0. Unit V
Production Costs (Chapter 12)

1. In this chapter, look for the answers to these questions:
What is a production function? What is marginal product? How are they related?
What are the various costs, and how are they related to each other and to output?
How are costs different in the short run vs. the long run?
What are “economies of scale”?

2. Short Run and Long run The Short Run: Fixed Plant
The Short Run: Fixed Plant
The short run is a time frame in which the quantities of some resources are fixed.
In the short run, a firm can usually change the quantity of labor it uses but not the quantity of capital.
The Long Run: Variable Plant
The long run is a time frame in which the quantities of all resources can be changed.
A sunk cost is irrelevant to the firm’s decisions.

3. Short Run Production
To increase output with a fixed plant, a firm must increase the quantity of labor it uses.
We describe the relationship between output and the quantity of labor by using three related concepts:
Total product
Marginal product
Average product

4. The Production Function
A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good.
It can be represented by a table, equation, or graph.
Example:
Farmer Jack grows wheat.
He has 5 acres of land.
He can hire as many workers as he wants.

5. The Production Function
Total Product
Total product (TP) is the total quantity of a good produced in a given period.
Total product is an output rate—the number of units produced per unit of time.
Total product increases as the quantity of labor employed increases.

6. The Production Function
The figure shows the total product and the total product curve.
Points A through H on the curve correspond to the columns of the table.
The TP curve is like the PPF: It separates attainable points and unattainable points.

7. EXAMPLE: Farmer Jack’s Production Function
500
1,000
1,500
2,000
2,500
3,000 1 2 3 4 5
No. of workers
Quantity of output
Q (bushels of wheat)
L (no. of workers)
1000 1
1800 2
2400 3
2800 4
3000 5

8. Marginal Product
Marginal product is the change in total product that results from a one-unit increase in the quantity of labor employed.
Marginal product tells us the contribution to total product of adding one more worker.
E.g., if Farmer Jack hires one more worker, his output rises by the marginal product of labor.
Notation: ∆ (delta) = “change in…”
Examples: ∆Q = change in output, ∆L = change in labor
Marginal product of labor (MPL) = ∆Q ∆L

9. Marginal Product The figure shows total product and marginal product.
The figure shows total product and marginal product.
We can illustrate marginal product
as the orange bars that form steps along the total product curve.
The height of each step represents marginal product.

10. Marginal Product
The table calculates marginal product and the orange bars in part (b) illustrate it.
Notice that the steeper the slope of the TP curve, the greater is marginal product.

11. Marginal Product
The total product and marginal product curves in this figure incorporate a feature of all production processes:
Increasing marginal returns initially
Decreasing marginal returns eventually
Negative marginal returns

12. EXAMPLE: Total & Marginal Product
3000 5
2800 4
2400 3
1800 2
1000 1
Q (bushels of wheat)
L (no. of workers)
MPL
∆Q = 1000
∆L = 1
1000
∆Q = 800
∆L = 1
800
∆Q = 600
∆L = 1
600
∆Q = 400
∆L = 1
400
∆Q = 200
∆L = 1
200

13. EXAMPLE: MPL = Slope of Prod Function
500
1,000
1,500
2,000
2,500
3,000 1 2 3 4 5
No. of workers
Quantity of output
L (no. of workers)
Q (bushels of wheat)
MPL
MPL equals the slope of the production function.
Notice that MPL diminishes as L increases.
This explains why the production function gets flatter as L increases.
1000 1
1000
800 2
1800
600 3
2400
400 4
2800
200 5
3000

14. Why MPL Is Important Rational people think at the margin.
When Farmer Jack hires an extra worker,
his costs rise by the wage he pays the worker
his output rises by MPL
Comparing them helps Jack decide whether he would benefit from hiring the worker.

15. Increasing Marginal Returns
Increasing marginal returns occur when the marginal product of an additional worker exceeds the marginal product of the previous worker.
Increasing marginal returns occur when a small number of workers are employed and arise from increased specialization and division of labor in the production process.

16. Why MPL Diminishes
Decreasing marginal returns occur when the marginal product of an additional worker is less than the marginal product of the previous worker.
E.g., Farmer Jack’s output rises by a smaller and smaller amount for each additional worker. Why?
If Jack increases workers but not land, the average worker has less land to work with, so will be less productive.
In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.).

17. Why MPL Diminishes The law of decreasing returns states that:
Decreasing marginal returns are so pervasive that they qualify for the status of a law:
The law of decreasing returns states that:
As a firm uses more of a variable input, with a given quantity of fixed inputs, the marginal product of the variable input eventually decreases.

18. SHORT-RUN PRODUCTION
The figure graphs the average product against the quantity of labor employed.
The average product curve is AP.
When marginal product exceeds average product, average product is increasing.

19. SHORT-RUN PRODUCTION
When marginal product is less than average product, average product is decreasing.
When marginal product equals average product, average product is at its maximum.

20. SHORT-RUN COST
To produce more output in the short run, a firm employs more labor, which means the firm must increase its costs.
We describe the relationship between output and cost using three cost concepts:
Total cost
Marginal cost
Average cost

21. SHORT-RUN COST Total Cost Total Cost divides into two parts:
A firm’s total cost (TC) is the cost of all the factors of production the firm uses.
Total Cost divides into two parts:
Fixed cost (FC) is the cost of a firm’s fixed factors of production used by a firm—the cost of land, capital, and entrepreneurship.
Fixed costs don’t change as output changes.

22. SHORT-RUN COST TC = FC + VC
Variable cost (VC) is the cost of the variable factor of production used by a firm— the cost of labor.
To change its output in the short run, a firm must change the quantity of labor it employs, so total variable cost changes as output changes.
Total cost is the sum of total fixed cost and total variable cost. That is,
TC = FC + VC

23. SHORT-RUN COST
Fixed cost (FC) is constant—it graphs as a horizontal line.
Variable cost (VC) increases as output increases.
Total cost (TC) also increases as output increases.

24. SHORT-RUN COST
The vertical distance between the total cost curve and the total variable cost curve is total fixed cost, as illustrated by the two arrows.

25. Marginal Cost
Marginal Cost (MC) is the increase in Total Cost from producing one more unit:
∆TC ∆Q
MC =
Marginal cost tells us how total cost changes as total product changes.

26. EXAMPLE: Marginal CostQ TC MC
Recall, Marginal Cost (MC) is the change in total cost from producing one more unit:
$100
$70 1
170
∆TC ∆Q
MC = 50 2
220 40 3
260
Usually, MC rises as Q rises, due to diminishing marginal product.
Sometimes (as here), MC falls before rising.
(In other examples, MC may be constant.) 50 4
310 70 5
380
100 6
480
140 7
620

27. SHORT-RUN COST Average Cost
There are three average cost concepts:
Average fixed cost (AFC) is total fixed cost per unit of output.
Average variable cost (AVC) is total variable cost per unit of output.
Average total cost (ATC) is total cost per unit of output.

28. SHORT-RUN COST TC = TFC + TVC
The average cost concepts are calculated from the total cost concepts as follows:
TC = TFC + TVC
Divide each total cost term by the quantity produced, Q, to give
Q Q Q
TC = TFC + TVC
or,
ATC = AFC + AVC

29. A C T I V E L E A R N I N G 1: Costs
Fill in the blank spaces of this table. Q VC TC
AFC
AVC
ATC MC
$50
n.a.
n.a.
n.a.
$10 1 10
$10
$60.00 2 30 80 30 3
16.67 20
36.67 4
100
150
12.50
37.50 5
150 30 60 6
210
260
8.33 35
43.33

30. A C T I V E L E A R N I N G 1: Answers
Use ATC = TC/Q
Use AFC = FC/Q
Use relationship between MC and TC
Use AVC = VC/Q Q VC TC
AFC
AVC
ATC MC
First, deduce FC = $50 and use FC + VC = TC. $0
$50
n.a.
n.a.
n.a.
$10 1 10 60
$50.00
$10
$60.00 20 2 30 80
25.00 15
40.00 30 3 60
110
16.67 20
36.67 40 4
100
150
12.50 25
37.50 50 5
150
200
10.00 30
40.00 60 6
210
260
8.33 35
43.33

31. EXAMPLE: Average Fixed CostQ FC
AFC
Average fixed cost (AFC) is fixed cost divided by the quantity of output:
AFC = FC/Q
$100
14.29
16.67 20 25
33.33 50
$100
n.a. 1
100 2
100 3
100
Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units. 4
100 5
100 6
100 7
100

32. EXAMPLE: Average Variable CostQ VC
AVC
Average variable cost (AVC) is variable cost divided by the quantity of output:
AVC = VC/Q $0
74.29
63.33
56.00
52.50
53.33 60
$70
n.a. 1 70 2
120 3
160
As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. 4
210 5
280 6
380 7
520

33. EXAMPLE: Average Total Cost
Average total cost (ATC) equals total cost divided by the quantity of output:
ATC = TC/Q Q TC
ATC
74.29
14.29
63.33
16.67
56.00 20
52.50 25
53.33
33.33 60 50
$70
$100
n.a.
AVC
AFC
$100
88.57 80 76
77.50
86.67
110
$170
n.a. 1
170 2
220 3
260
Also,
ATC = AFC + AVC 4
310 5
380 6
480 7
620

34. EXAMPLE: Average Total Cost$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs Q TC
ATC
Usually, as in this example, the ATC curve is U-shaped.
$100
n.a. 1
170
$170 2
220
110 3
260
86.67 4
310
77.50 5
380 76 6
480 80 7
620
88.57

35. EXAMPLE: The Various Cost Curves Together
EXAMPLE: The Various Cost Curves Together $0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
ATC
AVC
AFC MC

36. SHORT-RUN COST
The vertical distance between these two curves is equal to average fixed cost, as illustrated by the two arrows.
REMEMBER -- The marginal cost curve (MC) intersects the average variable cost curve and the average total cost curve at their minimum points.

37. SHORT-RUN COST Why the Average Total Cost Curve Is U-Shaped
Average total cost, ATC, is the sum of average fixed
cost, AFC, and average variable cost, AVC.
The shape of the ATC curve combines the shapes of
the AFC and AVC curves.
The U shape of the average total cost curve arises
from the influence of two opposing forces:
Spreading total fixed cost over a larger output
Decreasing marginal returns

38. EXAMPLE: Why ATC Is Usually U-shaped$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
As Q rises:
Initially, falling AFC pulls ATC down.
Eventually, rising AVC pulls ATC up.

39. EXAMPLE: ATC and MC When MC < ATC, ATC ATC is falling.$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
When MC < ATC,
ATC is falling.
When MC > ATC,
ATC is rising.
The MC curve crosses the ATC curve at the ATC curve’s minimum.
ATC MC

40. SHORT-RUN COST Cost Curves and Product Curves
The technology that a firm uses determines its costs.
At low levels of employment and output, as the firm hires more labor, marginal product and average product rise, and marginal cost and average variable cost fall.
Then, at the point of maximum marginal product, marginal cost is a minimum.
As the firm hires more labor, marginal product decreases and marginal cost increases.

41. SHORT-RUN COST
But average product continues to rises, and average variable cost continues to fall.
Then, at the point of maximum average product, average variable cost is a minimum.
As the firm hires even more labor, average product decreases and average variable cost increases.

42. SHORT-RUN COST
This figure illustrates the relationship between the product curves and cost curves.
A firm’s marginal cost curve is linked to its marginal product curve.
If marginal product rises, marginal cost falls.
If marginal product is a maximum, marginal cost is a minimum.

43. SHORT-RUN COST
A firm’s average variable cost curve is linked to its average product curve.
If average product rises, average variable cost falls.
If average product is a maximum, average variable cost is a minimum.

44. SHORT-RUN COST At small outputs, MP and AP rise and MC and AVC fall.
At intermediate outputs,
MP falls and MC rises and
AP rises and AVC falls.
At large outputs,
MP and AP fall and
MC and AVC rise.

45. SHORT-RUN COST Shifts in Cost Curves Technology
A technological change that increases productivity shifts the total product curve upward. It also shifts the marginal product curve and the average product curve upward.
With a better technology, the same inputs can produce more output, so an advance in technology lowers the average and marginal costs and shifts the short-run cost curves downward.

46. SHORT-RUN COST Prices of Factors of Production
An increase in the price of a factor of production increases costs and shifts the cost curves.
But how the curves shift depends on which resource price changes.
An increase in rent or another component of fixed cost
Shifts the fixed cost curves (TFC and AFC) upward.
Shifts the total cost curve (TC) upward.
Leaves the variable cost curves (AVC and TVC) and the marginal cost curve (MC) unchanged.

47. SHORT-RUN COST
An increase in the wage rate or another component of variable cost
Shifts the variable curves (TVC and AVC) upward.
Shifts the marginal cost curve (MC) upward.
Leaves the fixed cost curves (AFC and TFC) unchanged.

48. LONG-RUN COST Plant Size and Cost
When a firm changes its plant size, its cost of producing a given output changes.
Will the average total cost of producing a gallon of smoothie fall, rise, or remain the same?
Each of these three outcomes arise because when a firm changes the size of its plant, it might experience:
Economies of scale
Diseconomies of scale
Constant returns to scale

49. Economies of Scale
Economies of scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by a larger percentage and average total cost decreases.
The main source of economies of scale is greater specialization of both labor and capital.

50. Diseconomies of Scale
Diseconomies of scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by a smaller percentage and average total cost increases.
Diseconomies of scale arise from the difficulty of coordinating and controlling a large enterprise.
Eventually, management complexity brings rising average total cost.

51. Constant Returns to Scale
Constant returns to scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by the same percentage and average total cost remains constant.
Constant returns to scale occur when a firm is able to replicate its existing production facility including its management system.

52. LONG-RUN COST The Long-Run Average Cost Curve
The long-run average cost curve shows
the lowest average cost at which it is
possible to produce each output when the
firm has had sufficient time to change both
its plant size and labor employed.

53. EXAMPLE: LRATC with 3 Factory Sizes
Firm can choose from 3 factory sizes: S, M, L.
Each size has its own SRATC curve.
The firm can change to a different factory size in the long run, but not in the short run. Q
Avg Total Cost
ATCS
ATCM
ATCL

54. EXAMPLE: LRATC with 3 Factory Sizes
To produce less than QA, firm will choose size S in the long run.
To produce between QA and QB, firm will choose size M in the long run.
To produce more than QB, firm will choose size L in the long run. Q
Avg Total Cost
ATCS
ATCM
ATCL
LRATC QA QB

55. A Typical LRATC Curve
In the real world, factories come in many sizes, each with its own SRATC curve.
So a typical LRATC curve looks like this: Q
ATC
LRATC

56. How ATC Changes as the Scale of Production Changes
Economies of scale: ATC falls as Q increases.
Constant returns to scale: ATC stays the same as Q increases.
Diseconomies of scale: ATC rises as Q increases. Q
ATC
LRATC

57. CONCLUSION
Costs are critically important to many business decisions, including production, pricing, and hiring.
This chapter has introduced the various cost concepts.
The following chapters will show how firms use these concepts to maximize profits in various market structures.

58. CHAPTER SUMMARY
Implicit costs do not involve a cash outlay, yet are just as important as explicit costs to firms’ decisions.
The production function shows the relationship between output and inputs.
The marginal product of labor is the increase in output from a one-unit increase in labor, holding other inputs constant. The marginal products of other inputs are defined similarly.
Marginal product usually diminishes as the input increases. Thus, as output rises, the production function becomes flatter, and the total cost curve becomes steeper.

59. CHAPTER SUMMARY Variable costs vary with output; fixed costs do not.
Marginal cost is the increase in total cost from an extra unit of production. The MC curve is usually upward-sloping.
Average variable cost is variable cost divided by output.
Average fixed cost is fixed cost divided by output. AFC always falls as output increases.
Average total cost (sometimes called “cost per unit”) is total cost divided by the quantity of output. The ATC curve is usually U-shaped.

60. CHAPTER SUMMARY
The MC curve intersects the ATC curve at minimum average total cost. When MC < ATC, ATC falls as Q rises. When MC > ATC, ATC rises as Q rises.
In the long run, all costs are variable.
Economies of scale: ATC falls as Q rises. Diseconomies of scale: ATC rises as Q rises. Constant returns to scale: ATC remains constant as Q rises.