1. Cost Curves 成本曲线

2.  A total cost curve （总成本曲线） is the graph of a firm’s total cost function.  An average total cost curve （平均成本曲线） is the graph of a firm’s average total cost function.  A variable cost curve （可变成本曲线） is the graph of a firm’s variable cost function.  An average variable cost curve （平均可变成本曲 线） is the graph of a firm’s average variable cost function.

3.  An fixed cost curve （固定成本曲线） is the graph of a firm’s fixed cost function.  An average fixed cost curve （平均固定成本曲线 ） is the graph of a firm’s average fixed cost function.  A marginal cost curve （边际成本曲线） is the graph of a firm’s marginal cost function.

4.  How are these cost curves related to each other?  How are a firm’s long-run and short-run cost curves related?

5.  F is the firm’s fixed cost,  It’s the total cost to a firm’s short-run fixed inputs （固定投入）.  does not vary with the firm’s output level.  c v (y) is the firm’s variable cost function.  c v (y) is the total cost to a firm of its variable inputs （可变投入） when producing y output units.

6.  c(y) is the total cost of all inputs, fixed and variable, when producing y output units. c(y) is the firm’s total cost function;

7. y $ F

8. y $ c v (y)

9. y $ F

10. y $ F c(y) F

11.  The firm’s total cost function is For y > 0, the firm’s average total cost function is

12.  What does an average fixed cost curve look like?  AFC(y) graph looks like...

13. $/output unit AFC(y) y0 AFC(y)  0 as y 

14. How is the graph of AC(y) looks like...?

15.  Now we turn to the average cost curves AC(y).  To understand the shape of AC(y), we need to know the relation between AP and AVC(y)  We claim: as AP L increases, AVC(y) decreases.  Why?

16. AP L Substitute L 2 into Shot Run Production Function Q 2 =f(L 2 ) L L2L2 AVC y Q2Q2 AP L

17. $/output unit AVC(y) y0

18. $/output unit AFC(y) AVC(y) y0

19.  And ATC(y) = AFC(y) + AVC(y)

20. $/output unit AFC(y) AVC(y) ATC(y) y0 ATC(y) = AFC(y) + AVC(y)

21. $/output unit AFC(y) AVC(y) ATC(y) y0 AFC(y) = ATC(y) - AVC(y) AFC

22. $/output unit AFC(y) AVC(y) ATC(y) y0 Since AFC(y)  0 as y , ATC(y)  AVC(y) as y  AFC

23. $/output unit AFC(y) AVC(y) ATC(y) y0 Since AFC(y)  0 as y , ATC(y)  AVC(y) as y  And since short-run AVC(y) must eventually increase, ATC(y) must eventually increase in a short-run.

24.  Marginal cost is the rate-of-change of variable production cost as the output level changes. That is,

25.  The firm’s total cost function is and the fixed cost F does not change with the output level y, so  MC is the slope of both the variable cost and the total cost functions.

26. How is the graph of MC(y) looks like...? Recall the law of deminishing marginal returns ( 边际收益递减规律 ) ?

27. MC=w/MP L MP L L L1L1 MC y Look at where Diminishing Returns begin MP L

28. MC=w/MP L Look at where Diminishing Returns begin L L1L1 y MC Q1Q1 MP L MC

29.  the Law of Diminishing (Marginal) Returns must cause the firm’s marginal cost of production to increase eventually.  That is, at the beginning as MP L increases, MC decreases;  And later as MP L decreases, MC increases.

30.  Since MC(y) is the derivative of c v (y), c v (y) must be the integral of MC(y). That is,

31. MC(y) y0 Area is the variable cost of making y’ units $/output unit Relation between MC(y) and c v (y)

32.  How is marginal cost related to average variable cost?

33. Since

34. Therefore, as

35. Since Therefore, as

36. $/output unit y AVC(y) MC(y)

37. $/output unit y AVC(y) MC(y)

38. $/output unit y AVC(y) MC(y)

39. $/output unit y AVC(y) MC(y)

40. $/output unit y AVC(y) MC(y) The short-run MC curve intersects the short-run AVC curve from below at the AVC curve’s minimum.

41. Similarly, since

42. Therefore, as

43. Similarly, since Therefore, as

44. $/output unit y MC(y) ATC(y) as

45.  The short-run MC curve intersects the short-run AVC curve from below at the AVC curve’s minimum.  And, similarly, the short-run MC curve intersects the short-run ATC curve from below at the ATC curve’s minimum.

46. $/output unit y AVC(y) MC(y) ATC(y)

47.  Proposition 1: LR cost is smaller than SR cost, i.e..

48.  Reason: To increase output, in the long run, a firm can adjust all factors; in the short-run, the firm can only some factors.  Long-run production is more flexible  It has been shown with the help of LR and SR expansion paths (in chapter 20).  Now we show it with the help of total cost curves.

49. x1x1 x2x2 Short-run output expansion path Long-run costs are:

50. x1x1 x2x2 Short-run output expansion path Long-run costs are: Short-run costs are:

51. x1x1 x2x2 Short-run output expansion path Long-run costs are: Short-run costs are:

52. x1x1 x2x2 Short-run output expansion path Long-run costs are: Short-run costs are: one point in common

53.  This says that the long-run total cost curve always has one point in common with any particular short-run total cost curve.  Short-run total cost exceeds long-run total cost except for the output level where the short-run input level restriction is the long-run input level choice.

54. y $ c(y) c s (y) A short-run total cost curve always has one point in common with the long-run total cost curve, and is elsewhere higher than the long-run total cost curve.

55.  A firm has a different short-run total cost curve for each possible short-run circumstance.  Suppose the firm can be in one of just three short- runs; x 2 = x 2 or x 2 = x 2  x 2 < x 2  < x 2 . or x 2 = x 2 .

56. y 0 F = w 2 x 2 F c s (y;x 2 ) $

57. y F 0 F = w 2 x 2 F F  = w 2 x 2  c s (y;x 2 ) $

58. y F 0 F = w 2 x 2 F  = w 2 x 2  A larger amount of the fixed input increases the firm’s fixed cost. c s (y;x 2 ) $ F

59. y F 0 F = w 2 x 2 F  = w 2 x 2  A larger amount of the fixed input increases the firm’s fixed cost. Why does a larger amount of the fixed input reduce the slope of the firm’s total cost curve? c s (y;x 2 ) $ F

60. MP 1 is the marginal physical productivity of the variable input 1, so one extra unit of input 1 gives MP 1 extra output units. Therefore, the extra amount of input 1 needed for 1 extra output unit is units of input 1.

61. MP 1 is the marginal physical productivity of the variable input 1, so one extra unit of input 1 gives MP 1 extra output units. Therefore, the extra amount of input 1 needed for 1 extra output unit is units of input 1. Each unit of input 1 costs w 1, so the firm’s extra cost from producing one extra unit of output is

62. is the slope of the firm’s total cost curve.

63. If input 2 is a complement to input 1 then MP 1 is higher for higher x 2. Hence, MC is lower for higher x 2. That is, a short-run total cost curve starts higher and has a lower slope if x 2 is larger.

64. y F 0 F = w 2 x 2 F  = w 2 x 2  F  F  = w 2 x 2  c s (y;x 2  ) c s (y;x 2 ) $ F

65.  The firm has three short-run total cost curves.  In the long-run the firm is free to choose amongst these three since it is free to select x 2 equal to any of x 2, x 2 , or x 2 .  How does the firm make this choice?

66. y F 0 F  yy  For 0  y  y, choose x 2 = x 2. c s (y;x 2  ) c s (y;x 2 ) $ F

67. y F 0 F  yy  For 0  y  y, choose x 2 = x 2. For y  y  y , choose x 2 = x 2 . c s (y;x 2  ) c s (y;x 2 ) $ F

68. y F 0 F  c s (y;x 2  ) yy  For 0  y  y, choose x 2 = x 2. For y  y  y , choose x 2 = x 2 . For y   y, choose x 2 = x 2 . c s (y;x 2 ) $ F

69. y F 0 F  c s (y;x 2  ) yy  For 0  y  y, choose x 2 = x 2. For y  y  y , choose x 2 = x 2 . For y   y, choose x 2 = x 2 . c(y), the firm’s long- run total cost curve. $ F

70.  The firm’s long-run total cost curve consists of the lowest parts of the short-run total cost curves.  The long-run total cost curve is the lower envelope ( 下包络线 ) of the short-run total cost curves.

71.  If input 2 is available in continuous amounts then there is an infinity （无数多） of short-run total cost curves but the long-run total cost curve is still the lower envelope of all of the short-run total cost curves.

72. $ y F 0 F  c s (y;x 2 ) c s (y;x 2  ) c(y) F

73.  For any output level y, the long-run total cost curve always gives the lowest possible total production cost.  Therefore, the long-run av. total cost curve must always give the lowest possible av. total production cost.  The long-run av. total cost curve must be the lower envelope of all of the firm’s short-run av. total cost curves.

74.  E.g. suppose again that the firm can be in one of just three short-runs; x 2 = x 2 or x 2 = x 2  (x 2 < x 2  < x 2  ) or x 2 = x 2  then the firm’s three short-run average total cost curves are...

75. y $/output unit AC s (y;x 2  ) AC s (y;x 2  ) AC s (y;x 2 )

76.  The firm’s long-run average total cost curve is the lower envelope of the short-run average total cost curves...

77. y $/output unit AC s (y;x 2  ) AC s (y;x 2  ) AC s (y;x 2 ) AC(y) The long-run av. total cost curve is the lower envelope of the short-run av. total cost curves.

78.  Q: Is the long-run marginal cost curve the lower envelope of the firm’s short-run marginal cost curves?

79.  A: No.

80.  The firm’s three short-run average total cost curves are...

81. y $/output unit AC s (y;x 2  ) AC s (y;x 2  ) AC s (y;x 2 )

82. y $/output unit AC s (y;x 2  ) AC s (y;x 2  ) AC s (y;x 2 ) MC s (y;x 2 )MC s (y;x 2  ) MC s (y;x 2  )

83. y $/output unit AC s (y;x 2  ) AC s (y;x 2  ) AC s (y;x 2 ) MC s (y;x 2 )MC s (y;x 2  ) MC s (y;x 2  ) AC(y)

84. y $/output unit AC s (y;x 2  ) AC s (y;x 2  ) AC s (y;x 2 ) MC s (y;x 2 )MC s (y;x 2  ) MC s (y;x 2  ) AC(y)

85. y $/output unit AC s (y;x 2  ) AC s (y;x 2  ) AC s (y;x 2 ) MC s (y;x 2 )MC s (y;x 2  ) MC s (y;x 2  ) MC(y), the long-run marginal cost curve.

86.  For any output level y > 0, the long-run marginal cost of production equals to the short-run marginal cost of output chosen by the firm ， that is, LRMC(y) = SRMC(y)

87.  This is always true,  So for the continuous case, where x 2 can be fixed at any value of zero or more, the relationship between the long-run marginal cost and all of the short-run marginal costs is...

88. AC(y) $/output unit y SRACs

89. AC(y) $/output unit y SRMCs

90. AC(y) MC(y) $/output unit y SRMCs u For each y > 0, the long-run MC equals the MC for the short-run chosen by the firm.

91.  Types of cost curves  Fixed, variable and total cost functions  Average fixed, average variable and average cost functions  Marginal cost functions  Marginal and variable cost functions  Marginal and average variable cost functions  Short run and long run cost curves

92. 总成本 : TFC 、 TVC 、 TC 平均成本： AVC 、 AFC 、 AC 边际成本 :MC 0 C Q TFC 总不变成本曲线 Q 0 C TVC 总可变成本曲线 TFC 0 Q C TC 总成本曲线 AFC 0 Q C 平均不变成本曲线 MC 0 Q C 边际成本曲线 AC 0 Q C 平均总成本曲线 AVC 0 Q C 平均可变成本曲线

93. Relation among MC AC and AVC

94. 对于生产函数 ，有两种可变投入 K 、 L ，资本的租赁 价格为 1 元，劳动的工资为 1 元，固定投入为 1000 元。 1 ）写出成本曲线。 2 ）计算 AC, AVC, AFC, MC 3 ）计算 minAC 和 minAVC 时的 AC,AVC,y 。

95.  假设某企业Ａ的生产函数为：  另一家企业Ｂ的生产函数为：  其中 y 为产量，Ｋ和Ｌ分别为资本和劳动的投 入量。  ａ. 如果两家企业使用同样多的资本和劳动，哪 一家企业的产量大？  ｂ. 如果资本的投入限于９单位，而劳动的投入 没有限制，哪家企业劳动的边际产量更大？