1. Product Curves
AP is slope of line from origin to point on TP curve q
q/L
112 C TP 30 60 B 20 AP 10 MP
Labor 2 3 4 5 6 7 8 9 10 1 8 2 3 4 5 6 7 9 10 1
Labor
Chapter 7

2. Practice Bridget's Brewery production function is given by
where K is the number of vats she uses and L is the number of labor hours. Does this production process exhibit increasing, constant or decreasing returns to scale? Holding the number of vats constant at 4, is the marginal product of labor increasing, constant or decreasing as more labor is used?
Chapter 7

3. Solution Multiplying the K and L by 2 yields:
we know the production process exhibits constant returns to scale. Holding the number of vats constant at 4 will still result in a downward sloping marginal product of labor curve. That is the marginal product of labor decreases as more labor is used.
Chapter 7

4. Chapter 7
The Cost of Production

5. Measuring Cost: Which Costs Matter?
Accountants tend to take a retrospective view of firms’ costs, whereas economists tend to take a forward-looking view
Accounting Cost
Actual expenses plus depreciation charges for capital equipment
Economic Cost
Cost to a firm of utilizing economic resources in production, including opportunity cost
Chapter 7

6. Measuring Cost: Which Costs Matter?
Economic costs distinguish between costs the firm can control and those it cannot
Concept of opportunity cost plays an important role
Opportunity cost
Cost associated with opportunities that are foregone or the value of the next best alternative use of a resource
Chapter 7 7

7. Opportunity Cost An Example
A firm owns its own building and pays no rent for office space
Does this mean the cost of office space is zero?
The building could have been rented instead
Foregone rent is the opportunity cost of using the building for production and should be included in the economic costs of doing business
Chapter 7 7

8. Opportunity Cost
A person starting their own business must take into account the opportunity cost of their time
Could have worked elsewhere making a competitive salary
Accountants and economists often treat depreciation differently as well
Chapter 7

9. Measuring Cost: Which Costs Matter?
Although opportunity costs are hidden and should be taken into account, sunk costs should not
Sunk Cost
Expenditure that has been made and cannot be recovered
Should not influence a firm’s future economic decisions
Chapter 7 7

10. Sunk Cost
Firm buys a piece of equipment that cannot be converted to another use
Expenditure on the equipment is a sunk cost
Has no alternative use so cost cannot be recovered – opportunity cost is zero
Decision to buy the equipment might have been good or bad, but now does not matter
Chapter 7

11. Prospective Sunk Cost An Example
Firm is considering moving its headquarters
A firm paid $500,000 for an option to buy a building
The cost of the building is $5 million for a total of $5.5 million
The firm finds another building for $5.25 million
Which building should the firm buy?
Chapter 7 7

12. Prospective Sunk Cost Example (cont.)
The first building should be purchased
The $500,000 is a sunk cost and should not be considered in the decision to buy
What should be considered is
Spending an additional $5,250,000 or
Spending an additional $5,000,000
Chapter 7

13. Measuring Cost: Which Costs Matter?
Some costs vary with output, while some remain the same no matter the amount of output
Total cost can be divided into:
Fixed Cost
Does not vary with the level of output
Variable Cost
Cost that varies as output varies
Chapter 7 12

14. Fixed and Variable Costs
Total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or…
Short time horizon – most costs are fixed
Long time horizon – many costs become variable
Chapter 7 11

15. Fixed Cost Versus Sunk Cost
Fixed cost and sunk cost are often confused
Fixed Cost
Cost paid by a firm that is in business regardless of the level of output
Sunk Cost
Cost that has been incurred and cannot be recovered
Chapter 7 12

16. Measuring Costs Marginal Cost (MC):
The cost of expanding output by one unit
Fixed costs have no impact on marginal cost, so it can be written as:
Chapter 7 14

17. Measuring Costs Average Total Cost (ATC) Cost per unit of output
Also equals average fixed cost (AFC) plus average variable cost (AVC)
Chapter 7 15

18. A Firm’s Short Run Costs
Chapter 7

19. Determinants of Short Run Costs – An Example
Assume the wage rate (w) is fixed relative to the number of workers hired
Variable costs is the per unit cost of extra labor times the amount of extra labor: wL
Chapter 7 18

20. Determinants of Short Run Costs – An Example
Remembering that
And rearranging
Chapter 7 20

21. Determinants of Short Run Costs – An Example
We can conclude:
…and a low marginal product (MPL) leads to a high marginal cost (MC) and vice versa
Chapter 7 21

22. Determinants of Short Run Costs
Consequently (from the table):
MC decreases initially with increasing returns
0 through 4 units of output
MC increases with decreasing returns
5 through 11 units of output
Chapter 7 22

23. Cost Curves for a Firm TC VC Cost 400 300 200 100 FC 50 Output 1 2 3 4
($ per
year)
100
200
300
400 1 2 3 4 5 6 7 8 9 10 11 12 13 VC
Total cost
is the vertical
sum of FC
and VC.
Variable cost
increases with
production and
the rate varies with
increasing and
decreasing returns.
Fixed cost does not
vary with output FC 50
Chapter 7 33

24. Cost Curves MC
ATC
AVC
AFC
Chapter 7

25. Cost Curves for a Firm
The line drawn from the origin to the variable cost curve:
Its slope equals AVC
The slope of a point on VC or TC equals MC
Therefore, MC = AVC at 7 units of output (point A) 1 2 3 4 5 6 7 8 9 10 11 12 13
Output P
100
200
300
400 FC VC TC A
Chapter 7 39

26. Cost in the Long Run
In the long run a firm can change all of its inputs
In making cost minimizing choices, must look at the cost of using capital and labor in production decisions
Now: The firms’ long-run cost minimizing decision
Chapter 7 43

27. Cost in the Long Run Capital is either rented/leased or purchased
Assume Delta is considering purchasing an airplane for $150 million
Plane lasts for 30 years – economic depreciation for the plane = $5 million per year
If the firm had not purchased the plane, it would have earned interest on the $150 million (of 10%)
Forgone interest is an opportunity cost that must be considered also
Chapter 7

28. Cost in the Long Run User cost of capital, then, can be described as:
r = Depreciation Rate + Interest Rate
In our example, depreciation rate was 3.33% and interest was 10%, so
r = 3.33% + 10% = 13.33%
Chapter 7 43

29. Cost Minimizing Input Choice
How does a firm select inputs to produce a given output at minimum cost?
Assumptions
Two Inputs: Labor (L) and capital (K)
Price of labor: wage rate (w)
The price of capital
r = depreciation rate + interest rate
Chapter 7 43

30. Cost in the Long Run The Isocost Line C = wL + rK
A line showing all combinations of L & K that can be purchased for the same cost
Total cost of production is sum of firm’s labor cost, wL, and its capital cost, rK:
C = wL + rK
For each different level of cost, the equation shows another isocost line
Chapter 7 44

31. Cost in the Long Run Rewriting C as an equation for a straight line:
K = C/r - (w/r)L
Slope of the isocost:
-(w/r) is the ratio of the wage rate to rental cost of capital.
This shows the rate at which capital can be substituted for labor with no change in cost
Chapter 7 45

32. Choosing Inputs
We will address how to minimize cost for a given level of output by combining isocosts with isoquants
We choose the output we wish to produce and then determine how to do that at minimum cost
Isoquant is the quantity we wish to produce
Isocost is the combination of K and L that gives a set cost
Chapter 7 46

33. Producing a Given Output at Minimum Cost
Capital
per
year
Q1 is an isoquant for output Q1.
There are three isocost lines, of which 2 are possible choices in which to produce Q1. C2 Q1 A K1 L1 K3 L3 K2 L2 C1
Isocost C2 shows quantity
Q1 can be produced with
combination K2,L2 or K3,L3.
However, both of these
are higher cost combinations
than K1,L1. C0
Labor per year
Chapter 7 52

34. Input Substitution When an Input Price Change
If the price of labor changes, then the slope of the isocost line changes, -(w/r)
It now takes a new quantity of labor and capital to produce the output
If price of labor increases relative to price of capital, then capital is substituted for labor
Chapter 7

35. Input Substitution When an Input Price Change
Capital
per
year C2
If the price of labor
rises, the isocost curve
becomes steeper due to
the change in the slope -(w/L). Q1 C1
The new combination of K and L is used to produce Q1.
Combination B is used in place of combination A. K2 L2 B K1 L1 A
Chapter 7
Labor per year 55

36. Cost in the Long Run
How does the isocost line relate to the firm’s production process?
Chapter 7 56

37. Cost in the Long Run
The minimum cost combination can then be written as:
Minimum cost for a given output will occur when each dollar of input added to the production process will add an equivalent amount of output.
Chapter 7 57

38. Cost in the Long Run
If w = $10, r = $2, and MPL = MPK, which input would the producer use more of?
Chapter 7 58

39. Example If MPL = 10, MPK = 5 and w= r = $10
Which input should the firm increase/decrease usage?
What if w increased to $20?
Chapter 7

40. Long Run Versus Short Run Cost Curves
Long-Run Average Cost (LAC)
Most important determinant of the shape of the LR AC and MC curves is relationship between scale of the firm’s operation and inputs required to minimize cost
Constant Returns to Scale
If input is doubled, output will double
AC cost is constant at all levels of output
Chapter 7 78

41. Long Run Versus Short Run Cost Curves
Increasing Returns to Scale
If input is doubled, output will more than double
AC decreases at all levels of output
Decreasing Returns to Scale
If input is doubled, output will less than double
AC increases at all levels of output
Chapter 7 79

42. Long Run Versus Short Run Cost Curves
In the long run:
Firms experience increasing and decreasing returns to scale and therefore long-run average cost is “U” shaped.
Source of U-shape is due to returns to scale instead of diminishing returns to a factor of production (labor) like the short-run curve
Long-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit
Chapter 7 81

43. Economies and Diseconomies of Scale
Can double output for less than double the original cost
Diseconomies of Scale
Doubling the output costs more than twice the original cost
U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels
Chapter 7 87

44. Long Run Costs Increasing Returns to Scale Economies of Scale
Output more than doubles when the quantities of all inputs are doubled
Economies of Scale
Doubling of output requires less than a doubling of cost
Why the difference: can have constant returns to scale but still have economies of scale:
Chapter 7

45. Long Run Versus Short Run Cost Curves
We will use short and long run costs to determine the optimal plant size
We can show the short run average costs for 3 different plant sizes
This decision is important because once built, the firm may not be able to change plant size for a while
Chapter 7 91

46. Long Run Cost with Economies and Diseconomies of Scale
Chapter 7
102

47. Long Run Cost with Constant Returns to Scale
What is the firm’s long run cost curve?
Firms can change scale to change output in the long run
The long run cost curve is the dark blue portion of the SAC curve which represents the minimum cost for any level of output
Firm will always choose plant that minimizes the average cost of production
Chapter 7
103

48. Long Run Cost with Constant Returns to Scale
The long-run average cost curve envelops the short-run average cost curves
The LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels
Chapter 7
104

49. Production with Two Outputs – Economies of Scope
Many firms produce more than one product and those products are closely linked
Examples:
Chicken farm--poultry and eggs
Automobile company--cars and trucks
University--teaching and research
Chapter 7
105

50. Production with Two Outputs – Economies of Scope
Advantages
Both use capital and labor
The firms share management resources
Both use the same labor skills and types of machinery
Chapter 7
107

51. Production with Two Outputs – Economies of Scope
Firms must choose how much of each to produce
The alternative quantities can be illustrated using product transformation curves
Curves showing the various combinations of two different outputs (products) that can be produced with a given set of inputs
Chapter 7
108

52. Product Transformation Curve
Number
of tractors
Each curve shows
combinations of output
with a given combination
of L & K. O2
O1 illustrates a low level
of output. O2 illustrates
a higher level of output with
two times as much labor
and capital. O1
Number of cars
Chapter 7
111

53. Product Transformation Curve
Product transformation curves are negatively sloped
To get more of one output, must give up some of the other output
Constant returns exist in this example
Second curve lies twice as far from origin as the first curve
Curve is concave/bowed-outward
Joint production has advantages
Chapter 7
112

54. Production with Two Outputs – Economies of Scope
There is no direct relationship between economies of scope and economies of scale
May experience economies of scope and diseconomies of scale
May have economies of scale and not have economies of scope
Chapter 7
113

55. Production with Two Outputs – Economies of Scope
The degree of economies of scope (SC) can be measured by percentage of cost saved producing two or more products jointly:
C(q1) is the cost of producing q1
C(q2) is the cost of producing q2
C(q1,q2) is the joint cost of producing both products
Chapter 7
114

56. Production with Two Outputs – Economies of Scope
With economies of scope, the joint cost is less than the sum of the individual costs
Interpretation:
If SC > 0  Economies of scope
If SC < 0  Diseconomies of scope
The greater the value of SC, the greater the economies of scope
Chapter 7
115