1. EA Session 7 July 13, 2007 Prof. Samar K. Datta
Cost Theory
EA Session 7
July 13, 2007
Prof. Samar K. Datta

2. Overview Short run costs Long run costs & economies of scale
Economies of scope & product transformation curve

3. SHORT RUN COSTS
Marginal Cost (MC) is the cost of expanding output by one unit => MC = dTC/dQ
Average Total Cost (ATC) is the cost per unit of output, or average fixed cost (AFC) plus average variable cost (AVC) => ATC = TC/Q = TFC/Q + TVC/Q = AFC + AVC
The relationship between the production function and cost can be exemplified by:
Increasing returns
With increasing returns, output is increasing relative to input and variable cost and total cost will fall relative to output.
Decreasing returns
With decreasing returns, output is decreasing relative to input and variable cost and total cost will rise relative to output. 14

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

5. Cost Curves for a Firm Unit Costs AFC falls continuously
When MC < AVC or MC < ATC, AVC & ATC decrease
When MC > AVC or MC > ATC, AVC & ATC increase
When MC = AVC = ATC then AVC and ATC are at minimum
Output (units/yr.)
Cost
($ per
unit) 25 50 75
100 1 2 3 4 5 6 7 8 9 10 11 MC
ATC
AVC
AFC 41

6. PRODUCING A GIVEN OUTPUT AT MINIMUM COST
Capital
per
year Q1
Q1 is an isoquant
for output Q1.
Isocost curve C0 shows
all combinations of K and L
that cost C0. C0 C1 C2
CO C1 C2 are
three
isocost lines A K1 L1 K3 L3 K2 L2
Isocost C2 shows quantity
Q1 can be produced with
combination K2L2 or K3L3.
However, both of these
are higher cost combinations
than K1L1.
Labor per year 52

7. THE INFLEXIBILITY OF SHORT-RUN PRODUCTION
Capital
per
year L2 Q2 K2 D C
Long-Run
Expansion Path
The long-run expansion
path is drawn as before.. Q1 A B L1 K1 L3 P
Short-Run
Expansion Path
Labor per year 77

8. RETURNS TO SCALE Constant Returns to Scale
If input is doubled, output will double and average cost is constant at all levels of output.
Increasing Returns to Scale
If input is doubled, output will more than double and average cost decreases at all levels of output.
Decreasing Returns to Scale
If input is doubled, the increase in output is less than twice as large and average cost increases with output. 78

9. LONG-RUN AVERAGE AND MARGINAL COST
($ per unit
of output
LMC A
LAC
Output 85

10. ECONOMIES AND DISECONOMIES OF SCALE
Measuring Economies of Scale
Therefore, the following is true:
EC < 1: MC < AC
economies of scale
EC = 1: MC = AC
constant economies of scale
EC > 1: MC > AC
diseconomies of scale 89

11. LONG-RUN COST WITH CONSTANT RETURNS TO SCALE
($ per unit
of output)
LAC =
LMC
With many plant sizes with minimum SAC = $10
the LAC = LMC and is a straight line
$10 Q1
SAC1
SMC1 Q2
SAC2
SMC2 Q3
SAC3
SMC3
Output 96

12. LONG-RUN COST WITH ECONOMIES AND DISECONOMIES OF SCALE
The long-run average cost curve is the envelope of the firm’s short-run average cost curves, assuming continually variable plant size.
Cost
($ per unit
of output
SMC1
SAC1
LAC
SAC3
SMC3
SAC2
SMC2
If the output is Q1 a manager
would chose the small plant
SAC1 and SAC $8.
Point B is on the LAC because
it is a least cost plant for a
given output.
$10 Q1 $8 B A
LMC
The long-run cost curve is the dark blue portion of the SAC curve which represents the minimum cost for any level of output, assuming only three discrete plant sizes.
Output
102

13. ECONOMIES OF SCOPE
Economies of scope exist when the joint output of a single firm is greater than the output that could be achieved by two different firms each producing a single output.
Firms must choose how much of each to produce.
The alternative combinations can be illustrated using product transformation curves.
106

14. PRODUCT TRANSFORMATION CURVE
Each curve shows
combinations of output
with a given combination
of L & K.
Number
of tractors O2
O1 illustrates a low level
of output. O2 illustrates
a higher level of output with
two times as much labor
and capital.
Number of cars
111

15. ECONOMIES OF SCOPE
The degree of economies of scope measures the savings in cost and can be written:
C(Q1) is the cost of producing Q1
C(Q2) is the cost of producing Q2
C(Q1Q2) is the joint cost of producing both products
If SC > 0 -- Economies of scope
If SC < 0 -- Diseconomies of scope
114

16. DYNAMIC CHANGES IN COSTS –THE LEARNING CURVE (optional)
The learning curve measures the impact of worker’s experience on the costs of production.
It describes the relationship between a firm’s cumulative output and amount of inputs needed to produce a unit of output.
120

17. DYNAMIC CHANGES IN COSTS –THE LEARNING CURVE (optional)
The learning curve in the figure is based on the relationship:
124

18. DYNAMIC CHANGES IN COSTS –THE LEARNING CURVE (optional)
L equals A + B and this measures labor input to produce the first unit of output
Labor input remains constant as the cumulative level of output increases, so there is no learning
125

19. DYNAMIC CHANGES IN COSTS –THE LEARNING CURVE (optional)
L approaches A, and A represent minimum labor input/unit of output after all learning has taken place.
The more important the learning effect.
126

20. DYNAMIC CHANGES IN COSTS –THE LEARNING CURVE (optional)
The chart shows a sharp drop
in lots to a cumulative amount of
20, then small savings at
higher levels.
Hours of labor
per machine lot 10 8
Doubling cumulative output causes
a 20% reduction in the difference
between the input required and
minimum attainable input requirement. 6 4 2
Cumulative number of
machine lots produced 10 20 30 40 50
128

21. ECONOMIES OF SCALE VERSUS LEARNING (optional)
Cost
($ per unit
of output)
LAC1 B
Economies of Scale
LAC2
Learning C A
Output
132