Transcript Chapter 7

Chapter Seven
Costs
Topics
 Measuring Costs.
 Short-Run Costs.
 Long-Run Costs.
 Lower Costs in the Long Run.
 Cost of Producing Multiple Goods.
7-2
Economic Cost
 Economic cost or opportunity cost the value of the best alternative use of a
resource.
 Explicit costs - firm’s direct, out-of-pocket
payments for inputs to its production
process during a given time period. ,
 Workers’ wages, managers’ salaries, etc. and
payments for materials.
 Implicit costs – cost of use inputs that may
not have an explicit price.
 value of the working time of the firm’s owner
7-3
Capital Costs
 Durable good- a product that is usable
for years.
 Sunk cost - an expenditure that cannot
be recovered
7-4
Short-Run Cost Measures
 Fixed cost (F) - a production expense that
does not vary with output.
 Variable cost (VC) - a production expense
that changes with the quantity of output
produced.
 Cost (total cost, C) - the sum of a firm’s
variable cost and fixed cost:
C = VC + F
7-5
Marginal Cost.
 marginal cost (MC) - the amount by which
a firm’s cost changes if the firm produces
one more unit of output.
C
MC 
q
 And since only variable costs change with
output:
VC
MC 
q
7-6
Average Costs.
 average fixed cost (AFC) - the fixed cost
divided by the units of output produced:
AFC = F/q.
 average variable cost (AVC) - the variable
cost divided by the units of output produced:
AVC = VC/q.
 average cost (AC) - the total cost divided by
the units of output produced:
AC = C/q
AC = AFC + AVC.
7-7
Table 7.1 Variation of Short-Run
Cost with Output
7-8
Cost, \$
Figure 7.1 ShortRun Cost Curves
(a)
400
C
VC
27
A
216
1
20
1
B
120
48
0
F
2
4
6
8
Cost per unit, \$
(b)
10
Quantity, q, Units per day
60
MC
28
27
a
AC
AVC
b
20
8
AFC
0
2
4
6
10
8
Quantity, q, Units per day
7-9
Cost per unit, \$
Relationship between average and
marginal cost curves
60
When MC is
lower than
When
AC,MC
AC is
is
lower
than
decreasing…
AVC, AVC is
decreasing…
and when MC is
larger
and
whenthan
MCAC,
is
AC isthan
increases
larger
AVC,
AVC is increases
28
27
a
AC
AVC
b
20
8
0
MC
2
4
6
…so MC = AC, at
the lowest point of
the AC curve!
…so MC = AVC, at
the lowest point of
the AVC curve!
10
8
Quantity, q, Units per d ay
7-10
Figure 7.2 Variable Cost and Total
Product of Labor
7-11
Shape of the Marginal Cost Curve
MC = VC/q.
 But in the short run,
VC = w (can you tell why?)
 Therefore,
MC = w/q
of labor is:
q/ L = MPL
 Therefore,
MC = w/ MPL
7-12
Shape of the Average Cost Curves
AVC = VC/q.
 But in the short-run, with only labor as an
input:
AVC = VC/q = wL/q
 And since q/L = APL, then
AVC = VC/q = w/APLL
7-13
Application Short-Run Cost Curves for a
Furniture Manufacturer
7-14
Table 7.2 Effect of a Specific Tax of
\$10 per Unit on Short-Run Costs
7-15
Costs per unit, \$
Figure 7.3 Effect of a Specific Tax on
Cost Curves
80
A \$10.00 tax shifts
both the AVC and
MC by exactly
\$10…
MC a = MC b + 10
MC b
\$10
AC a = AC b + 10
37
\$10
AC b
27
0
5
8
10
15
q, Units per day
7-16
Solved Problem 7.1
 What is the effect of a lump-sum
franchise tax on the quantity at which a
firm’s after tax average cost curve
reaches its minimum? (Assume that the
firm’s before-tax average cost curve is
U-shaped.)
7-17
Solved Problem 7.1
7-18
Long-Run Costs
 Fixed costs are avoidable in the long
run.
 in the long F = 0.
 As a result, the long-run total cost equals:
C = VC
7-19
Input Choice
 isocost line - all the combinations of
inputs that require the same (iso-) total
expenditure (cost).
 The firm’s total cost equation is:
C = wL + rK.
Capital
Labor Costs
Costs
7-20
Input Choice (Cont).
 The firm’s total cost equation is:
C = wL + rK.
 We get the Isocost equation by setting fixing the
costs at a particular level:
C = wL + rK.
 And then solving for K (variable along y-axis):
K=
C r
w L
r
7-21
Table 7.3 Bundles of Labor and
Capital That Cost the Firm \$100
7-22
K, Units of capital per year
Figure 7.4 A Family of Isocost Lines
Isocost Equation
For each extra unit
of capital it uses,
the firm must use
two fewer units of
labor to hold its
cost constant.
10 =
\$100
\$10
e
d
7.5
5
C - w L
K=
r
r
Initial Values
C = \$100
w = \$5
r = \$10
c
K = 2.5
2.5
Slope = -1/2 = w/r
b
L = 5
\$100 isocost
a
5
10
15
\$100
= 20
\$5
L, Units of labor per year
7-23
Figure 7.4 A Family of Isocost Lines
K, Units of capital per year
Isocost Equation
15 =
\$150
\$10
10 =
\$100
\$10
e
C - w L
K=
r
r
An increase in C…. Initial Values
C = \$150
w = \$5
r = \$10
\$100 isocost
\$150 isocost
a
\$100
= 20
\$5
\$150
= 30
\$5
L, Units of labor per year
7-24
Figure 7.4 A Family of Isocost Lines
K, Units of capital per year
Isocost Equation
C - w L
r
r
Initial Values
C = \$50
w = \$5
r = \$10
K=
15 =
\$150
\$10
10 =
\$100
\$10
5=
\$50
\$10
A decrease in C….
e
\$50 isocost
\$100 isocost
\$150 isocost
a
\$50
= 10
\$5
\$100
= 20
\$5
\$150
= 30
\$5
L, Units of labor per year
7-25
Combining Cost and Production
Information.
 The firm can choose any of three equivalent
approaches to minimize its cost:
 Lowest-isocost rule - pick the bundle of inputs
where the lowest isocost line touches the isoquant.
 Tangency rule - pick the bundle of inputs where
the isoquant is tangent to the isocost line.
 Last-dollar rule - pick the bundle of inputs where
the last dollar spent on one input gives as much
extra output as the last dollar spent on any other
input.
7-26
K, Units of capital per hour
Figure 7.5 Cost Minimization
q = 100 isoquant
\$3,000
isocost
Which of these
three Isocost would
allow the firm to
produce the 100
units of output at
the lowest possible
cost?
\$2,000
isocost
\$1,000
isocost
100
0
x
50
Isocost Equation
C - w L
K=
r
r
Isoquant Slope
MPL
= MRTS
MPK
Initial Values
q = 100
C = \$2,000
w = \$24
r = \$8
L, Units of labor per hour
7-27
K, Units of capital per hour
Figure 7.5 Cost Minimization
Isocost Equation
C - w L
K=
r
r
Isoquant Slope
MPL
= MRTS
MPK
q = 100 isoquant
\$3,000
isocost
y
303
\$2,000
isocost
\$1,000
isocost
x
100
28
0
24
50
Initial Values
q = 100
C = \$2,000
w = \$24
r = \$8
z
116
L, Units of labor per hour
7-28
Cost Minimization
 At the point of tangency, the slope of the
isoquant equals the slope of the isocost.
Therefore,
w
MRTS  
r
MPL
MRTS  
MPK
MPL w

MPK r
MPL MPK

w
r
last-dollar rule: cost is
minimized if inputs
are chosen so
that the last dollar
as much extra output
as the last dollar
spent on capital.
7-29
K, Units of capital per hour
Figure 7.5 Cost Minimization
MPL = 0.6q/L
MPK = 0.4q/K
q = 100 isoquant
\$3,000
isocost
y
303
1.2
MPL
MPK
0.4
= 0.05
=
=
=
r
w
24
8
\$2,000
isocost
Spending one more dollar
on labor at x gets the firm
as much extra output as
spending the same
amount on capital.
\$1,000
isocost
x
100
z
28
0
Initial Values
q = 100
C = \$2,000
w = \$24
r = \$8
24
50
116
L, Units of labor per hour
K, Units of capital per hour
Figure 7.5 Cost Minimization
MPL = 0.6q/L
MPK = 0.4q/K
q = 100 isoquant
\$3,000
isocost
y
303
\$2,000
isocost
MPL
=
w
MPK
r =
\$1,000
isocost
x
100
if So
the…the
firm shifts
firm one
dollar
should
from
shift
capital to
labor,
evenoutput
more falls by
0.017
resources
because
from
there
iscapital
less capital
to labor—
but
also
which
increases
increases
by 0.1
because
the marginal
there is
more
product
laboroffor
capital
a net
gain
andofdecreases
0.083 more
output
the marginal
at the same
cost….
product of labor.
z
28
0
2.5
24 = 0.1
0.13
0.02
8 =
Initial Values
q = 100
C = \$2,000
w = \$24
r = \$8
24
50
116
L, Units of labor per hour
Figure 7.6 Change in Factor Price
K, Units of capital per hour
Minimizing Cost Rule
q = 100 isoquant
Original
isocost,
\$2,000
A decrease in w….
New isocost,
\$1,032
100
x
v
52
0
MPL
MPK
w = r
Initial Values
q = 100
C = \$2,000
w = \$24
r = \$8
w2 = \$8
C2 = \$1,032
50
77
L, Workers per hour
7-32
Solved Problem 7.3
 If it manufactures at home, a firm faces
input prices for labor and capital of wˆ
and rˆ and produces qˆ units of output
using L ˆ units of labor and K ˆ units of
capital.Abroad, the wage and cost of
capital are half as much as at home. If
the firm manufactures abroad, will it
change the amount of labor and capital
it uses to produce qˆ? What happens to
its cost of producing qˆ?
7-33
Solved Problem 7.3
7-34
How Long-Run Cost Varies with Output
 expansion path - the cost-minimizing
combination of labor and capital for each
output level
7-35
K, Units of capital per hour
Figure 7.7(a) Expansion Path
\$4,000
isocost
\$3,000
isocost
Expansion path
\$2,000
isocost
z
200
y
150
x
100
q = 200 Isoquant
q = 150 Isoquant
q = 100 Isoquant
0
50
75
100
L, Workers per hour
7-36
Figure 7.7(b) Expansion Path and
Long-Run Cost Curve (cont’d)
7-37
Solved Problem 7.4
 What is the long-run cost function for a
fixed-proportions production function
(Chapter 6) when it takes one unit of
labor and one unit of capital to produce
one unit of output? Describe the longrun cost curve.
7-38
Figure 7.8 LongRun Cost Curves
7-39
Economies of Scale
 economies of scale - property of a cost
function whereby the average cost of
production falls as output expands.
 diseconomies of scale - property of a
cost function whereby the average cost
of production rises when output
increases.
7-40
Table 7.4 Returns to Scale and
Long-Run Costs
7-41
Table 7.5 Shape of Average Cost
7-42
Long-Run Average Cost
 In its long-run planning, a firm chooses a
plant size and makes other investments
so as to minimize its long-run cost on
the basis of how many units it produces.
 Once it chooses its plant size and
equipment, these inputs are fixed in the
short run.
 Thus, the firm’s long-run decision determines its
short-run cost.
7-43
Average cost, \$
Figure 7.9 Long-Run Average Cost as the
Envelope of Short-Run Average Cost Curves
LRAC
SRAC 3
SRAC 1
SRAC 2
b
12
10
SRAC 3
d
a
c
e
0
q1
q2
q, Output per day
7-44
Application Long-Run Cost Curves in Furniture
Manufacturing and Oil Pipelines
7-45
Application Long-Run Cost Curves in Furniture
Manufacturing and Oil Pipelines
7-46
Application Choosing an Ink-Jet or a
Laser Printer
7-47
Figure 7.10 Long-Run and
Short-Run Expansion Paths
7-48
How Learning by Doing Lowers Costs
 learning by doing - the productive skills
and knowledge that workers and
managers gain from experience
7-49
Figure 7.11 Learning by Doing