1. PPA 723: Managerial Economics
Lecture 11:
Costs

2. Managerial Economics, Lecture 11: Costs
Outline
Short-Run Cost Curves
The Input Mix Decision
Long-Run Cost Curves

3. Managerial Economics, Lecture 11: Costs
Review
Short run production concepts:
Total, average, and marginal products.
MPL=APL at maximum APL
Law of Diminishing Marginal Returns
Long-run production concepts
Isoquant
MRTS = MPL/MPK
Returns to Scale

4. Managerial Economics, Lecture 10: Production

5. Managerial Economics, Lecture 11: Costs
From Production to Cost
Production concepts examine the amount of input(s) needed to produce a given output.
Cost concepts examine the cost of the inputs needed to produce a given output.
Thus cost concepts combine production concepts with input prices.

6. Managerial Economics, Lecture 11: Costs
Short-Run Cost Measures
Fixed cost (F): production expense that does not vary with output.
Variable cost (VC): production expense that changes with quantity of output produced.
Total cost (C):
C = VC + F

7. Managerial Economics, Lecture 11: Costs
Average Cost Concepts
Average fixed cost:
AFC = F /q
Average variable cost:
AVC = VC /q
Average (total) cost:
AC = C/q = AFC + AVC

8. Managerial Economics, Lecture 11: Costs
Marginal Cost
Marginal cost, MC, is the cost of producing the last unit
MC is the change in cost, C, when output changes by q
That is, MC = C/q

9. Managerial Economics, Lecture 11: Costs
Sunk Fixed Cost
We usually assume fixed cost is sunk, i.e., expenditure that cannot be recovered.
The opportunity cost of capital is zero
because you can't get this expenditure back no matter what you do.
So ignore it when making decisions
Example: walk out of a bad movie early, regardless of what you paid to attend
Otherwise, fixed cost is called avoidable.

10. Managerial Economics, Lecture 11: Costs

11. Managerial Economics, Lecture 11: Costs
400 C VC 27 A 1
216
Figure 7.1
Short-Run Cost Curves 20 1 B
120 48 F 2 4 6 8 10
(b)
Quantity, q
, Units per day
Cost per unit, $ 60 MC AC 28 a 27
AVC b 20 8
AFC 2 4 6 8 10
Quantity, q
, Units per day

12. Managerial Economics, Lecture 11: Costs
MC, AC, and AVC Curves
AC and AVC curves fall when MC is below them, and rise when MC is above them.
Therefore, the MC curve intersects the AC and AVC curves at their minimum points.

13. Managerial Economics, Lecture 11: Costs
Example
Suppose the short-run cost function is
C = q + q2
What are the:
fixed cost
variable cost
average cost
average fixed cost
average variable cost?

14. Managerial Economics, Lecture 11: Costs
Answer
If C = q + q2
Fixed cost = F = 125
Variable cost = VC = 2q + q2
Average cost = AC = C/q = 125/q q
Average fixed cost = AFC = 125/q
Average variable cost = AVC = 2 + q
Note: marginal cost = MC = 2 + 2q

15. Managerial Economics, Lecture 11: Costs
Production Functions & Cost Curves
A production function shows the inputs needed to produce a given output.
A firm's cost is found by multiplying the quantity of each input by its price and summing across inputs.
Higher average or marginal productivity implies lower average or marginal cost, so cost curves are U-shaped—the inverse of product curves.

16. Managerial Economics, Lecture 11: Costs
Application
Short-Run Cost Curves for a Printing Firm
(with continually rising AVC)
Cost, kroner 50 MC 40 30 AC
AVC 20 10
AFC
100
200
300 q
, Units per year

17. Managerial Economics, Lecture 11: Costs
Cost Effects of $10 Tax
This tax affects variable but not fixed cost
After-tax (a) cost = before-tax (b) cost + 10q:
Ca = Cb + 10q
At every quantity, AVC, AC, and MC curves shift up by $10:
AVCa = AVCb + $10
ACa = ACb + $10
MCa = MCb + $10

18. Managerial Economics, Lecture 11: Costs
Figure 7.3
Effects of a Specific Tax on Cost Curves
Costs per
unit, $ MC a = MC b + 10 80 MC b
$10 AC a = AC b + 10 37
$10 AC b 27 5 8 10 15 q
, Units per day

19. Managerial Economics, Lecture 11: Costs
Long-Run Costs
A firm adjusts all its inputs so its cost of production is as low as possible.
If capital and other variable costs can be varied, LR fixed costs equal zero (F = 0).
Thus LR total cost = LR variable cost:
C = VC

20. Managerial Economics, Lecture 11: Costs
Input Choice
To understand LR cost curves, we must examine a firm’s input mix decision.
A firm chooses from all technologically efficient combinations of inputs, the economically efficient combination of inputs.

21. Managerial Economics, Lecture 11: Costs
The Iso-Cost Line
Isocost line: all combinations of inputs that require the same (iso) total expenditure (cost).
If cost is C = wL + rK
then isocost is
where is a fixed level of cost
An isocost line is analogous to a budget constraint.

22. Managerial Economics, Lecture 11: CostsK
, Units of
Figure 7.4 A Family of Isocost Lines
capital per year
$150 15 = — — — $ 10
$100 e 10 = — — — $ 10 d c
$50 5 = — — —
$10 b $
50 isocost
$100 isocost
$150 isocost a
$50
$100
$150 — — — = 10 — — — = 20 — — — = 30 $ 5 $ 5 $ 5 L
, Units of labor per year

23. Managerial Economics, Lecture 11: Costs
Properties of Isocost Lines
The intercepts depend on factor prices.
intersects capital axis at
intersects labor axis at
Isocosts farther from origin involve higher costs.
The slope of each isocost line is the same.
As with a budget line, the slope is the price of the factor on the horizontal axis divided by the price of the factor on the vertical axis.
That is, slope = K/L = -w/r

24. Managerial Economics, Lecture 11: Costs
Minimizing Costs
To pick lowest-cost combination of inputs to produce a given level of output when isoquants are smooth:
Pick the lowest possible isocost line that touches the relevant isoquant.
The isocost and isoquant lines are tangent at this point, that is,
MRTS = w/r

25. Managerial Economics, Lecture 11: Costs
Figure 7.5 Cost minimization for
Norwegian printing firm K
, Units of
capital per year q
= 100 isoquant
3,000-kr
isocost y
303
2,000-kr
isocost
1,000-kr
isocost x
100 z 28 24 50
116 L
, Units of labor per year

26. Managerial Economics, Lecture 11: Costs
Last Dollar Rule
As in the case of utility maximization, this analysis leads to a last dollar rule: make sure the last dollar spent on one input produces as much extra output as last dollar spent on any other input

27. Managerial Economics, Lecture 11: Costs
Cost Minimizing vs. Output Maximizing
With smooth isoquants: firm determines best factor proportions by either
Minimizing cost: what is the lowest cost, C*, at which the firm can produce output q*?
Maximizing output: What is the most output, q*, that can be produced at cost C*?

28. Managerial Economics, Lecture 11: Costs
Long-Run Cost
Examine the lowest-cost factor combination for various levels of output
Define the expansion path:
Defined by cost-minimizing combination of labor and capital for each output level
The curve through tangency points is LR expansion path
The expansion path shows same relationship between LR cost and output as the LR cost curve.

29. Managerial Economics, Lecture 11: Costs
Figure 7.7a Expansion Path and
Long-Run cost Curve
(a) Expansion Path K
, Units of
capital per year
4,000-kr isocost
3,000-kr
isocost
Expansion path
2,000-kr
isocost z
200 y
150 x
100
200 isoquant
150 isoquant
100 isoquant 50 75
100 L
, Workers per year

30. Managerial Economics, Lecture 11: Costs
Figure 7.7b Expansion Path and Long-Run cost Curve
(b) Long-Run Cost Curve C
, Cost, kroner
Long-run cost curve
4,000 Z
3,000 Y
2,000 X
100
150
200 q
, Units per year

31. Managerial Economics, Lecture 11: Costs
Shape of LR Cost Curves
Short-run:
SR AC initially downward sloping because AFC is downward sloping
SR AC later upward sloping because of diminishing returns
Long-run
No fixed cost in LR (usually)
Shape of cost curves determined by production function returns to scale.

32. Managerial Economics, Lecture 11: Costs
(a) Cost Curve
Cost, $ C
Figure 7.8 Long-Run Cost Curves q * q
, Quantity per day
(b) Marginal and Average Cost Curves
Cost per MC
unit, $ AC q * q
, Quantity per day

33. Managerial Economics, Lecture 11: Costs
Economies of Scale
economies of scale
AC falls as output expands
no economies of scale
AC does not change as output increases
diseconomies of scale
AC rises when output increases

34. Managerial Economics, Lecture 11: Costs
Long-Run & Short-Run Cost Curves
In LR, firm chooses optimal plant size to minimize its LR cost for a given q
Because the firm cannot vary its capital in SR but can in LR
SR cost  LR cost
SR cost > LR cost if the "wrong" level of capital is used in SR

35. Managerial Economics, Lecture 11: Costs
Figure 7.9 Long-Run Average Cost as the Envelope of
Short-Run Average Cost Curves
Average cost, $
LRAC
SRAC 3
SRAC 2
SRAC 1
SRAC 3 b 12 d 10 a c e q q q
, Output per day 1 2

36. Managerial Economics, Lecture 11: Costs
Long-Run Cost Curves in Printing
Cost, kroner 40
SRAC 1
SRMC 1
SRMC 2 30
SRAC 2 20
LRAC =
LRMC 10
200
600
1,200 q
, Output per year

37. Managerial Economics, Lecture 11: Costs
Long-Run Cost Curves Oil Pipelines
Cost per barrel-mile
150
100 8
"
SRAC 10
"
SRAC 12
"
SRAC 50 16
"
SRAC 20
"
SRAC 26
"
SRAC 40
"
SRAC 10
LRAC 10 20 40
100
200
400
1000
2000
Thousand barrels per day