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Chapter 7
Minimizing Costs
1. measuring costs
2. short-run cost minimization
3. long-run cost minimization
4. costs are lower in long run
5. costs of producing multiple goods
simultaneously
Key issues
Applications & problems
• taxes and depreciation
• labor only firm
• allocating time on an exam
• demolishing buildings
• agricultural subsidies and land restrictions
• tomato harvester
Two-step procedure to choose
technology
1. pick all technologically efficient production
processes
2. from these technologically efficient
production processes, pick the one that is
economically efficient (minimizes cost)
Two reasons to study costs
1. understanding relationship between costs of
inputs and production helps us determine
least costly way to produce
2. relationship between output and costs
determines nature of an industry
• how many firms are in the industry

• how high price is relative to cost
Business vs. economic costs
• business costs: only explicit costs (out of pocket)
• economic costs: explicit cost + implicit cost =
opportunity cost
• opportunity cost
• value of best alternative use of the resource
• classic example: "There's no such thing as a free lunch"
• “What have you given up to study opportunity costs”
2
Cost of running your own firm
• explicit cost: $40,000 per year (rent, materials,
wage payments)
• instead of paying yourself a salary, you keep any
profit at year's end
• your labor opportunity cost = $25,000/year you
could have earned working for another firm
• business cost = $40,000
• economic cost = $65,000 = $40,000 + $25,000
Capital costs
• capital is a durable good: a product that is
usable for years
• capital may be rented or purchased
If capital is rented
• rental payment is the opportunity cost
• using the rental rate avoids 2 measurement
problems
• don't have to worry how to allocate the initial
purchase cost over time
• any adjustment in the cost of capital over time

is reflected in the rental rate
If capital is purchased
• firm's bookkeeper may
• expense cost by recording purchase price when it's
made, or
• amortize cost by spreading it over life of capital
according to IRS's arbitrary rules
• economists amortize capital cost based on its
opportunity cost at each moment of time:
• amount that firm could charge others to rent capital
• thus, economists always use rental rate
Depreciate a business vehicle
• Toyota Land Cruiser (sports utility vehicle) and
Cadillac Seville (car) both cost $45,000
• tax law let’s you depreciate Land Cruiser in 6
years vs. 23 for Seville
• after 5 years depreciated $42,408 for Land Cruiser
vs. $14,460 for Seville
• “reason”
• Land Cruiser weighs more than 6,000 pounds and
Seville doesn't
• Congress uses 6,000 pounds as a criterion to distinguish
between trucks and cars
Short-run cost measures
• fixed cost (F): production expense that does
not vary with output
• variable cost (VC): production expense that
changes with quantity of output produced
• total cost (C):
C = VC + F

3
Sunk fixed cost
• usually assume fixed cost is sunk: expenditure that
you cannot be recovered
• opportunity cost of capital is zero
• because you can't get this expenditure back no matter
what you do, so ignore it when making decisions
• example: walk out of a bad movie early,
regardless of what you paid to attend
• otherwise, fixed cost is called avoidable
Marginal cost (MC)
• cost of producing the last unit
• change in cost, ∆C, when output changes by
∆q
• ∆C/∆q (or dC/dq)
Average cost concepts
• average fixed cost:
AFC = F /q
• average variable cost:
AVC = VC /q
• average (total) cost:
AC = C/q = AFC + AVC
Figure 7.1
Short-Run Cost Curves
120
216
400
48
0610
10

428
Quantity, q, Units per day
Quantity, q, Units per day
6
b
a
B
A
428
C
F
1
1
27
20
VC
MC
AC
AVC
AFC
Cost, $
Cost per unit, $
(a)
(b)
60
28
27
20
8
0

MC curve cuts AC and AVC at
their minimum points
• AC and AVC curves fall when MC is below
them, and rise when MC is above them
• therefore, MC cuts AC and AVC curves at
their minimum points
4
Production function determines
shape of cost curve
• production function shows how many inputs
needed to produce a given level of output
• firm's cost: multiply quantity of each input
by its price and sum
Norwegian printing firm
• short-run AC curve is U-shaped even
though AVC is strictly upward sloping
• firm's capital is fixed at 100
Application Short-Run Cost Curves for a Printing Firm
Cost, kroner
100 200 300
q, Units per year
AFC
AVC
AC
MC
0
20
30
40
50

10
Cost effects of $10 specific tax
• affects variable but not fixed cost
• after-tax (a) cost = before-tax (b) cost + 10q:
C
a
= C
b
+ 10q
• at every quantity, AVC, AC, and MC curves shift
up by $10:
AVC
a
= AVC
b
+ $10
AC
a
= AC
b
+ $10
MC
a
= MC
b
+ $10
Figure 7.3 Effects of a Specific Tax on Cost Curves
Costs per
unit, $
1558100

q, Units per day
80
37
27
$10
AC
a
= AC
b
+ 10
AC
b
MC
b
MC
a
= MC
b
+ 10
$10
Cost effects of lump-sum tax
• affects fixed cost but not variable cost
• after-tax (a) cost = before-tax (b) cost plus
lump-sum tax (
L
):
C
a
= C
b

+
L
• thus
AC
a
= AC
b
+
L
/q
MC
a
= MC
b
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Solved Problem 7.1
Costs per
unit, $
/q
q, Units per day
AC
b
q
a
C
q
b
AC
a
=

AC
b
+
/
q
M
Lump-sum tax: California
$800-per-year tax is levied “for the privilege
of doing business in California”
Lump-sum tax: New York
$900,600 for three-year license to sell hot
dogs in front of NY City's Metropolitan
Museum of Art
Long-run costs
• firm adjusts all its inputs so its cost of
production is as low as possible
• if capital and other variable can be varied,
no LR fixed costs (F = 0)
• then LR total cost = LR variable cost:
C = VC
Input choice
choose from all technologically efficient
combinations of inputs, the economically
efficient combination of inputs
Costs of input bundles
• isocost: all combinations of inputs that
require the same (iso) total expenditure
(cost)
•if cost is C = wL + rK
• then isocost is

• where is a fixed level of cost
,CwLrK=+
C
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Figure 7.4 A Family of Isocost Lines
K, Units of
capital per year
a
b
d
e
c
$150 isocost$100 isocost$50 isocost
$100
———
$5
=
20
$150
———
$5
=
30
$50
———
$5
=
10
$100
———

$10
10
=
$50
———
$10
5
=
$150
———
$10
15
=
L, Units of labor per year
Properties of isocost lines
1. where isocost line hits axes depends on and factor
prices
• intersects capital axis at
• intersects labor axis at
2. isocosts farther from origin have higher costs:
3. slope of each isocost line is the same:
∆K/∆L = -w/r
/Cr
/Cw
Cw
K
L
rr
=−
Figure 7.5 Cost minimization for Norweigian printing firm

K, Units of
capital per year
y
x
z
11650240
L , Units of labor per year
100
303
28
q = 100 isoquant
3,000-kr
isocost
2,000-kr
isocost
1,000-kr
isocost
Equivalent cost-minimizing rules
to pick lowest-cost combination of inputs to
produce a given level of output when isoquants
are smooth:
• lowest-isocost rule: pick bundle of inputs where
lowest isocost line touches isoquant
• tangency rule: isoquant is tangent to isocost line:
MRTS = |ratio of the input prices| = w/r
• last-dollar rule: last dollar spent on one input
produces as much extra output as last dollar
spent on any other input
Derivation of last dollar rule
L

K
M
Pw
MRTS
M
Pr
==
L
K
M
PMP
wr
=
Cost minimizing vs. output
maximizing
with smooth isoquants: firm determines best
factor proportions by either
• cost minimizing: what is the lowest cost, C*, at
which the firm can produce output q*?
• output maximizing: What is the most output,
q*, that can be produced at cost C*?
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Relative factor price changes
• cause firm to change the mix of inputs used
• firm substitutes relatively less expensive
inputs for more expensive ones
• In Figure 7.6, r = 8 kr
• original wage = 24 kr, so w/r = 3
• new wage = 8 kr, so w/r = 1
Figure 7.6 Change in Factor Price

K, Units of
capital per year
v
x
77500 L, Workers per year
100
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q = 100 isoquant
Original
isocost,
2,000 kr
New isocost,
1,032 kr
LR cost varies with output
• examine lowest-cost factor combination for
various levels of output
• expansion path:
• cost-minimizing combination of labor and capital for
each output level
• curve through tangency points is LR expansion path
• expansion path shows same relationship between
LR cost and output as the LR cost curve
Figure 7.7a Expansion Path and Long-Run cost Curve
K, Units of
capital per year
x
y
z
10075500 L, Workers per year
150

200
100
Expansion path
(a) Expansion Path
3,000-kr
isocost
2,000-kr
isocost
4,000-kr isocost
100 isoquant
150 isoquant
200 isoquant
Figure 7.7b Expansion Path and Long-Run cost Curve
C, Cost, kroner
X
Y
Z
0 q, Units per year
4,000
3,000
2,000
Long-run cost curve
(b) Long-Run Cost Curve
200100 150
Solved Problem
• suppose that the wage rate falls (while the
rental rate of capital remains unchanged)
• what happens to the expansion path?
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Shape of LR cost curves

• reason why LR AC is U-shaped different than SR
•SR:
•SR AC initially downward sloping because AFC is
downward sloping
•SR AC later upward sloping because of diminishing
returns
•LR
• no fixed cost in LR (usually)
• production function returns to scale determine shape
Figure 7.8 Long-Run Cost Curves
Cost, $
q* q, Quantity per day
(a) Cost Curve
C
Cost per
unit, $
q* q, Quantity per day
MC
AC
(b) Marginal and Average Cost Curves
Economies of scale
AC rises when output increasesdiseconomies of scale
AC does not change as output
increases
no economies of scale
AC falls as output expandseconomies of scale
Causes of economies of scale
• returns to scale in production function
• sufficient condition for AC economies of scale
• not necessary condition

• in LR, firm may change ratio of K/L as it
expands output, so could have economies of
scale in costs without increasing returns to
scale in production
Costs lower in long run
• in LR, firm chooses optimal plant size level
to minimize its LR cost given q
• because the firm cannot vary its capital in
SR but can in LR
• SR cost ≥ LR cost
• SR cost > LR cost if the "wrong" level of
capital is used in SR
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Figure 7.9 Long-Run Average Cost as the Envelope of
Short-Run Average Cost Curves
Average cost, $
a
b
d
e
SRAC
1
SRAC
2
SRAC
3
SRAC
3
LRAC
c

q
2
q
1
q, Output per day
10
0
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Long-Run Cost Curves in Printing and Oil Pipelines
(a) Norwegian Printing Firm
Cost, kroner
200 600 1,200
q, Output per year
0
20
30
40
10
SRAC
1
SRMC
1
SRAC
2
SRMC
2
LRAC
=
LRMC
Long-Run Cost Curves in Printing and Oil Pipelines

(b) Oil Pipelines
2000100040020010 20 40 1000
Thousand barrels per day
Cost per barrel-mile
150
100
50
10
8"SRAC
10"SRAC
16"SRAC
12"SRAC
26"SRAC
20
"
SRAC
40
"
SRAC
LRAC
Why LR cost ≤ SR cost
• firms have more flexibility in long run
• technical progress may lower cost over time
• learning by doing: productive skills and
knowledge of better ways to produce that
workers and managers gain from experience
Figure 7.11a Learning by Doing
Labor costs
per plane, $
250100 150 200500

C-141 planes
(a) Learning by Doing on C-141 Aircraft
500
400
300
200
100
Average labor cost
Figure 7.11b Learning by Doing
Average cost
A
B
C
b
c
q, Output per period
(b) Economies of Scale and Learning by Doing
Learning by doing
Economies of scale
q
2
q
3
AC
3
AC
2
AC
1
q

1
10
Cost of producing multiple goods
• outputs are linked if a single input is used to
produce all of them
• mutton and wool both come from sheep
• beef and hides come from cattle
• heating fuel and gasoline come from oil
• it is less expensive to produce goods jointly
than separately (beef & hides)
Joint production
• Laura spends one day collecting mushrooms and
wild strawberries in the wood
• economies of scope (PPF
1
)
• picking only mushrooms: 8 pints
• pick only strawberries: 6 pints
• pick some of each: 6 pints of mushrooms and 4 pints of
strawberries
• no economies of scope (PPF
2
)
• mushrooms grow in one section and strawberries in
another
•PPF
2
is a straight line
Figure 7.12 Joint Production
Mushrooms,

Pints per day
PPF
2
PPF
1
64
Wild strawberries, Pints per day
8
6
0
Measuring scope (SC)
• C(q
1
, 0) = cost of producing q
1
units of first
good by itself
• C(0, q
2
) = cost of producing only q
2
units of
second good
• C(q
1
, q
2
) = cost of producing both goods
together
1212

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(,0) (0, ) (, )
(, )
Cq C q Cq q
SC
Cq q
+−
=
Scope
cheaper to produce
separately
SC < 0
diseconomies of scope
cost same either waySC = 0
no economies of scope
cheaper to produce
goods jointly
SC > 0
economies of scope
Economies of scope
• refining: cheaper to produce motor gasoline,
distillate fuels, and other refined products together
• auto manufacturing: four automobile
manufacturers
• 25% less expensive (SC = 0.25) to produce large cars
together with small cars and trucks than to produce
large cars separately and small cars and trucks together
• no economies of scope from producing trucks together
with small and large cars
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Diseconomies of scope
using railroads to transport freight and passengers
together
• 41% less expensive (SC = -0.41) to transport
passengers and freight separately than together
• in early 1970s: passenger service was transferred
from the private railroad companies to Amtrak,
and services are separate
Summary
cost minimization from all technologically
efficient production processes, choose one
that is economically efficient
1. Measuring costs
• use economic cost: explicit + implicit costs
• opportunity cost: value of next best
alternative use includes both explicit and
implicit costs
2. Short-run costs
• some factors are fixed in the SR
• costs vary with only variable (nonfixed)
inputs
3. Long-run costs
• all factors can be varied, so all costs are variable
• AC = AVC
• costs minimized where
• lowest isocost touches the relevant isoquant
• isocost is tangent to the isoquant
• last dollar spent on any input increases output by as
much as last dollar spent on any other input
4. Costs are lower in long run

• more flexibility in LR
• technological progress
• learning by doing
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5. Costs of producing multiple
goods
• economies of scope: less expensive to
produce goods jointly rather than separately
• diseconomies of scope: less expensive to
produce separately