1. Economics of Input and Product Substitution
Chapter 7

2. Topics of Discussion Concepts of isoquants and iso-cost line
Least-cost use of inputs
Long-run expansion of input use
Economics of business expansion and contraction
Production possibilities frontier
Profit maximizing combination of products

3. Physical Relationships

4. Isoquant means “equal quantity”
Output is
identical along
an isoquant
Two inputs
Page 133

5. Slope of an Isoquant MRTS = Capital ÷ labor
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
Page 133

6. Slope of an Isoquant MRTS = Capital ÷ labor
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.
Page 133

7. MRTS
here is
-4÷1= -4
Page 133

8. What is the slope over
range B?
Page 133

9. What is the slope over
range B?
MRTS
here is
-1÷1= -1
Page 133

10. What is the slope over
range C?
Page 133

11. What is the slope over
range C?
MRTS
here is
-.5÷1= -.5
Page 133

12. Introducing Input Prices

13. Plotting the Iso-Cost Line
Firm can afford 10 units of
capital at a rental rate of $100
for a budget of $1,000
Capital 10
Labor
100
Page 136

14. Plotting the Iso-Cost Line
Firm can afford 10 units of
capital at a rental rate of $100
for a budget of $1,000
Capital 10
Firm can afford 100 units of
labor at a wage rate of $10 for
a budget of $1,000
Labor
100
Page 136

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 135

16. Line AB represents the original iso-cost line for capital and labor…
Change in budget or both costs
Line AB represents
the original iso-cost
line for capital and
labor…
Change in wage rate
Change in rental rate
Page 136

17. Page 136 The iso-cost line would shift out
Original iso-cost line
Change in budget or both costs
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.
Change in wage rate
Change in rental rate
Page 136

18. Original iso-cost line
Change in budget or both costs
Change in wage rate
Change in rental rate
If wage rates fell in half, the line would shift out to AF. The iso-cost line would shift in to line AD if wage rates doubled…
Page 136

19. The iso-cost line would shift out to line BE if rental
Original iso-cost line
Change in budget or both costs
Change in wage rate
Change in rental rate
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…
Page 136

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:
MPPLABOR ÷ MPPCAPITAL = -(wage rate ÷ rental rate)
Slope of an
isoquant
Slope of iso-
cost line
Page 139

22. Least Cost Decision Rule
The least cost combination of labor and capital in out example also occurs where:
MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate
MPP per dollar
spent on labor
MPP per dollar
spent on capital =
Page 139

23. Least Cost Decision Rule
This decision rule holds for a larger number of inputs as well…
The least cost combination of labor and capital in out example also occurs where:
MPPLABOR ÷ wage rate = MPPCAPITAL ÷ rental rate
MPP per dollar
spent on labor
MPP per dollar
spent on capital =
Page 139

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

25. Least Cost Input Choice for 100 Units
Iso-cost line for $1,000.
Its slope reflects price of
labor and capital.
Page 138

26. We can determine this graphically by observing where these two curves
Least Cost Input Choice for 100 Units
We can determine
this graphically by
observing where
these two curves
are tangent….
Page 138

27. Least Cost Input Choice for 100 Units
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
Page 138

28. Least Cost Input Choice for 100 Units
At the point of tangency, we know that:
slope of isoquant = slope of iso-cost line, or…
MPPLABOR ÷ MPPCAPITAL = - (wage rate ÷ rental rate)
Page 138

29. 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.
Page 138

30. Least Cost Input Choice for 100 Units
This therefore represents
the cheapest combination of capital and labor to produce 100 units of output…
Page 138

31. Least Cost Input Choice for 100 Units
If I told you the value of C1
and L1 and asked you for
the value of A* and B*,
how would you find them?
Page 138

32. Least Cost Input Choice for 100 Units
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 7 60
Page 138

33. Least Cost Input Choice for 100 Units
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 7 60
130
Page 138

34. Least Cost Input Choice for 100 Units
And the rental rate is $100, then point A* must represents 13 units of capital, or:
$1,300 $100 = 13 13 7 60
130
Page 138

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

36. What Happens if Wage Rate Declines?
Assume the initial
wage rate and cost
of capital results in
the iso-cost line AB
Page 140

37. What Happens if Wage Rate Declines?
means that the firm
can now afford B*
instead of B…
Page 140

38. What Happens if Wage Rate Declines?
The new point of tangency
occurs at H rather than G.
Page 140

39. What Happens if Wage Rate Declines?
As a consequence,
the firm would
desire to use more
labor and less
capital…
Page 140

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

41. What Inputs to Use for a Specific Budget?M
An iso-cost line for
a specific budget
Capital N
Labor
Page 141

42. What Inputs to Use for a Specific Budget?
A set of isoquants
for different levels
of output…
Page 141

43. What Inputs to Use for a Specific Budget?
Firm can afford to
produce only 75 units
of output using C3 units
of capital and L3 units
of labor
Page 141

44. What Inputs to Use for a Specific Budget?
The firm’s budget
is not large enough
to operate at 100
or 125 units…
Page 141

45. What Inputs to Use for a Specific Budget?
Firm is not spending
available budget here…
Page 141

46. Economics of Business Expansion

47. The Planning Curve SAC = LAC = PLR
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 (QLR) of the firm:
SAC = LAC = PLR
where MC represents marginal cost and PLR represents the long run price, respectively.
Page 145

48. What can we say about the four
firms in this graph?
Page 145

49. Size 1 would lose
money at price P
Page 145

50. Firm size 2, 3 and 4
would earn a profit
at price P…. Q3
Page 145

51. Firm #2’s profit would be the area shown below…Q3
Page 145

52. Firm #3’s profit would be the area shown below…Q3
Page 145

53. Firm #4’s profit would be the area shown below…Q3
Page 145

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

55. How to Expand Firm’s Capacity
Optimal input
combination
for output=10
Page 146

56. How to Expand Firm’s Capacity
Two options:
1. Point B ?
Page 146

57. How to Expand Firm’s Capacity
Two options:
1. Point B?
2. Point C?
Page 146

58. Expanding Firm’s Capacity
Optimal input
combination
for output=20
with budget FG
Optimal input
combination
for output=10
with budget DE
Page 146

59. Expanding Firm’s Capacity
This combination
costs more to
produce 20 units
of output since
budget HI exceeds
budget FG
Page 146

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. Shows the substitution between two products given the most efficient
use of firm’s resources
Page 149

62. Slope of the PPF MRPT =  canned fruit ÷ canned vegetables
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 148

63. Slope over range between D and E is –1.30, or: -1310 Page 149
Drops from
108 to 95
Increases from
30 to 40
Page 149

64. 95,000
- 108,000
-13,000
40,000
30,000
10,000 ÷ =
- 1.30
Page 148

65. Inefficient
use of firm’s
resources
Page 149

66. Level of output unattainable with with firm’s existing resources
Inefficient
use of firm’s
existing resources
Page 149

67. Accounting for Product Prices

68. Plotting the Iso-Revenue Line
30,000 cases of canned fruit
required at price of $33.33/case
to achieve A TARGET revenue
of $1 million
Canned
fruit
30,000
Canned
vegetables
40,000
Page 150

69. Plotting the Iso-Revenue Line
30,000 cases of canned fruit
required at price of $33.33/case
to achieve revenue of $1 million
Canned
fruit
30,000
40,000 cases of canned vegetables
required at price of $25.00/case
to achieve revenue of $1 million
Canned
vegetables
40,000
Page 150

70. iso-revenue line, indicating the number of cases needed
Original iso-revenue line
Changes in income or both prices
Line AB is the original
iso-revenue line, indicating
the number of cases needed
to reach a specific sales
target.
Change in price of fruit
Change in price of vegetables
Page 150

71. 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.
Original iso-revenue line
Changes in income or both prices
Change in price of fruit
Change in price of vegetables
Page 150

72. The iso-revenue line would shift out to line BC is the
Original iso-revenue line
Changes in income or both prices
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
Change in price of fruit
Change in price of vegetables
Page 150

73. The iso-revenue line would shift out to line AD if the
Original iso-revenue line
Changes in income or both prices
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.
Change in price of fruit
Change in price of vegetables
Page 150

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
= –
Slope of an
PPF curve
Slope of iso-
revenue line
Page 152

76. Assume Line AB represents revenue for $1 million.
Page 153

77. We want to find the profit maximizing combination to “can”
given the current
prices of canned fruit
and vegetables.
Page 153

78. 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
Page 153

79. Page 152 125,000 18,000 MRPT cases of cases of equals fruit vegetables
-0.75
Page 152

80. Price ratio = -($25.00 ÷ $33.33) = - 0.75 Page 152 125,000 18,000 MRPT
cases of
fruit
18,000
cases of
vegetables
MRPT
equals
-0.75
Page 152

81. = – Price ratio = -($25.00 ÷ $33.33) = - 0.75
125,000
cases of
fruit
18,000
cases of
vegetables
MRPT
equals
-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 $ 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 × $ ,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 × $ ,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. 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.
Page 153

86. This gives us a new iso-revenue curve… line CB.
Page 153

87. 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….
Page 153

88. 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.
Page 153

89. 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.
Page 153

90. Summary #1 Concepts of iso-cost line and isoquants
Marginal rate of technical substitution (MRTS)
Least cost combination of inputs for a specific output level
Effects of change in input price
Level of output and combination of inputs for a specific budget
Key decision rule …seek point where MRTS = ratio of input prices, or where MPP per dollar spent on inputs are equal

91. Summary #2
Concepts of iso-revenue line and the production possibilities frontier
Marginal rate of product transformation (MRPT)
Concept of profit maximizing combination of products
Effects of change in product price
Key decision rule – maximize profits where MRPT equals the ratio of the product prices

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