This chapter discusses concepts related to production including isoquants, iso-cost lines, and production possibilities frontiers. It examines finding the least-cost combination of inputs and the profit-maximizing combination of outputs. A change in input or output prices will shift the iso-cost line or iso-revenue line and alter the optimal production levels. The key concepts are that production is most efficient where the marginal rate of technical substitution equals the input price ratio and profits are maximized where the marginal rate of product transformation equals the output price ratio.

1. Economics of Input and Product Substitution Chapter 7

3. Physical Relationships

4. Page 107 Output is identical along an isoquant Isoquant means “equal quantity” Two inputs

5. Slope of an Isoquant The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution, or MRTS. The value of the MRTS in our example is given by: MRTS =  Capital ÷  labor Pages 106-107

6. Slope of an Isoquant The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution, or MRTS. The value of the MRTS in our example is given by: MRTS =  Capital ÷  labor If output remains unchanged along an isoquant, the loss in output from decreasing labor must be identical to the gain in output from adding capital. Pages 106-107

7. Page 107 MRTS here is -4 ÷1= -4

8. Page 107 What is the slope over range B?

9. Page 107 What is the slope over range B? MRTS here is -1 ÷1= -1

10. Page 107 What is the slope over range C?

11. Page 107 What is the slope over range C? MRTS here is -.5 ÷1= -.5

12. Introducing Input Prices

13. Plotting the Iso-Cost Line Capital Labor Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1,000 Page 109 10 100

14. Plotting the Iso-Cost Line Capital Labor Firm can afford 100 units of labor at a wage rate of $10 for a budget of $1,000 Page 109 10 100 Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1,000

15. Slope of an Iso-cost Line The slope of an iso-cost in our example is given by: Slope = - (wage rate ÷ rental rate) or the negative of the ratio of the price of the two Inputs. See footnote 5 on page 179 for the derivation of this slope based upon the budget constraint ( hint: solve equation below for the use of capital ). ( $10 × use of labor )+( $100 × use of capital )=$1,000 Page 109

16. Original iso-cost line Change in budget or both costs Change in wage rate Change in rental rate Page 109 Line AB represents the original iso-cost line for capital and labor…

17. Original iso-cost line Change in budget or both costs Change in wage rate Change in rental rate Page 109 The iso-cost line would shift out to line EF if the firm’s available budget doubled (or costs fell in half) or back to line CD if the available budget halved (or costs doubled.

18. Original iso-cost line Change in budget or both costs Change in wage rate Change in rental rate Page 109 If wage rates doubled the line would shift out to AF while the iso-cost line would shift in to line AD if wage rates doubled…

19. Original iso-cost line Change in budget or both costs Change in wage rate Change in rental rate Page 109 The iso-cost line would shift out to line BE if rental rate fell in half while the line would shift in to line BC if the rental rate for capital doubled…

20. Least Cost Combination of Inputs

21. Least Cost Decision Rule The least cost combination of two inputs (labor and capital in our example) occurs where the slope of the iso-cost list is tangent to the isoquant: MPP LABOR ÷ MPP CAPITAL = -(wage rate ÷ rental rate) Page 111 Slope of an isoquant Slope of iso- cost line

22. Least Cost Decision Rule The least cost combination of labor and capital in out example also occurs where: MPP LABOR ÷ wage rate = MPP CAPITAL ÷ rental rate Page 111 MPP per dollar spent on labor MPP per dollar spent on capital =

23. Least Cost Decision Rule The least cost combination of labor and capital in out example also occurs where: MPP LABOR ÷ wage rate = MPP CAPITAL ÷ rental rate Page 111 MPP per dollar spent on labor MPP per dollar spent on capital = This decision rule holds for a larger number of inputs as well…

24. Least Cost Combination of Inputs to Produce a Specific Level of Output

25. Page 111 Iso-cost line for $1,000. Its slope reflects price of labor and capital. Least Cost Input Choice for 100 Units

26. Page 111 Least Cost Input Choice for 100 Units We can determine this graphically by observing where these two curves are tangent ….

27. Page 111 We can shift the original iso-cost line from AB out in a parallel fashion to A*B* (which leaves prices unchanged) which just touches the isoquant at G Least Cost Input Choice for 100 Units

28. Page 111 Least Cost Input Choice for 100 Units At the point of tangency, we know that: slope of isoquant = slope of iso-cost line, or… MPP LABOR ÷ MPP CAPITAL = - (wage rate ÷ rental rate)

29. Page 111 Least Cost Input Choice for 100 Units At the point of tangency, therefore, the MPP per dollar spent on labor is equal to the MPP per dollar spent on capital!!! See equation (8.5) on page 181, which is analogous to equation (4.2) back on page 76 for consumers.

30. This therefore represents the cheapest combination of capital and labor to produce 100 units of output… Page 111 Least Cost Input Choice for 100 Units

31. If I told you the value of C 1 and L 1 and asked you for the value of A* and B*, how would you find them? Page 111 Least Cost Input Choice for 100 Units

32. If I told you that point G represents 7 units of capital and 60 units of labor, and that the wage rate is $10 and the rental rate is $100, then at point G we must be spending $1,300, or: $100 × 7+$10 × 60=$1,300 Page 111 Least Cost Input Choice for 100 Units 7 60

33. Page 111 Least Cost Input Choice for 100 Units 130 7 60 If point G represents a total cost of $1,300, we know that every point on this iso-cost line also represents $1,300. If the wage rate is $10, then point B* must represent 130 units of labor, or: $1,300  $10 = 130

34. Page 111 Least Cost Input Choice for 100 Units 130 13 7 60 And the rental rate is $100, then point A* must represents 13 units of capital, or: $1,300  $100 = 13

35. What Happens if the Price of an Input Changes?

36. Page 112 Assume the initial wage rate and cost of capital results in the iso-cost line AB What Happens if Wage Rate Declines?

37. Page 112 Wage rate decline means that the firm can now afford B* instead of B… What Happens if Wage Rate Declines?

38. Page 112 What Happens if Wage Rate Declines? The new point of tangency occurs at H rather than G.

39. Page 112 What Happens if Wage Rate Declines? As a consequence, the firm would desire to use more labor and less capital…

40. Least Cost Combination of Inputs and Output for a Specific Budget

41. What Inputs to Use for a Specific Budget? M N Labor Capital An iso-cost line for a specific budget Page 113

42. Page 113 What Inputs to Use for a Specific Budget? A set of isoquants for different levels of output…

43. Page 113 Firm can afford to produce only 75 units of output using C 3 units of capital and L 3 units of labor What Inputs to Use for a Specific Budget?

44. Page 113 The firm’s budget is not large enough to operate at 100 or 125 units… What Inputs to Use for a Specific Budget?

45. Page 113 Firm is not spending available budget here… What Inputs to Use for a Specific Budget?

46. Economics of Business Expansion

47. The Planning Curve The long run average cost (LAC) curve reflects points of tangency with a series of short run average total cost (SAC) curves. The point on the LAC where the following holds is the long run equilibrium position (Q LR ) of the firm: SAC = LAC = P LR where MC represents marginal cost and P LR represents the long run price, respectively. Page 114

48. Page 117 What can we say about the four firms in this graph?

49. Page 117 Size 1 would lose money at price P

50. Page 117 Q 3 Firm size 2, 3 and 4 would earn a profit at price P….

51. Page 117 Q 3 Firm #2’s profit would be the area shown below…

52. Page 117 Q 3 Firm #3’s profit would be the area shown below…

53. Page 117 Q 3 Firm #4’s profit would be the area shown below…

54. Page 145 If price were to fall to P LR , only size 3 would not lose money; it would break-even . Size 4 would have to down size its operations!

55. Page 118 Optimal input combination for output=10 How to Expand Firm’s Capacity

56. Page 118 How to Expand Firm’s Capacity Two options: 1. Point B ?

57. Page 118 How to Expand Firm’s Capacity Two options: 1. Point B? 2. Point C?

58. Page 118 Optimal input combination for output=10 with budget DE Optimal input combination for output=20 with budget FG Expanding Firm’s Capacity

59. Page 118 This combination costs more to produce 20 units of output since budget HI exceeds budget FG Expanding Firm’s Capacity

60. Production Possibilities The goal is to find that combination of products that maximizes revenue for the maximum technical efficiency on the production possibilities frontier.

61. Page 120 Shows the substitution between two products given the most efficient use of firm’s resources

62. Slope of the PPF The slope of the production possibilities curve is referred to as the Marginal Rate of Product Transformation , or MRPT. The value of the MRPT in our example is given by: MRPT =  canned fruit ÷  canned vegetables Page 119

63. Page 120 Drops from 108 to 95 Increases from 30 to 40 Slope over range between D and E is –1.30, or: -13  10

65. Page 120 Inefficient use of firm’s resources

66. Page 120 Level of output unattainable with with firm’s existing resources Inefficient use of firm’s existing resources

67. Accounting for Product Prices

68. Plotting the Iso-Revenue Line Canned fruit Canned vegetables 30,000 cases of canned fruit required at price of $33.33/case to achieve A TARGET revenue of $1 million Page 122 30,000 40,000

69. Plotting the Iso-Revenue Line Canned fruit Canned vegetables 40,000 cases of canned vegetables required at price of $25.00/case to achieve revenue of $1 million Page 122 30,000 40,000 30,000 cases of canned fruit required at price of $33.33/case to achieve revenue of $1 million

70. Page 122 Original iso-revenue line Changes in income or both prices Change in price of fruit Change in price of vegetables Line AB is the original iso-revenue line, indicating the number of cases needed to reach a specific sales target.

71. Page 122 Original iso-revenue line Changes in income or both prices Change in price of fruit Change in price of vegetables The iso-revenue line would shift out to line EF if the revenue target doubled (or prices fell in half) while the line would shift in to line CD if revenue targets fell in half or prices doubled.

72. Page 122 Original iso-revenue line Changes in income or both prices Change in price of fruit Change in price of vegetables The iso-revenue line would shift out to line BC is the price of fruit fell in half but shift in to line BD if the price of fruit doubled

73. Page 122 Original iso-revenue line Changes in income or both prices Change in price of fruit Change in price of vegetables The iso-revenue line would shift out to line AD if the price of vegetables fell in half but shift in to line AC is the price of fruit doubled.

74. Profit Maximizing combination of Product Prices

75. Combination of Products The profit maximizing combination of two products is found where the slope of the production possibilities frontier (PPF) is equal to the slope of the iso-revenue Curve, or where:  Canned fruit Price of vegetables  Canned vegetables Price of fruit = – Page 124 Slope of an PPF curve Slope of iso- revenue line

76. Page 124 Assume Line AB represents revenue for $1 million.

77. Page 124 We want to find the profit maximizing combination to “can” given the current prices of canned fruit and vegetables.

78. Page 124  Canned fruit Price of vegetables  Canned vegetables Price of fruit = – Shifting line AB out in a parallel fashion holds both prices constant at their current level

79. Page 120 18,000 cases of vege- tables MRPT equals -0.75 125,000 cases of fruit

80. Page 120 18,000 cases of vege- tables MRPT equals -0.75 125,000 cases of fruit Price ratio = -($25.00 ÷ $33.33) = - 0.75

81. 18,000 cases of vege- tables MRPT equals -0.75 125,000 cases of fruit Price ratio = -($25.00 ÷ $33.33) = - 0.75  Canned fruit Price of vegetables  Canned vegetables Price of fruit = – Page 152

82. Doing the Math… Let’s assume the price of a case of canned fruit is $33.33 while the price of a case of canned vegetables is $25.00 . If point M represents 125,000 cases of fruit and 18,000 cases of vegetables, then total revenue at point M is: Revenue = 125,000 × $33.33 + 18,000 × $25.00 = $4,166,250 + $450,000 = $4,616,250

83. Doing the Math… At these same prices, if we instead produce 108,000 cases of fruit and and 30,000 cases of vegetables, then total revenue would fall to: Revenue = 108,000 × $33.33 + 30,000 × $25.00 = $3,599,640 + $750,000 = $4,349,640 which is $266,610 less than the $4,616,250 earned at point M.

84. Effects of a Change in the Price of One Product

85. Page 125 If the price of canned fruit fell in half, the firm must sell twice as many cases of canned fruit to earn $1 million if it focused solely on fruit production.

86. Page 125 This gives us a new iso-revenue curve… line CB.

87. Page 125 To see the effects of this price change, we can shift the new iso-revenue curve out to the point of tangency with the PPF curve….

88. Page 125 Shifting the new iso-revenue curve in a parallel fashion out to a point of tangency with the PPF curve, we get a new combination of products required to maximize profit.

89. Page 125 The firm would shift from point M on the PPF to point N as a result of the decline in the price of fruit. That is, to maximize profit, the firm would cut back its production of canned fruit and produce more canned vegetables.

92. Chapter 8 focuses on market equilibrium conditions under perfect competition ….