1. Chapter 7
The Cost of Production

2. Fixed and Variable Costs
Total output is a function of variable inputs and fixed inputs.
Therefore, the 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…
Chapter 7 11

3. 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 have been incurred and cannot be recovered
Chapter 7 12

4. Measuring Costs
Marginal Cost (MC):
Chapter 7 14

5. Measuring Costs
Average Total Cost (ATC)
Chapter 7 15

6. A Firm’s Short Run Costs
Chapter 7

7. 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
Chapter 7 33

8. Cost Curves MC
ATC
AVC
AFC
Chapter 7

9. Cost Curves When MC is below AVC, AVC is falling
When MC is above AVC, AVC is rising
When MC is below ATC, ATC is falling
When MC is above ATC, ATC is rising
Therefore, MC crosses AVC and ATC at the minimums
Chapter 7

10. 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

11. 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
$5 million per year – economic depreciation for the plane
Chapter 7

12. Cost in the Long Run
If the firm had not purchased the plane, it would have earned interest on the $150 million
Forgone interest is an opportunity cost that must be considered
Chapter 7 43

13. Cost in the Long Run
User Cost of Capital = Economic Depreciation + (Interest Rate)*(Value of Capital)
= $5 mil + (.10)($150 mil – depreciation)
Year 1 = $5 million + (.10)($150 million) = $20 million
Year 10 = $5 million +(.10)($100 million) = $15 million
Chapter 7 43

14. Cost in the Long Run User cost can also be described as;
Rate per dollar of capital, r
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

15. 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
Chapter 7 44

16. Cost in the Long Run Rewriting C as an equation for a straight line:
K = C/r - (w/r)L
Slope of the isocost:
Chapter 7 45

17. 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
Chapter 7 52

18. Input Substitution When an Input Price Change
If the price of labor changes, then the slope of the isocost line change, 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, and capital is substituted for labor
Chapter 7

19. 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

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

21. Cost in the Long Run Cost minimization with Varying Output Levels
A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output.
Slope equals K/L
Chapter 7 65

22. 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 50
Chapter 7 72

23. Expansion Path & Long-run Costs
Firms expansion path has same information as long-run total cost curve
To move from expansion path to LR cost curve
Find tangency with isoquant and isocost
Determine min cost of producing the output level selected
Graph output-cost combination
Chapter 7

24. A Firm’s Long-Run Total Cost Curve
Cost/ Year
1000
2000
3000
Long Run Total Cost D E F
Output, Units/yr
100
300
200
Chapter 7 72

25. To produce q1, min cost at K1,L1 If increase output to Q2, min cost
Short-Run vs. Long-Run
Capital
per
year F E L2 Q2 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
Labor per year
Chapter 7 77

26. Long-Run Average and Marginal Cost
($ per unit
of output
LMC A
LAC
Output
Chapter 7 85

27. Economies and Diseconomies of Scale
Increase in output is greater than the increase in inputs.
Diseconomies of Scale
Increase in output is less than the increase in inputs.
U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels
Chapter 7 87

28. 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
Chapter 7

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

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

31. 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 type of machinery.
Chapter 7
107

32. Production with Two Outputs – Economies of Scope
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

33. 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

34. Product Transformation Curve
Product transformation curves are negatively slope
To get more of one output, must give up some of the other output
Curve is concave
Joint production has its advantages
Chapter 7
112

35. 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

36. 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