1. Consumer’s Surplus 消费者剩余

2.  In previous chapters  From underlying preference or utility function to consumer’s demand function  In practice,  From observed demand behavior to estimate preferences or utility.

3.  You can buy as much gasoline as you wish 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.

4.  Use r 1 to denote the most a consumer would pay for a 1st gallon -- reservation price （保留价格） for the 1st gallon.  r 1 is the dollar equivalent of the marginal utility of the 1st gallon.  use r 2 to denote the most she would pay for a 2nd gallon -- this is her reservation price for the 2nd gallon.  r 2 is the dollar equivalent of the marginal utility of the 2nd gallon.

5.  Generally, if she already has n-1 gallons of gasoline then r n denotes the most she will pay for an nth gallon.  r n is the dollar equivalent of the marginal utility of the nth gallon.

6.  r 1 + … + r n will be the dollar equivalent of the total change to utility from consuming 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 consuming n gallons of gasoline at a price of $p G each.

7.  What is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $p G ?

8. 123456 r1r1 r2r2 r3r3 r4r4 r5r5 r6r6 pGpG $ value of net utility gains-to- trade Consumer’s surplus （消费者剩余） or Net consumer’s surplus （净消费者剩余） Gross consumer’s surplus （总消费者剩余） or gross benefit （总效益） Yellow area

9.  The dollar equivalent net utility gain for the 1st gallon is $(r 1 - p G )  and is $(r 2 - p G ) for the 2nd gallon,  and so on, so the dollar value of the gain-to-trade is $(r 1 - p G ) + $(r 2 - p G ) + … for as long as r n - p G > 0.

10.  If gasoline can be purchased in any quantity then...

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

12.  Unfortunately, estimating a consumer’s reservation-price curve is difficult,  so, as an approximation, we use the consumer’s ordinary demand curve.  This approximation gives the Consumer’s Surplus measure of net utility gain.

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

14.  The difference of ordinary demand curve and reservation price curve is induced by income effect.  If income effects are small, then the approximation is good.  But, if the consumer’s utility function is quasilinear, income effect is zero, two curves are exactly the same, why??

15. The consumer’s utility function is quasilinear in x 2. Take p 2 = 1. Then the consumer’s choice problem is to maximize subject to

16. The consumer’s utility function is quasilinear in x 2. Take p 2 = 1. Then the consumer’s choice problem is to maximize subject to

17. That is, choose x 1 to maximize The first-order condition is That is, This is the equation of the consumer’s ordinary demand for commodity 1.

18. Ordinary demand curve, p1p1 CS

19. Ordinary demand curve, p1p1 CS

20. Ordinary demand curve, p1p1 CS

21. Ordinary demand curve, p1p1 CS is exactly the consumer’s utility gain from consuming x 1 ’ units of commodity 1.

22.  Price changes??  The change to a consumer’s total utility due to a change to p 1 is approximately the change in her Consumer’s Surplus.

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

24. p1p1 CS before p 1 (x 1 )

25. p1p1 CS after p 1 (x 1 )

26. p1p1 Lost CS measures the loss in Consumer’s Surplus.

27.  Two additional dollar measures of the total utility change caused by a price change are Compensating Variation( 补偿变化 ) and Equivalent Variation （ 等价变化）.

28.  p 1 rises.  Q: What is the least extra income that, at the new prices, just restores the consumer’s original utility level?

29.  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.

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

31. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1”

32. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1”

33. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” CV = m 2 - m 1.

34. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. CV = m 2 - m 1. 使消费者回到初始无差异曲线上所必需的收入变化称作收入的补偿变化

35.  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.

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

37. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1”

38. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1”

39. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” EV = m 1 - m 2.

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

41. x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. CV = m 2 - m 1. 使消费者回到初始无差异曲线上所必需的收入变化称作收入的补偿变化 CV

42.  Both 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 消费者剩余.

43.  Changes in a firm’s welfare can be measured in dollars much as for a consumer.

44. m (output units) Output price (p) Marginal Cost

45. m (output units) Output price (p) Marginal Cost

46. m (output units) Output price (p) Marginal Cost Revenue =

47. m (output units) Output price (p) Marginal Cost Variable Cost of producing m’ units is the sum of the marginal costs

48. 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.

49.  How can such gains-to-trade be measured?  Three such measures are:  Consumer’s Surplus （消费者剩余）  Equivalent Variation （等价变换）, and  Compensating Variation （补偿变换）.  Only in one special circumstance (quasilinear preference ) do these three measures coincide.  Producer’s surplus