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INTERMEDIATE
MICROECONOMICS
AND ITS APPLICATION
Chapter 6
Costs
Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Requests for
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Basic Concepts of Costs
• Opportunity cost is the cost of a good or
service as measured by the alternative uses
that are foregone by producing the good or
service.
– If 15 bicycles could be produced with the
materials used to produce an automobile, the
opportunity cost of the automobile is 15 bicycles.
• The price of a good or service often may
reflect its opportunity cost.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Basic Concepts of Costs
• Accounting cost is the concept that goods
or services cost what was paid for them.
• Economic cost is the amount required to
keep a resource in its present use; the
amount that it would be worth in its next
best alternative use.
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Labor Costs
• Like accountants, economists regard the
payments to labor as an explicit cost.
• Labor services (worker-hours) are
purchased at an hourly wage rate (w): The
cost of hiring one worker for one hour.
• The wage rate is assumed to be the amount
workers would receive in their next best
alternative employment.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Capital Costs
• While accountants usually calculate capital
costs by applying some depreciation rule to
the historical price of the machine,
economists view this amount as a sunk cost.
• A sunk cost is an expenditure that once
made cannot be recovered.
• These costs do not focus on foregone
opportunities.
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Capital Costs
• Economists consider the cost of a machine
to be the amount someone else would be
willing to pay for its use.
• The cost of capital services (machine-hours)
is the rental rate (v) which is the cost of
hiring one machine for one hour.
• This is an implicit cost if the machine is
owned by the firm.
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APPLICATION 6.1: Stranded
Costs
• Until the mid 1990s, the electric power
industry in the United States was heavily
regulated.
• The expected decline in the wholesale price
of electricity resulting from deregulation
has sparked a debate over “stranded costs”.
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The Nature of Stranded Costs
• When the average costs of generating
electricity exceed the price of electricity in
the open market, the generating facilities
become “uneconomic.”
• The historical costs of these facilities have
been “stranded” by deregulation.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
The Nature of Stranded Costs
• To economists, these are sunk costs.
• Generating facilities that have become
“uneconomic” have zero market value, a
situation that occurs frequently in many
other business (for example, machines that
produce 78 RPM recordings).
• Economist Joseph Schumpeter coined such
situations, “creative destruction.”
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The Legal Framework--Socking
It to the Consumer
• Utilities companies argue that they were
promised a “fair” return on their investment,
so they should be compensated for the
impact of deregulation.
• Southern California Edison Company was
awarded stranded cost compensation that
exceeded the company’s value on the New
York Stock Exchange.
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The Legal Framework--Socking
It to the Consumer
• A result of mandated stranded-cost
compensation is the slowing of the pace of
deregulation.
– Since consumers see little of the price decline,
they have little incentive to push for
deregulation.
– Would-be entrants are also not encouraged by
consumers because of the stranded-cost
compensation.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Entrepreneurial Costs
• Owners of the firm are entitled to the
difference between revenue and costs which
is generally called (accounting) profit.
• However, if they incur opportunity costs for
their time or other resources supplied to the
firm, these should be considered a cost of
the firm.
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The Legal Framework--Socking
It to the Consumer
• A computer programmer that started a
software firm would supply time, the value
of which is an opportunity cost.
– The wages the programmer would have earned
if he or she worked elsewhere could be used as
a measure of this cost.
• Economic profit is revenue minus all costs
including these entrepreneurial costs.
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Two Simplifying Assumptions
• The firm uses only two inputs: labor (L,
measured in labor hours) and capital (K,
measured in machine hours).
– Entrepreneurial services are assumed to be
included in the capital costs.
• Firms buy inputs in perfectly competitive
markets so the firm faces horizontal supply
curves at prevailing factor prices.
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Economic Profits and Cost
Minimization
• Total costs = TC = wL + vK.
• Assuming the firm produces only one
output, total revenue equals the price of the
product (P) times its total output [q = f(K,L)
where f(K,L) is the firm’s production
function].
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Economic Profits and Cost
Minimization
• Economic profits () is the difference
between a firm’s total revenues and its total
economic costs.
  Total revenues - Total costs
 Pq  wL  vK
 Pf ( K , L)  wL  vK.
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Cost-Minimizing Input Choice
• Assume, for purposes of this chapter, that
the firm has decided to produce a particular
output level (say, q1).
– The firm’s total revenues are P·q1.
• How the firm might choose to produce this
level of output at minimal costs is the
subject of this chapter.
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Cost-Minimizing Input Choice
• Cost minimization requires that the
marginal rate of technical substitution
(RTS) of L for K equals the ratio of the
inputs’ costs, w/v:
w
RTS ( of L for K) 
v
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Graphic Presentation
• The isoquant q1 shows all combinations of
K and L that are required to produce q1.
• The slope of total costs, TC = wL + vK, is
-w/v.
• Lines of equal cost will have the same slope
so they will be parallel.
• Three equal total costs lines, labeled TC1,
TC2, and TC3 are shown in Figure 6.1.
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FIGURE 6.1: Minimizing the
Costs of Producing q1
Capital
per week
TC1
TC2
TC3
K*
q1
0
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L*
Labor
per week
Graphic Presentation
• The minimum total cost of producing q1 is
TC1 (since it is closest to the origin).
• The cost-minimizing input combination is
L*, K* which occurs where the total cost
curve is tangent to the isoquant.
• At the point of tangency, the rate at which
the firm can technically substitute L for K
(the RTS) equals the market rate (w/v).
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
An Alternative Interpretation
• From Chapter 5
MPL
RTS (of L for K) 
.
MPK
• Cost minimization requires
MPL w
RTS 
 ,
MPK v
• or, rearranging
MPL MPK

.
w
v
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The Firm’s Expansion Path
• A similar analysis could be performed for
any output level (q).
• If input costs (w and v) remain constant,
various cost-minimizing choices can be
traces out as shown in Figure 6.2.
• For example, output level q1 is produced
using K1, L1, and other cost-minimizing
points are shown by the tangency between
the total cost lines and the isoquants.
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The Firm’s Expansion Path
• The firm’s expansion path is the set of
cost-minimizing input combinations a firm
will choose to produce various levels of
output (when the prices of inputs are held
constant).
• Although in Figure 6.2, the expansion path
is a straight line, that is not necessarily the
case.
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FIGURE 6.2: Firm’s Expansion
Path
Capital
per week
TC1
TC2
TC3
Expansion path
q3
K1
q2
q1
0
L1
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Labor
per week
Cost Curves
• A firm’s expansion path shows how
minimum-cost input use increases when the
level of output expands.
• With this it is possible to develop the
relationship between output levels and total
input costs.
• These cost curves are fundamental to the
theory of supply.
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Cost Curves
• Figure 6.3 shows four possible shapes for
cost curves.
• In Panel a, output and required input use is
proportional which means doubling of
output requires doubling of inputs. This is
the case when the production function
exhibits constant returns to scale.
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FIGURE 6.3: Possible Shapes of
the Total Cost Curve
TC
Total
cost
Quantity
per week
(a) Constant Returns to Scale
0
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Cost Curves
• Panels b and c reflect the cases of decreasing
and increasing returns to scale, respectively.
• With decreasing returns to scale the cost
curve is convex, while the it is concave with
increasing returns to scale.
• Decreasing returns to scale indicate
considerable cost advantages from large scale
operations.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
FIGURE 6.3: Possible Shapes of
the Total Cost Curve
TC
Total
cost
Total
cost
Quantity
per week
(a) Constant Returns to Scale
0
Total
cost
TC
0
Quantity
per week
(c) Increasing Returns to Scale
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
TC
Quantity
per week
(b) Decreasing Returns to Scale
0
Cost Curves
• Panel d reflects the case where there are
increasing returns to scale followed by
decreasing returns to scale.
• This might arise because internal coordination and control by managers is
initially underutilized, but becomes more
difficult at high levels of output.
• This suggests an optimal scale of output.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
FIGURE 6.3: Possible Shapes of
the Total Cost Curve
TC
Total
cost
Total
cost
Quantity
per week
(a) Constant Returns to Scale
0
Total
cost
TC
0
Quantity
per week
(b) Decreasing Returns to Scale
TC
0
Total
cost
Quantity
per week
(c) Increasing Returns to Scale
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
TC
0
Quantity
per week
(d) Optimal Scale
Average Costs
TC
Average cost  AC 
q
• Average cost is total cost divided by output;
a common measure of cost per unit.
• If the total cost of producing 25 units is
$100, the average cost would be
$100
AC 
 $4
25
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Marginal Cost
Change in TC
Marginal cost  MC 
Change in q
• The additional cost of producing one more
unit of output is marginal cost.
• If the cost of producing 24 units is $98 and
the cost of producing 25 units is $100, the
marginal cost of the 25th unit is $2.
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Marginal Cost Curves
• Marginal costs are reflected by the slope of
the total cost curve.
• The constant returns to scale total cost curve
shown in Panel a of Figure 6.3 has a
constant slope, so the marginal cost is
constant as shown by the horizontal
marginal cost curve in Panel a of Figure 6.4.
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FIGURE 6.4: Average and
Marginal Cost Curves
AC, MC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
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Marginal Cost Curves
• With decreasing returns to scale, the total
cost curve is convex (Panel b of Figure 6.3).
• This means that marginal costs are
increasing which is shown by the positively
sloped marginal cost curve in Panel b of
Figure 6.4.
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FIGURE 6.4: Average and
Marginal Cost Curves
AC, MC
AC, MC
MC
AC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
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Quantity
per week
(b) Decreasing Returns to Scale
0
Marginal Cost Curves
• Increasing returns to scale results in a
concave total cost curve (Panel c of Figure
6.3).
• This causes the marginal costs to decrease
as output increases as shown in the
negatively sloped marginal cost curve in
Panel c of Figure 6.4.
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FIGURE 6.4: Average and
Marginal Cost Curves
AC, MC
AC, MC
MC
AC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
AC, MC
0
AC
MC
Quantity
per week
(c) Increasing Returns to Scale
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Quantity
per week
(b) Decreasing Returns to Scale
0
Marginal Cost Curves
• When the total cost curve is first concave
followed by convex as shown in Panel d of
Figure 6.3, marginal costs initially decrease
but eventually increase.
• Thus, the marginal cost curve is first
negatively sloped followed by a positively
sloped curve as shown in Panel d of Figure
6.4.
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FIGURE 6.4: Average and
Marginal Cost Curves
AC, MC
AC, MC
MC
AC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
Quantity
per week
(b) Decreasing Returns to Scale
0
AC, MC
AC, MC
0
AC
MC
Quantity
per week
(c) Increasing Returns to Scale
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MC
0
AC
q* Quantity
per week
(d) Optimal Scale
Average Cost Curves
• If a firm produces only one unit of output,
marginal cost would be the same as average
cost
• Thus, the graph of the average cost curve
begins at the point where the marginal cost
curve intersects the vertical axis.
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Average Cost Curves
• For the constant returns to scale case,
marginal cost never varies from its initial
level, so average cost must stay the same as
well.
• Thus, the average cost curve are the same
horizontal line as shown in Panel a of
Figure 6.4.
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Average Cost Curves
• With convex total costs and increasing
marginal costs, average costs also rise as
shown in Panel b of Figure 6.4.
• Because the first few units are produced at
low marginal costs, average costs will
always b less than marginal cost, so the
average cost curve lies below the marginal
cost curve.
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Average Cost Curves
• With concave total cost and decreasing
marginal costs, average costs will also
decrease as shown in Panel c in Figure 6.4.
• Because the first few units are produced at
relatively high marginal costs, average is
less than marginal cost, so the average cost
curve lies below the marginal cost curve.
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Average Cost Curves
• The U-shaped marginal cost curve shown in
Panel d of Figure 6.4 reflects decreasing
marginal costs at low levels of output and
increasing marginal costs at high levels of
output.
• As long as marginal cost is below average
cost, the marginal will pull down the
average.
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Average Cost Curves
• When marginal costs are above average
cost, the marginal pulls up the average.
• Thus, the average cost curve must intersect
the marginal cost curve at the minimum
average cost; q* in Panel d of Figure 6.4.
• Since q* represents the lowest average cost,
it represents an “optimal scale” of
production for the firm.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
APPLICATION 6.2: Findings on
Long-Run Costs
• Entries in Table 1 represent long-run
average cost estimates for different size
firms as a percentage of the minimal
average-cost firm in the industry.
• These estimates, except for trucking,
suggest lower average cost for medium and
large firms.
• Figure 1 shows the average cost firm
suggested by the data.
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FIGURE 1: Long-Run Average Cost
Curve Found in Many Empirical Studies
Average
cost
AC
0
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q*
Quantity
per period
TABLE 1: Long-Run AverageCost Estimates
Firm Size
Industry
Small
Medium
Large
Aluminum
Automobiles
Electric power
HMOs
Hospitals
Life insurance
Lotteries (state)
Sewage treatment
Trucking
166.6
144.5
113.2
118.0
129.6
113.6
175.0
104.0
100.0
131.3
122.7
101.1
106.3
111.1
104.5
125.0
101.0
102.1
100.0
100.0
101.5
100.0
100.0
100.0
100.0
100.0
105.6
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APPLICATION 6.3: Airlines’
Costs
• Costs for airlines have been of interest to
economists because of recent changes such
as deregulation, bankruptcy, and mergers.
• Two general findings:
– Costs seem to differ substantially among U.S.
firms.
– Costs for U.S. airlines appear to be significantly
lower than for airlines in other countries.
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Reasons for Differences among
U.S. Firms
• Airlines that fly longer average distances or
operate a greater number of flights over a
given network tend to have lower costs.
– Firms can spread the fixed costs associated with
terminals, maintenance facilities, and
reservation systems over a larger output
volume.
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Reasons for Differences among
U.S. Firms
• Firms that operate older fleets or that
operate fleets with many different types of
planes tend to have higher maintenance and
fuel costs.
• Wage costs, especially for pilots, also differ
significantly among the airlines.
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International Airline Regulation
and Costs
• Many foreign carriers’ have not adopted the
“hub and spoke” system which appears to
be more efficient.
• Foreign firms are subject to more
regulation.
– This situation appears to be changing. For
example, Australia ended rigid controls and
costs fell by 15 to 20 percent.
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Distinction between the Short
Run and the Long Run
• The short run is the period of time in
which a firm must consider some inputs to
be absolutely fixed in making its decisions.
• The long run is the period of time in which
a firm may consider all of its inputs to be
variable in making its decisions.
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Holding Capital Input Constant
• For the following, the capital input is
assumed to be held constant at a level of K1,
so that, with only two inputs, labor is the
only input the firm can vary.
• As examined in Chapter 5, this implies
diminishing marginal productivity to labor.
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Short-Run Total Costs
• Total cost for the firm is
TC = vK + wL
• The short-run analysis is denoted by
STC = vK1 + wL.
• The term vK1 is called (short-run) fixed
costs; costs associated with inputs that are
fixed in the short run.
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Short-Run Total Costs
• The term wL is referred to as (short-run)
variable costs; costs associated with inputs
that can be varied in the short run.
• Using the terms SFC for short-run fixed
costs and SVC for short-run variable costs,
the firms short-run costs are given by
STC = SFC + SVC.
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Short-Run Fixed and Variable
Cost Curves
• Since short-run fixed costs do not change
with output, the short-fun fixed cost (SFC)
curve is horizontal as shown in Panel a of
Figure 6.5.
• Panel b of figure 6.5 shows one possible
relationship between short-run variable
costs (SVC) and output.
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FIGURE 6.5: Fixed and Variable
Costs in the Short Run
Fixed
costs
Variable
costs
SVC
SFC
0
Quantity
per week
0
q’
Quantity
per week
(a) Short-Run Fixed Cost Curve(b) Short-Run Variable Cost Curve
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Short-Run Variable Cost Curve
• Initially the marginal productivity of labor
rises as more labor is added to the
production process as the fixed input is
“underutilized.”
• Because the marginal product of labor is
increasing, the short-run variable cost curve
is concave.
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Short-Run Variable Cost Curve
• Beyond some output level, say q’, however,
the marginal product of labor will
eventually decline causing the costs of
production to rise rapidly.
• This implies that the short-run variable cost
curve (SVC) will then be convex beyond q’.
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Short-Run Total Cost Curve
• The short-run total cost curve is the
summation of the short-run fixed cost curve
and the short-run variable cost curve.
• This curve, which is shown in Figure 6.6,
intersects the vertical axis at SFC and has
the shape of the SVC curve.
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FIGURE 6.6: Short-Run Total
Cost Curve
STC
Total
costs
SFC
0
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Quantity
per week
Input Inflexibility and Cost
Minimization
• Since capital is fixed, short-run costs are not
the minimal costs of producing variable
output levels.
• Assume the firm has fixed capital of K1 as
shown in Figure 6.7.
• To produce q0 of output, the firm must use
L1 units of labor, with similar situations for
q1, L1, and q2, L2.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
FIGURE 6.7: “Nonoptimal” Input
Choices Must Be Made in the Short Run
Capital
per week
STC0
STC2
STC1
K1
q2
q1
q0
0
L0
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L1
L2
Labor
per week
Input Inflexibility and Cost
Minimization
• The cost of output produced is minimized
where the RTS equals the ratio of prices,
which only occurs at q1, L1.
• Q0 could be produce at less cost if less capital
than K1 and more labor than L0 were used.
• Q2 could be produced at less cost if more
capital than K1 and less labor than L2 were
used.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Per-Unit Short-Run Cost Curves
STC
Short - run average cost  SAC 
q
and
Change in STC
Short - run marginal cost  SMC 
Change in q
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Per-Unit Short-Run Cost Curves
• Having capital fixed in the short run yields a
total cost curve that has both concave and
convex sections, the resulting short-run
average and marginal cost relationships will
also be U-shaped.
• These two curves are shown in Figure 6.8.
• When SMC < SAC, average cost is falling,
but when SMC > SAC average cost increase.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
FIGURE 6.8: Per-Unit Short-Run
Cost Curves
Unit
cost
SMC
SAC
0
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Quantity
per week
Relationship between Short-Run and
Long-Run per-Unit Cost Curves
• Figure 6.9 shows all cost relationships for a
firm that has U-shaped long-run average
and marginal cost curves.
• At output level q* long-run average costs
are minimized and MC = AC.
• Associated with q* is a certain level of
capital, K*.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
FIGURE 6.9: Short-Run and Long-Run
Average and Marginal Cost Curves at
Optimal Output Level
AC, MC
MC
AC
SMC
SAC
0
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
q*
Quantity
per week
Relationship between Short-Run and
Long-Run per-Unit Cost Curves
• In the short-run, when the firm using K*
units of capital produces q*, short-run and
long-run total costs are equal.
• In addition, as shown in Figure 6.9
AC = MC = SAC(K*) = SMC(K*).
• For output above q* short-run costs are
higher than long-run costs. The higher perunit costs reflect the facts that K is fixed.
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APPLICATION 6.4: Congestion
Costs
• For any traffic facility (road, bridge, tunnel,
and so forth), output is measured in number
of vehicles per hour.
• Capital costs are largely fixed, as
depreciation occurs regardless of the level
of traffic.
• Variable costs consist primarily of
motorists’ time.
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APPLICATION 6.4: Congestion
Costs
• Studies, based on people’s willingness to
spend time commuting, indicate travel time
“costs” about $8 per hour.
• The marginal cost of producing “one more
trip” is the overall increase in travel time
experienced by all motorists when one more
vehicle uses a traffic facility.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
APPLICATION 6.4: Congestion
Costs
• The high costs associated with adding an
extra automobile to an already crowded
facility are not directly experienced by the
motorist driving the car, because these costs
are imposed on other motorists.
• This divergence between the private costs
and the total social costs leads to motorists
opting for overutilizeing traffic facilities.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Congestion Tolls
• The standard economists answer to this
problem is to adopt taxes that bring social
and private marginal costs into agreement.
• This implies the adoption of highway,
bridge, or tunnel tolls, that accurately reflect
social costs.
• Since these costs vary by time of day, tolls
should also vary over the day.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Toll-Collecting Technology
• This approach was previously not feasible
since collection booths for tolls would add
more to the congestion that in aiding to the
solving of the problem.
• However, the development of low-cost
electronic toll collection techniques, now
make it possible using cards with pre-coded
computer chips.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Shifts in Cost Curves
• Any change in economic conditions that
affects the expansion path will also affect
the shape and position of the firm’s cost
curves.
• Three sources of such change are:
– change in input prices
– technological innovations, and
– economies of scope.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Changes in Input Prices
• A change in the price of an input will tilt the
firm’s total cost lines and alter its expansion
path.
• For example, a rise in wage rates will cause
firms to use more capital (to the extent
allowed by the technology) and the entire
expansion path will rotate toward the capital
axis.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Changes in Input Prices
• Generally, all cost curves will shift upward
with the extent of the shift depending upon
how important labor is in production and
how successful the firm is in substituting
other inputs for labor.
– With important labor and poor substitution
possibilities, a significant increase in costs will
result.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Technological Innovations
• Because technological advances alter a
firm’s production function, isoquant maps
as well as the firm’s expansion path will
shift when technology changes.
• Unbiased improvements would shift
isoquants toward the origin enabeling firms
to produce the same level of output with
less of all inputs.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Technological Innovations
• Technological change that is biased toward
the use of one input will alter isoquant
maps, shift expansion paths, and affect the
shape and location of cost curves.
– For example, if workers became more skilled,
this would save only on labor input.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Economies of Scope
• Economies of scope is the reduction in the
costs of one product of a multiproduct firm
when the output of another product is
increased.
– For example, when hospitals do many surgeries
of one type, it may have cost advantages in
doing other types because of the similarities in
equipment and operating personnel used.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
APPLICATION 6.5: The
Microelectronic Revolution
• The effect of the development of
semiconductor technology has been
estimated to have halved the cost of
computing power every two or three years
since the early 1970s.
• Hand-held electronic calculators cost over
$100 to produce in the early 1970s, but cost
approximately $10 by 1975.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
APPLICATION 6.5: The
Microelectronic Revolution
• Similar types of saving have occurred with
personal computers (PCs).
• Studies by the Bureau of Economic
Analysis (BEA) of the Commerce
Department show that computer and related
peripheral equipment prices have been
falling at a rate of approximately 20 percent
per year since 1982.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
APPLICATION 6.5: The
Microelectronic Revolution
• While the price of computers has not fallen
in price, the performance obtained for this
price has improved rapidly.
• The BEA devised ways to estimate implicit
prices for various characteristics of
computers such as speed, memory, and data
storage.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
APPLICATION 6.5: The
Microelectronic Revolution
• These base-year prices were then used to
estimate what a computer with the
characteristics of a new machine would
have cost if the older implicit prices had
continued.
• The difference between the computed price
and the actual price paid represents the
estimate of the decline in price.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
A Numerical Example
• Assume Hamburger Heaven (HH) can hire
workers at $5 per hour and it rents all of its
grills for $5 per hour.
• Total costs for HH during one hour are
TC = 5K + 5L
where K and L are the number of grills and
the number of workers hired during that
hour, respectively.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
A Numerical Example
• Suppose HH wishes to produce 40
hamburgers per hour.
• Table 6.1 repeats the various ways HH can
produce 40 hamburgers per hour.
– This shows that total costs are minimized when
K = L = 4.
• Figure 6.10 shows the cost-minimizing
tangency.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
TABLE 6.1: Total Costs of
Producing 40 Hamburgers per Hour
Output (q)
Workers (L)
40
40
40
40
40
40
40
40
40
40
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
1
2
3
4
5
6
7
8
9
10
Grills (K)
16.0
8.0
5.3
4.0
3.2
2.7
2.3
2.0
1.8
1.6
Total Cost (TC)
$85.00
50.00
41.50
40.00
41.00
43.50
46.50
50.00
54.00
58.00
Figure 6.10: Cost-Minimizing Input
Choice for 40 Hamburgers per Hour
Grills
per hour
8
E
4
2
40 hamburgers per hour
Total cost = $40
0
2
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
4
8
Workers
per hour
Long-Run cost Curves
• HH’s production function is constant returns
to scale so
• As long as w = v = $5, all of the cost
minimizing tangencies will resemble the
one shown in Figure 6.10 and long-run cost
minimization will require K = L.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Long-Run cost Curves
• This situation, resulting from constant
returns to scale, is shown in Figure 6.11.
• HH’s long-run total cost function is a
straight line through the origin as shown in
Panel a.
• Its long-run average and marginal costs are
constant at $1 per burger as shown in Panel
b.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
FIGURE 6.11: Total, Average,
and Marginal Cost Curves
Total
costs
Average and
marginal costs
Total
costs
$80
60
40
20
Average and
marginal costs
$1.00
0 20 40 60 80 Hamburgers
per hour
(a) Total Costs
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
0 20
40
60
80
Hamburgers
per hour
(b) Average and Marginal Costs
Short-Run Costs
• Table 6.2 repeats the labor input required to
produce various output levels holding grills
fixed at 4.
• Diminishing marginal productivity of labor
causes costs to rise rapidly as output
expands.
• Figure 6.12 shows the short-run average and
marginal costs curves.
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
TABLE 6.2: Short-Run Costs of
Hamburger Production
Output (q)
Workers
(L)
10
20
30
40
50
60
70
80
90
100
0.25
1.00
2.25
4.00
6.25
9.00
12.25
16.00
20.25
25.00
Copyright (c) 2000 by Harcourt, Inc. All rights reserved.
Grills (K)
Total Cost
(STC)
Average
Cost (SAC)
Marginal
Cost (SMC)
4
4
4
4
4
4
4
4
4
4
$21.25
25.00
31.25
40.00
51.25
65.00
81.25
100.00
121.25
145.00
$2.125
1.250
1.040
1.000
1.025
1.085
1.160
1.250
1.345
1.450
$0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
FIGURE 6.12: Short-Run and Long-Run
Average and Marginal Cost Curves for
Hamburger Heaven
Average and
marginal costs
$2.50
SMC (4 grills)
2.00
SAC (4 grills)
1.50
1.00
AC, MC
.50
0
20
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40
60
80
100 Hamburgers
per hour