1. The Cost of Production Chapter 7

2. Introduction
The production technology measures the relationship between input and output.
Production technology, together with prices of factor inputs, determine the firm’s cost of production
Given the production technology, managers must choose how to produce.
The optimal, cost minimizing, level of inputs can be determined.

3. MEASURING COST: WHICH COSTS MATTER?
● 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.
● opportunity cost Cost associated with opportunities that are forgone when a firm’s resources are not put to their best alternative use.
● sunk cost Expenditure that has been made and cannot be recovered.

4. Fixed Costs and Variable Costs
total cost (TC or C) Total economic cost of production,
consisting of fixed and variable costs.
fixed cost (FC) Cost that does not vary with the level of output
and that can be eliminated only by shutting down.
variable cost (VC) Cost that varies as output varies.
Shutting Down
Shutting down doesn’t necessarily mean going out of business.
By reducing the output of a factory to zero, the company could eliminate the costs of raw materials and much of the labor. The only way to eliminate fixed costs would be to close the doors, turn off the electricity, and perhaps even sell off or scrap the machinery.

5. Marginal and Average Cost
marginal cost (MC) Increase in cost resulting from the production of one extra unit of output.
Because fixed cost does not change as the firm’s level of output changes, marginal cost is equal to the increase in variable cost or the increase in total cost that results from an extra unit of output.
We can therefore write marginal cost as

6. Marginal and Average Cost
TABLE A Firm’s Costs
Rate of Fixed Variable Total Marginal Average Average Average
Output Cost Cost Cost Cost Fixed Cost Variable Cost Total Cost
(Units (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars
per Year) per Year) per Year) per Year) per Unit) per Unit) per Unit) per Unit)
(FC) (VC) (TC) (MC) (AFC) (AVC) (ATC)
(1) (2) (3) (4) (5) (6) (7)

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

8. The Determinants of Short-Run Cost
The change in variable cost is the per-unit cost of the extra labor w times the amount of extra labor needed to produce the extra output ΔL. Because ΔVC = wΔL, it follows that
The extra labor needed to obtain an extra unit of output is ΔL/Δq = 1/MPL. As a result,

9. If marginal product of labor decreases significantly as more labor is hired
Costs of production increase rapidly
Greater and greater expenditures must be made to produce more output

11. 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 &
decreasing returns.
Fixed cost does not
vary with output FC 50

12. Cost Curves

13. Cost Curves for a Firm 1 2 3 4 5 6 7 8 9 10 11 12 13
Output P
100
200
300
400 FC VC TC
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)

14. COST IN THE LONG RUN
● user cost of capital Annual cost of owning and using a capital asset, equal to economic depreciation plus forgone interest.
We can also express the user cost of capital as a rate per dollar of capital:

15. The Rental Rate of Capital
The Price of Capital
The price of capital is its user cost, given by r = Depreciation rate + Interest rate.
The Rental Rate of Capital
● rental rate : Cost per year of renting one unit of capital.

16. COST IN THE LONG RUN
● isocost line Graph showing all possible combinations of labor and capital that can be purchased for a given total cost.
To see what an isocost line looks like, recall that the total cost C of producing any particular output is given by the sum of the firm’s labor cost wL and its capital cost rK:
If we rewrite the total cost equation as an equation for a straight line, we get
It follows that the isocost line has a slope of ΔK/ΔL = −(w/r), which is the ratio of the wage rate to the rental cost of capital.

17. Cost Minimizing Input Choice
Assumptions
Two Inputs: Labor (L) & capital (K)
Price of labor: wage rate (w)
The price of capital
r = depreciation rate + interest rate
Or rental rate if not purchasing
These are equal in a competitive capital market

18. 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 K2L2 or K3L3.
However, both of these
are higher cost combinations
than K1L1. C0
Labor per year

19. C2 Q1 C1 K2 L2 B K1 L1 A Capital per year 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
Labor per year

20. Cost in the Long Run
It follows that when a firm minimizes the cost of producing a particular output, the following condition holds:
We can rewrite this condition slightly as follows:

21. Cost in the Long Run
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

22. Cost in the Long Run
If w = $10, r = $2, and MPL = MPK, which input would the producer use more of?
Labor because it is cheaper
Increasing labor lowers MPL
Decreasing capital raises MPK
Substitute labor for capital until

23. Cost in the Long Run Cost minimization with Varying Output Levels
For each level of output, there is an isocost curve showing minimum cost for that output level
A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output.
Slope equals K/L

24. A Firm’s Expansion Path
Capital
per
year 25 50 75
100
150
The expansion path illustrates
the least-cost combinations of
labor and capital that can be
used to produce each level of
output in the long-run.
$3000
300 Units C
Expansion Path
$2000
200 Units B A
Labor per year
100
150
300
200

25. Long-Run Versus Short-Run Cost Curves
In the short run some costs are fixed
In the long run firm can change anything including plant size
Can produce at a lower average cost in long run than in short run
Capital and labor are both flexible

26. The Inflexibility of Short-Run ProductionQ2 K2 D C
Capital is fixed at K1
To produce q1, min cost at K1,L1
If increase output to Q2, min cost
is K1 and L3 in short run Q1 A B L1 K1
Long-Run
Expansion Path
In LR, can change capital and min costs falls to K2 and L2 L3 P
Short-Run
Expansion Path

27. 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 min cost
Constant Returns to Scale
If input is doubled, output will double
AC cost is constant at all levels of output.
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

28. Economies and Diseconomies of Scale
As output increases, the firm’s average cost of producing that output is likely to decline, at least to a point.
This can happen for the following reasons:
If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive.
Scale can provide flexibility. By varying the combination of inputs utilized to produce the firm’s output, managers can organize the production process more effectively.

29. Economies and Diseconomies of Scale
● economies of scale Situation in which output can be doubled for less than a doubling of cost.
● diseconomies of scale Situation in which a doubling of output requires more than a doubling of cost.
Increasing Returns to Scale: Output more than doubles when the quantities of all inputs are doubled.
Economies of Scale: A doubling of output requires less than a doubling of cost.

30. Long Run Costs EC is equal to 1, MC = AC
Costs increase proportionately with output
Neither economies nor diseconomies of scale
EC < 1 when MC < AC
Economies of scale
Both MC and AC are declining
EC > 1 when MC > AC
Diseconomies of scale
Both MC and AC are rising

31. Long-Run Cost with Economies and Diseconomies of Scale

32. Cont’ Advantages Both use capital and labor.
The firms share management resources.
Both use the same labor skills and type of machine
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

33. The learning curve in the figure is based on the relationship:

34. Dynamic Changes in Costs – The Learning Curve
If N = 1
L equals A + B and this measures labor input to produce the first unit of output
If  = 0
Labor input per unit of output remains constant as the cumulative level of output increases, so there is no learning
If  > 0 and N increases,
L approaches A, and A represents minimum labor input/unit of output after all learning has taken place.
The larger ,
The more important the learning effect.