Monetary Measures of Consumer's Surplus in Gasoline Market

1. Chapter Fourteen Consumer’s Surplus

2. 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?

3. Monetary Measures of Gains-to-Trade • 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?

4. 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.

5. $ Equivalent Utility Gains • 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 r1, her reservation price for the 1st gallon. • r1 is the dollar equivalent of the marginal utility of the 1st gallon.

6. $ Equivalent Utility Gains • Now that she has one gallon, ask “What is the most she would pay for a 2nd gallon?”. Call this r2, her reservation price for the 2nd gallon. • r2 is the dollar equivalent of the marginal utility of the 2nd gallon.

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

8. $ Equivalent Utility Gains • The sum 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.

9. $ Equivalent Utility Gains • A 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.

10. $ Equivalent Utility Gains r1 r2 r3 r4 r5 r6 1 2 3 4 5 6

11. $ Equivalent Utility Gains • What is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $pG?

12. $ Equivalent Utility Gains • For the 1st gallon the dollar equivalent of the net utility gain is $(r1 - pG). • For the 2nd gallon the dollar equivalent of the net utility gain is $(r2 - pG). • And so on, so the monetary value of the gain-to-trade is $(r1 - pG) + $(r2 - pG) + …for as long as rn - pG > 0.

13. $ Equivalent Utility Gains r1 r2 r3 r4 pG r5 r6 1 2 3 4 5 6

14. $ Equivalent Utility Gains $ value of net utility gains-to-trade r1 r2 r3 r4 pG r5 r6 1 2 3 4 5 6

15. $ Equivalent Utility Gains • Now suppose that gasoline is sold in half-gallon units. • Now let r1, r2, … , rn, … denote the consumer’s reservation prices for successive half-gallons of gasoline. • Our consumer’s new reservation price curve is

16. $ Equivalent Utility Gains r1 r3 r5 r7 r9 r11 1 2 3 4 5 6 7 8 9 10 11

17. $ Equivalent Utility Gains r1 r3 r5 r7 pG r9 r11 1 2 3 4 5 6 7 8 9 10 11

18. $ Equivalent Utility Gains $ value of net utility gains-to-trade r1 r3 r5 r7 pG r9 r11 1 2 3 4 5 6 7 8 9 10 11

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

20. $ Equivalent Utility Gains Reservation Price Curve for Gasoline ($) Res.Prices $ value of net utility gains-to-trade pG Gasoline

21. Consumer’s Surplus • 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 $pG.

22. 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.

23. Consumer’s Surplus • The change to a consumer’s total utility due to a change to p1 is approximately measured by the change in her Consumer’s Surplus.

24. Consumer’s Surplus For quasi-linear preferences, p1(x1) is the inverse ordinary demand curve for commodity 1 p1

25. Consumer’s Surplus p1 p1(x1) CS before

26. Consumer’s Surplus p1 p1(x1) CS after

27. Consumer’s Surplus p1 p1(x1), inverse ordinary demand curve for commodity 1. Lost CS

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

29. Compensating 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.

30. Compensating Variation p1=p1’ p2 is fixed. x2 u1 x1

31. Compensating Variation p1=p1’p1=p1” p2 is fixed. x2 u1 u2 x1

32. Compensating Variation p1=p1’p1=p1” p2 is fixed. x2 u1 u2 x1

33. Compensating Variation p1=p1’p1=p1” p2 is fixed. x2 u1 CV = m2 - m1. u2 x1

34. Equivalent Variation • 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.

35. Equivalent Variation p1=p1’ p2 is fixed. x2 u1 x1

36. Equivalent Variation p1=p1’p1=p1” p2 is fixed. x2 u1 u2 x1

37. Equivalent Variation p1=p1’p1=p1” p2 is fixed. x2 u1 u2 x1

38. Equivalent Variation p1=p1’p1=p1” p2 is fixed. x2 u1 EV = m1 - m2. u2 x1

39. Consumer’s Surplus, Compensating Variation and Equivalent Variation • 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.

40. Producer’s Surplus • Changes in the welfare of a firm can be measured in monetary units in much the same way as for a consumer.

41. Producer’s Surplus Output price (p) Marginal Cost y (output units)

42. Producer’s Surplus Output price (p) Marginal Cost Revenue= y (output units)

43. Producer’s Surplus Output price (p) Marginal Cost Variable Cost of producingy’ units is the sum of themarginal costs y (output units)

44. Producer’s Surplus Output price (p) Revenue less VCis the Producer’sSurplus. Marginal Cost Variable Cost of producingy’ units is the sum of themarginal costs y (output units)