunately, estimating a consumer’s reservation-price curve is difficult,  so, as an approximation, the reservation-price curve is replaced with the consumer’s demand curve. € Equivalent Utility Gains

 A consumer’s reservation-price curve is not quite the same as her demand curve. Why not?  A reservation-price curve describes sequentially the values of successive single units of a commodity.  A demand curve describes the most that would be paid for q units of a commodity purchased simultaneously. Consumer’s Surplus

 Approximating the net utility gain area under the reservation-price curve by the corresponding area under the demand curve gives the Consumer’s Surplus measure of net utility gain. Consumer’s Surplus

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

p1p1 p 1 (x 1 ), the inverse 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 demand curve for commodity 1

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

 p 1 rises.  Q: What is the least extra income that, at the new prices, just restores the consumer’s original utility level?  A: The Compensating Variation. Compensating Variation

 p 1 rises.  Q: What is the least extra income that, at the original prices, just restores the consumer’s original utility level?  A: The Equivalent Variation. Equivalent Variation

 In general, EV, CV and CS are different …, but the change in consumer's surplus is usually a good approximation. Consumer’s Surplus, Compensating Variation and Equivalent Variation

 Changes in a firm’s welfare can be measured in euros much as for a consumer. Producer’s Surplus