1. Chapter Twenty-One Cost Curves

7. y $ F

8. y $ c v (y)

9. y $ F c v (y)

10. y $ F c v (y) c(y) F

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

15. $/output unit AVC(y) y 0

16. $/output unit AFC(y) AVC(y) y 0

18. $/output unit AFC(y) AVC(y) ATC(y) y 0 ATC(y) = AFC(y) + AVC(y)

19. $/output unit AFC(y) AVC(y) ATC(y) y 0 AFC(y) = ATC(y) - AVC(y) AFC

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

21. $/output unit AFC(y) AVC(y) ATC(y) y 0 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.

25. Marginal and Variable Cost Functions MC(y) y 0 Area is the variable cost of making y’ units $/output unit

27. Marginal & Average Cost Functions Since

28. Marginal & Average Cost Functions Since Therefore, as

29. Marginal & Average Cost Functions Since Therefore, as as

30. Marginal & Average Cost Functions as

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

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

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

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

35. $/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.

36. Marginal & Average Cost Functions Similarly, since

37. Marginal & Average Cost Functions Similarly, since Therefore, as

38. Marginal & Average Cost Functions Similarly, since Therefore, as as

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

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

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

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

45. 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  ) c s (y;x 2  ) $ F 

46. 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  ) c s (y;x 2  ) $ F 

47. Short-Run & Long-Run Total Cost Curves 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

48. Short-Run & Long-Run Total Cost Curves 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.

49. Short-Run & Long-Run Total Cost Curves 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

50. Short-Run & Long-Run Total Cost Curves 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

51. Short-Run & Long-Run Total Cost Curves is the slope of the firm’s total cost curve.

52. Short-Run & Long-Run Total Cost Curves is the slope of the firm’s total cost curve. 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.

53. 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  ) c s (y;x 2  ) $ F 

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

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

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

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

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

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

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

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

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

69. 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.

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

74. 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  )

75. 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)

76. 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)

77. 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.

79. 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.

82. Short-Run & Long-Run Marginal Cost Curves AC(y) $/output unit y SRACs

83. Short-Run & Long-Run Marginal Cost Curves AC(y) $/output unit y SRMCs