1. Lecture 9: The Cost of Production
Readings: Chapters 11

2. The Cost of Production
What determines the shape of the firm’s total cost curve?
The shape of the total cost curve depends on:
Input prices
Technology

3. The Cost of Production: the Production Function
Q: How are input prices and technology related to a firm’s cost curve?
Begin with a model of a firm’s organizational problem in which the firm is assumed to:
Purchase L units of homogeneous labour in a competitive labour market for price w.
Have invested K units of homogeneous capital which earns the competitive capital market price i.
Combine K units of capital and L units of labour to produce Q units of output, each unit of which is sold in a competitive output market for price p

4. The Cost of Production wL PQ K L Q Financial Flows iK Physical Flows
Physical Stocks

5. The Cost of Production : the Production Function
Q: What sort of decision model is this?
The firm has two planning horizons
short run — at least one fixed input; other inputs variable
long run — all inputs are variable
This is a short-run decision model in which the firm’s capital stock is fixed.
The firm can alter its capital stock over the long-run by altering investment flows.

6. The Cost of Production : the Production Function
Q: What determines the short-run relationship between labour input flows and output flows?
Two things govern this relationship:
1. The amount of capital (K).
2. The technology available to the firm.
Q: How can this relationship be characterized?
A production function: Q=f(L)

7. The Cost of Production : the Production Function
Q: What do most production functions look like?
The graph of most production functions are S shaped curves called Total Product (TP) curves.
The TP curve divides the set into an technically feasible and unfeasible sets.
The curve itself provides all the technically efficient plans available to the firm.

8. The Cost of Production: the Production Function
Total Product Curve
Figure 11.1 shows a total product curve.
The total product curve shows how total product changes with the quantity of labour employed.

10. The Cost of Production: the Production Function
The total product curve is similar to the PPF.
It separates attainable output levels from unattainable output levels in the short run.

11. The Cost of Production: Productivity
Marginal Product Curve
Figure 11.2 shows the marginal product of labour curve and how the marginal product curve relates to the total product curve.
The first worker hired produces 4 units of output.

13. The Cost of Production: Productivity
The second worker hired produces 6 units of output and total product becomes 10 units.
The third worker produces 3 units of output and total product becomes 13 units.
And so on.

14. The Cost of Production: Productivity
Q: Why does the TP curve for most firms have this characteristic S shape?
A: The S shape reflects the common experience that, for a given plant size, additions of labour initially cause the Marginal Product of Labour (MPL) to rise, but eventually the MPL will fall.
Q: What is the MPL?
A: The MPL is the addition to TP (output) that an additional worker would add: MPL = (DTP / DL)

15. The Cost of Production: Productivity
To make a graph of the marginal product of labour, we can stack the bars in the previous graph side by side.
The marginal product of labour curve passes through the mid-points of these bars.

16. Deriving Marginal Product From Total Product
Output TP 15 d 13 10 c 4 1 2 3 4 5
Labour MP 6 4 3 2
MPL 1 2 3 4 5
Labour
Copyright © 1997 Addison-Wesley Publishers Ltd.
Textbook p. 213

17. The Cost of Production: Productivity
Diminishing Marginal Returns Eventually
When the marginal product of a worker is less than the marginal product of the previous worker, the marginal product of labour decreases.
The firm experiences diminishing marginal returns.

18. The Cost of Production: Productivity
Q: Is there a quick way to derive the MPL curve from the TP curve?
A: At each level of employment (L), the slope of the tangent to the TP curve gives the MPL.
Q: Where is the dividing line between increasing and decreasing marginal returns to labour?
A: The inflection point on the TP curve.

19. The Cost of Production: ProductivityQ TP 3 1 L 3
MPL L

20. The Cost of Production: Productivity
Q: Is there a general productivity law implicit in this model of the production relationship?
A: The underlying principle is the Law of diminishing returns: given a certain level of fixed factor input (K), increases in the variable factor input (L) will eventually result in diminishing marginal product of the variable input (MPL)
Marginal Product can be calculated for any variable input (ie the MP of chemical fertilizer)

21. The Cost of Production: Productivity
Q: Are there other measures of productivity?
A: Average Product of Labour: APL = (TP / L)
The APL is the most popular measure of technical productivity. It is frequently misused as a measure of efficiency.
Average Product can be calculated for any variable input (ie the AP of chemical fertilizer)
Average Product is not a measure of efficiency

22. The Cost of Production: Productivity
Q: Is there a quick way to derive the APL curve from the TP curve?
A: At each level of employment (L), the slope of a line drawn through the TP curve gives the APL
Q: Where is the dividing line between increasing and decreasing average returns to labour?
A: Where a line drawn from the origin just touches the TP curve as a tangent.

23. The Cost of Production: ProductivityQ TP L
APL
MPL L

24. The Cost of Production: Productivity
Q: Does the declining MPL curve always pass down through the maximum of the APL curve?
As L ­, MP increases, reaches a maximum, and then declines
when MP > AP, AP ­
when MP < AP, AP ¯
when MP = AP, maximum AP

25. The Cost of Production: Productivity
When marginal product exceeds average product, average product increases.
When marginal product is below average product, average product decreases.
When marginal product equals average product, average product is at its maximum.

26. The Cost of Production: Productivity
The technological productivity of a firm can be described using the TP, APL, and MPL curves.
Q: Is technological productivity the same as economic efficiency?
No a more technologically productive (or technologically efficient) process will produce the same output with fewer factor inputs. A more economically efficient process will produce the same output at a lower opportunity cost.

27. The Short-Run Cost of Production
Q: What is the relationship between the technological efficiency and the firm’s costs?
A: Step 1: Invert the TP curve L Q L Q

28. The Short-Run Cost of Production
Step 2: Multiply the inverted TP curve by w to give the firm’s total variable cost (TVC) curve
TVC = wL(Q) $ Q

29. The Short-Run Cost of Production
In addition to the variable cost of labour is the fixed cost of paying for the factory.
Short-run cost curves
TC = TFC + TVC = Total Cost
TFC = total fixed cost
= cost of fixed inputs
TVC = total variable cost = cost of variable inputs
In our simple model Total Costs are:
TC = TFC + TVC = iK +wL
continued

30. The Short-Run Cost of Production
Total fixed cost is the same at each output level.
Total variable cost increases as output increases.
Total cost, which is the sum of TFC and TVC also increases as output increases.

32. The Short-Run Cost of Production
Q: The TP curve had a marginal product and average product curve associated with it. Does the TC curve have similar average and marginal curves associated with it?
A1: average total cost, ATC = TC/Q = AFC+AVC
average fixed cost = AFC = TFC / Q
average variable cost = AVC = TVC/ Q
A2: marginal cost, MC = DTC / DQ
MC = additional cost from one-unit increase in output Q
continued

33. The Short-Run Cost of Production
Q: What do the ATC and MC curves look like?
A: They can each be derived from the TC curve.
The ATC at each point on the TC curve is simply the slope of a line drawn from the origin through that point.
The MC at each point on the TC curve is simply the slope of a tangent line just touching the TC at that point.
The inflection point gives the minimum of the MC curve.

34. The Short-Run Cost of Production
Inflection Point Gives Minimum MC
TC = TFC +TVC $
Minimum of ATC curve
= MC Q

35. $ Q
ATC MC
$/Unit Q

36. The Short-Run Cost of Production
Q: What do the AFC and AVC curves look like?
The shape of these curves can be deduced using the same process as used to deduce the shape of the ATC curve.
With a little thought it is clear that the AVC is bowl shaped and the AFC is shaped like a rectangular hyperbole.

37. The Short-Run Cost of Production$
TFC Q
AFC Q

38. The Short-Run Cost of Production
The AVC curve is U-shaped. As output increases, average variable cost falls to a minimum and then increases.

40. The Short-Run Cost of Production
The ATC curve is also U-shaped.
The MC curve is very special.
The outputs over which AVC is falling, MC is below AVC.
The outputs over which AVC is rising, MC is above AVC.
The output at which AVC is at the minimum, MC equals AVC.

42. The Short-Run Cost of Production
Similarly, the outputs over which ATC is falling, MC is below ATC.
The outputs over which ATC is rising, MC is above ATC.
At the minimum ATC, MC equals ATC.

44. Marginal Cost and Average Costs
AVC
Cost 15 MC
ATC
AFC 10 5 5 10 15
Output
Copyright © 1997 Addison-Wesley Publishers Ltd.
Textbook p. 218

45. The Short-Run Cost of Production
AVC, ATC, and MC curves are U-shaped
As Q ­, MC ¯, reaches minimum, then MC­
when MC < ATC, ATC ¯
when MC > ATC, ATC ­
when MC = ATC, minimum ATC
same relation between MC and AVC
The critical result is that the rising MC curve cuts through the minimum point on the ATC and AVC curves.

46. The Short Run Cost of Production and Productivity
Q: What is the relationship between productivity and the cost of producing?
The relationship is simple:
The AVC is at a minimum when the APL is at a maximum
The MC is at a minimum when the MPL is at a maximum

47. Product Curves and Cost Curves
AP, MP
Max. AP,
Min. MC
­ MP,¯ MC;
­ AP,¯ AVC
Max. AP,
Min. AVC AP
¯ MP,­ MC;
­ AP,¯ AVC MP
¯ MP,­ MC;
¯ AP, ­ AVC 1 2
Labour
Cost MC
AVC 4 10 Q
Copyright © 1997 Addison-Wesley Publishers Ltd.
Textbook p. 219

48. The Long-Run Cost of Production
Q: What is the relationship between factor inputs and output in the Long-run?
In the long-run, all factors are variable, and there is no distinction between stocks and flows.
This implies that all costs are variable.
In our simple model this means that capital (K) is just as variable as labour (L).
The production function describing the maximum output associated with various input combinations would be Q = F(K,L)
continued

49. The Long-Run Cost of ProductionwL PQ
Q = f (K,L) L Q iK K
Financial Flows
Physical Flows

50. The Production Function
Long-Run Cost
The Production Function
The behavior of long-run cost depends upon the firm’s production function.
The firm’s production function is the relationship between the maximum output attainable and the quantities of both capital and labour.
The firm’s transition between the short run and long run revolves around the commitments made by the firm
Be sure the students realize that accurate forecasting of market demand for a firm’s product is key to profitability, since it must make the proper long-run commitment to a given plant size. Show the students that if faulty market analysis causes a firm to commit to a plant that is too small (too large) when the required range of production is actually relatively high (relatively low), the firm will suddenly be locked into a much less competitive production cost situation with potentially dire consequences.

51. Long-Run Cost Table 11.3 shows a firm’s production function.
As the size of the plant increases, the output that a given quantity of labour can produce increases.
But as the quantity of labour increases, diminishing returns occur for each plant.

53. Long-Run Cost
Diminishing Marginal Product of Capital
The marginal product of capital is the increase in output resulting from a one-unit increase in the amount of capital employed, holding constant the amount of labour employed.
A firm’s production function exhibits diminishing marginal returns to labour (for a given plant) as well as diminishing marginal returns to capital (for a quantity of labour).
For each plant, diminishing marginal product of labour creates a set of short run, U-shaped costs curves for MC, AVC, and ATC.

54. Long-Run Cost
Short-Run Cost and Long-Run Cost
The average cost of producing a given output varies and depends on the firm’s plant.
The larger the plant, the greater is the output at which ATC is at a minimum.
The firm has 4 different plants: 1, 2, 3, or 4 knitting machines.
Each plant has a short-run ATC curve.
The firm can compare the ATC for each output at different plants.

55. Long-Run Cost
ATC1 is the ATC curve for a plant with 1 knitting machine.

57. Long-Run Cost
ATC2 is the ATC curve for a plant with 2 knitting machines.

58. Long-Run Cost
ATC3 is the ATC curve for a plant with 3 knitting machines.

59. Long-Run Cost
ATC4 is the ATC curve for a plant with 4 knitting machines.

60. Long-Run Cost
The long-run average cost curve is made up from the lowest ATC for each output level.
So, we want to decide which plant has the lowest cost for producing each output level.
Let’s find the least-cost way of producing a given output level.
Suppose that the firm wants to produce 13 sweaters a day.

61. Long-Run Cost
13 sweaters a day cost $7.69 each on ATC1.

63. Long-Run Cost
13 sweaters a day cost $6.80 each on ATC2.

64. Long-Run Cost
13 sweaters a day cost $7.69 each on ATC3.

65. Long-Run Cost
13 sweaters a day cost $9.50 each on ATC4.

66. Long-Run Cost 13 sweaters a day cost $6.80 each on ATC2.
The least-cost way of producing 13 sweaters a day.

67. Long-Run Cost
Long-Run Average Cost Curve
The long-run average cost curve is the relationship between the lowest attainable average total cost and output when both the plant and labour are varied.
The long-run average cost curve is a planning curve that tells the firm the plant that minimizes the cost of producing a given output range.
Once the firm has chosen its plant, the firm incurs the costs that correspond to the ATC curve for that plant.

68. Long-Run Cost
Figure 11.8 illustrates the long-run average cost (LRAC) curve.

70. Long Run Cost and Productivity
Economies and Diseconomies of Scale
Economies of scale are features of a firm’s technology that lead to falling long-run average cost as output increases.
Diseconomies of scale are features of a firm’s technology that lead to rising long-run average cost as output increases.
Constant returns to scale are features of a firm’s technology that lead to constant long-run average cost as output increases.

71. Long Run Cost and Productivity
Figure 11.8 illustrates economies and diseconomies of scale.

73. Long Run Cost and Productivity
Minimum Efficient Scale
A firm experiences economies of scale up to some output level.
Beyond that output level, it moves into constant returns to scale or diseconomies of scale.
Minimum efficient scale is the smallest quantity of output at which the long-run average cost reaches its lowest level.
If the long-run average cost curve is U-shaped, the minimum point identifies the minimum efficient scale output level.

74. Long Run Cost and Productivity
SRACa Q0
Economies
of scale
ATC0 Q1
LRAC
SRACb
Diseconomies
of scale Q2
Constant returns
to scale Q
Copyright © 1997 Addison-Wesley Publishers Ltd.
Textbook p. 225

75. Long Run Cost and Productivity
Q: How is technical efficiency be described in the long-run?
Returns to Scale
constant returns to scale %­ output = %­ inputs
increasing returns to scale
(economies of scale) % ­ output > % ­ inputs
decreasing returns to scale
(diseconomies of scale) % ­ output < % ­ inputs
continued

76. Long Run Cost
Q: What does the TC, ATC and MC curves look like in the long-run?
Very much like the short-run curves. The only difference is that there are no fixed costs and all costs are variable costs.
Assuming that there are economies of scale that eventually end and are replaced with diminishing returns to scale, the cost function would have the standard shape.

77. LRTC $
LRMC
LRAC Q
$/Unit Q

78. Long-Run Cost
There is no AVC and no AFC because everything is variable and nothing is fixed.
Furthermore, the LRTC curve begins at the origin because of the absence of fixed costs.
End of Lecture 9