Chapter 7
The Cost of
Production
Topics to be Discussed

Measuring Cost: Which Costs Matter?

Cost in the Short Run

Cost in the Long Run

Long-Run Versus Short-Run Cost
Curves
Chapter 7
Slide 2
Introduction

The production technology measures the
relationship between input and output.

Given the production technology, managers
must choose how to produce.

To determine the optimal level of output and
the input combinations, we must convert from
the unit measurements of the production
technology to dollar measurements or costs.
Chapter 7
Slide 3
Measuring Cost:
Which Costs Matter?
Economic Cost vs. Accounting Cost

Accounting Cost


Actual expenses plus depreciation
charges for capital equipment
Economic Cost

Chapter 7
Cost to a firm of utilizing economic
resources in production, including
opportunity cost
Slide 4
Measuring Cost:
Which Costs Matter?

Opportunity cost.


Cost associated with opportunities that are
foregone when a firm’s resources are not
put to their highest-value use.
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?
Chapter 7
Slide 5
Economic versus Accountants
How an Economist
Views a Firm
How an Accountant
Views a Firm
Economic
profit
Accounting
profit
Revenue
Implicit
costs
Explicit
costs
Revenue
Explicit
costs
Copyright © 2004 South-Western
Costs in the short-run:
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…
TC  FC  VC
Chapter 7
Slide 7
Measuring Cost:
Which Costs Matter?
Fixed and Variable Costs

Fixed Cost
 Does

not vary with the level of output
Variable Cost
 Cost
Chapter 7
that varies as output varies
Slide 8
Measuring Cost:
Which Costs Matter?

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
 Decision
makers should ignore sunk costs
to maximize profit or minimize losses
Chapter 7
Slide 9
A Firm’s Short-Run Costs ($)
Rate of Fixed
Output Cost
(FC)
0
1
2
3
4
5
6
7
8
9
10
11
50
50
50
50
50
50
50
50
50
50
50
50
Variable
Cost
(VC)
Total
Cost
(TC)
Marginal
Cost
(MC)
0
50
78
98
112
130
150
175
204
242
300
385
50
100
128
148
162
180
200
225
254
292
350
435
--50
28
20
14
18
20
25
29
38
58
85
Average
Fixed
Cost
(AFC)
--50
25
16.7
12.5
10
8.3
7.1
6.3
5.6
5
4.5
Average
Variable
Cost
(AVC)
--50
39
32.7
28
26
25
25
25.5
26.9
30
35
Average
Total
Cost
(ATC)
--100
64
49.3
40.5
36
33.3
32.1
31.8
32.4
35
39.5
Cost in the Short Run

Marginal Cost (MC) is the cost of
expanding output by one unit. Since
fixed cost have no impact on marginal
cost, it can be written as:
VC TC
MC 

Q
Q
Chapter 7
Slide 11
Cost in the Short Run

Average Total Cost (ATC) is the cost
per unit of output, or average fixed cost
(AFC) plus average variable cost (AVC).
This can be written:
TFC TVC
ATC 

Q
Q
TC
ATC  AFC  AVC or
Q
Chapter 7
Slide 12
Cost in the Short Run

The relationship between the production function
and cost can be exemplified by either increasing
returns and cost or decreasing returns and cost.

Increasing returns and cost
With
increasing returns, output is increasing
relative to input and variable cost and total cost will
fall relative to output.

Decreasing returns and cost
With
decreasing returns, output is decreasing
relative to input and variable cost and total cost will
rise relative to output.
Chapter 7
Slide 13
Cost in the Short Run

For Example: Assume the wage rate
(w) is fixed relative to the number of
workers hired. Then:
VC
MC 
Q
VC  wL
Chapter 7
Slide 14
Cost in the Short Run

Continuing:
VC  wL
wL
MC 
Q
Q
MPL 
L
L
1
L for a 1 unit Q 

Q MPL
Chapter 7
Slide 15
Cost in the Short Run

In conclusion:
w
MC 
MPL

…and a low marginal product (MP)
leads to a high marginal cost (MC)
and vise versa.
Chapter 7
Slide 16
Cost in the Short Run

Consequently (from the table):

MC decreases initially with increasing
returns


MC increases with decreasing returns

Chapter 7
0 through 4 units of output
5 through 11 units of output
Slide 17
A Firm’s Short-Run Costs ($)
Rate of Fixed
Output Cost
(FC)
0
1
2
3
4
5
6
7
8
9
10
11
50
50
50
50
50
50
50
50
50
50
50
50
Variable
Cost
(VC)
Total
Cost
(TC)
Marginal
Cost
(MC)
0
50
78
98
112
130
150
175
204
242
300
385
50
100
128
148
162
180
200
225
254
292
350
435
--50
28
20
14
18
20
25
29
38
58
85
Average
Fixed
Cost
(AFC)
--50
25
16.7
12.5
10
8.3
7.1
6.3
5.6
5
4.5
Average
Variable
Cost
(AVC)
--50
39
32.7
28
26
25
25
25.5
26.9
30
35
Average
Total
Cost
(ATC)
--100
64
49.3
40.5
36
33.3
32.1
31.8
32.4
35
39.5
Cost Curves for a Firm
Total cost
is the vertical
sum of FC
and VC.
Cost 400
($ per
year)
TC
VC
Variable cost
increases with
production and
the rate varies with
increasing &
decreasing returns.
300
200
Fixed cost does not
vary with output
100
FC
50
0
Chapter 7
1
2
3
4
5
6
7
8
9
10
11
12
13
Slide 19
Output
Cost Curves for a Firm
Cost
($ per
unit)
100
MC
75
50
ATC
AVC
25
AFC
0
Chapter 7
1
2
3
4
5
6
7
8
9
10
11
Output (units/yr.)
Slide 20
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)
400
VC
300
200
A
100
0
Chapter 7
TC
Cost
FC
1
2
3
4
5
6
7
8
9
10
11
12
Slide 21
13
Output
Cost Curves for a Firm

Unit Costs


AFC falls
continuously
When MC < AVC or
MC < ATC, AVC &
ATC decrease
Cost
($ per
unit)
100
MC
75
50
ATC
AVC
25

When MC > AVC or
MC > ATC, AVC &
ATC increase
Chapter 7
AFC
0
1
2
3
4
5
6
7
8
9
10
11
Output (units/yr.)
Slide 22
Cost Curves for a Firm

Unit Costs


MC = AVC and ATC
at minimum AVC and
ATC
Minimum AVC
occurs at a lower
output than minimum
ATC due to FC
Cost
($ per
unit)
100
MC
75
50
ATC
AVC
25
AFC
0
1
2
3
4
5
6
7
8
9
10
11
Output (units/yr.)
Chapter 7
Slide 23
Cost in the Long Run
The
TheCost
UserMinimizing
Cost of Capital
Input Choice

The Isocost Line

C = wL + rK

Isocost: A line showing all combinations
of L & K that can be purchased for the
same cost
Chapter 7
Slide 24
Cost in the Long Run
The Isocost Line

Rewriting C as linear:


K = C/r - (w/r)L
 
Slope of the isocost: K L   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
Slide 25
Choosing Inputs

We will address how to minimize cost
for a given level of output.

Chapter 7
We will do so by combining isocosts with
isoquants
Slide 26
Producing a Given
Output at Minimum Cost
Capital
per
year
Q1 is an isoquant
for output Q1.
Isocost curve C0 shows
all combinations of K and L
that can produce Q1 at this
cost level.
K2
Isocost C2 shows quantity
Q1 can be produced with
combination K2L2 or K3L3.
However, both of these
are higher cost combinations
than K1L1.
CO C1 C2 are
three
isocost lines
A
K1
Q1
K3
C0
L2
Chapter 7
L1
C1
L3
C2
Labor per year
Slide 27
Isocost

The combinations of inputs
K
that produce a given level of
C1/r
output at the same cost:
wL + rK = C

C0/r
C1
C0/w C1/w
Rearranging,
K= (1/r)C - (w/r)L

For given input prices,
isocosts farther from the
origin are associated with
higher costs.

Changes in input prices
change the slope of the
isocost line.
New Isocost
Line associated
with higher
costs (C0 < C1).
C0
K
C/r
L
New Isocost
Line for a
decrease in the
wage (price of
labor: w0 > w1).
C/w0
C/w1 L
Input Substitution When
an Input Price Change
Capital
per
year
If the price of labor
changes, the isocost curve
becomes steeper due to
the change in the slope -(w/r).
This yields a new combination
of K and L to produce Q1.
Combination B is used in place
of combination A.
The new combination represents
the higher cost of labor relative
to capital and therefore capital
is substituted for labor.
B
K2
A
K1
Q1
C2
L2
Chapter 7
L1
C1
Labor per year
Slide 29
Cost in the Long Run

Isoquants and Isocosts and the
Production Function
MRTS  - K
L
 MPL
Slope of isocost line  K
and  MPL
Chapter 7
MPK
w
MPK
L
 w
r
r
Slide 30
Cost in the Long Run

The minimum cost combination can
then be written as:
MPL

Chapter 7
w
 MPK
r
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.
Slide 31
Cost in the Long Run

Question
 If
w = $10, r = $2, and MPL = MPK,
which input would the producer use
more of? Why?
Chapter 7
Slide 32
Cost in the Long Run

Cost minimization with Varying Output
Levels

Chapter 7
A firm’s expansion path shows the
minimum cost combinations of labor and
capital at each level of output.
Slide 33
A Firm’s Expansion Path
Capital
per
year
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.
150 $3000 Isocost Line
Expansion Path
$2000
Isocost Line
100
C
75
B
50
300 Unit Isoquant
A
25
200 Unit
Isoquant
50
Chapter 7
100
150
200
300
Labor per year
Slide 34
A Firm’s Long-Run Total Cost Curve
Cost
per
Year
Long Run Total Cost
F
3000
E
2000
D
1000
100
Chapter 7
200
300
Output, Units/yr
Slide 35
Long-Run Versus
Short-Run Cost Curves

What happens to average costs when
both inputs are variable (long run)
versus only having one input that is
variable (short run)?
Chapter 7
Slide 36
The Inflexibility of
Short-Run Production
E
Capital
per
year
The long-run expansion
path is drawn as before..
C
Long-Run
Expansion Path
A
K2
Short-Run
Expansion Path
P
K1
Q2
Q1
L1
Chapter 7
L2
B
L3
D
F
Labor per year
Slide 37
Long-Run Versus
Short-Run Cost Curves

Long-Run Average Cost (LAC)

Constant Returns to Scale

Chapter 7
If input is doubled, output will double
and average cost is constant at all
levels of output.
Slide 38
Long-Run Versus
Short-Run Cost Curves

Long-Run Average Cost (LAC)

Increasing Returns to Scale

Chapter 7
If input is doubled, output will more
than double and average cost
decreases at all levels of output.
Slide 39
Long-Run Versus
Short-Run Cost Curves

Long-Run Average Cost (LAC)

Decreasing Returns to Scale

Chapter 7
If input is doubled, the increase in
output is less than twice as large and
average cost increases with output.
Slide 40
Long-Run Versus
Short-Run Cost Curves

Long-Run Average Cost (LAC)

In the long-run:

Chapter 7
Firms experience increasing and
decreasing returns to scale and
therefore long-run average cost is “U”
shaped.
Slide 41
Long-Run Average
and Marginal Cost
Cost
($ per unit
of output
LMC
LAC
A
Output
Chapter 7
Slide 42
Long-Run Versus
Short-Run Cost Curves

Long-Run Average Cost (LAC)

Chapter 7
Long-run marginal cost leads long-run
average cost:

If LMC < LAC, LAC will fall

If LMC > LAC, LAC will rise

Therefore, LMC = LAC at the
minimum of LAC
Slide 43
Long-Run Versus
Short-Run Cost Curves

Question

Chapter 7
What is the relationship between longrun average cost and long-run marginal
cost when long-run average cost is
constant?
Slide 44
Long-Run Versus
Short-Run Cost Curves

Economies and Diseconomies of
Scale

Economies of Scale


Diseconomies of Scale

Chapter 7
Increase in output is greater than the
increase in inputs.
Increase in output is less than the
increase in inputs.
Slide 45
Long-Run Average Costs
$
LRAC
Economies
of Scale
Diseconomies
of Scale
Q*
Q
Long-Run Versus
Short-Run Cost Curves

The Relationship Between Short-Run
and Long-Run Cost

Chapter 7
We will use short and long-run cost to
determine the optimal plant size
Slide 47
Long-Run Cost with
Constant Returns to Scale
Cost
($ per unit
of output
With many plant sizes with SAC = $10
the LAC = LMC and is a straight line
SAC1
SAC2
SMC1
SMC2
SAC3
SMC3
LAC =
LMC
Q1
Chapter 7
Q2
Q3
Output
Slide 48
Long-Run Cost with
Constant Returns to Scale


Observation

The optimal plant size will depend on the
anticipated output (e.g. Q1 choose SAC1,etc).

The long-run average cost curve is the
envelope of the firm’s short-run average cost
curves.
Question

Chapter 7
What would happen to average cost if an output
level other than that shown is chosen?
Slide 49
Long-Run Cost with Economies
and Diseconomies of Scale
Cost
($ per unit
of output
SAC1
SAC3
SAC2
A
$10
LAC
$8
B
SMC1
SMC3
LMC
SMC2
Q1
Chapter 7
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.
Output
Slide 50
Long-Run Cost with
Constant Returns to Scale

What is the firms’ 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.
Chapter 7
Slide 51
Long-Run Cost with
Constant Returns to Scale

Observations

The LAC does not include the minimum
points of small and large size plants?
Why not?
Chapter 7
Slide 52
Summary

Managers, investors, and economists
must take into account the opportunity
cost associated with the use of the
firm’s resources.

Firms are faced with both fixed and
variable costs in the short-run.
Chapter 7
Slide 53
Summary

When there is a single variable input,
as in the short run, the presence of
diminishing returns determines the
shape of the cost curves.

In the long run, all inputs to the
production process are variable.
Chapter 7
Slide 54
Summary

The firm’s expansion path describes how its
cost-minimizing input choices vary as the
scale or output of its operation increases.

The long-run average cost curve is the
envelope of the short-run average cost
curves.

A firm enjoys economies of scale when it can
double its output at less than twice the cost.
Chapter 7
Slide 55
End of Chapter 7
The Cost of
Production