Chapter 7
The Cost of
Production
Chapter 7 Slide 2
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 3
Topics to be Discussed
? Production with Two Outputs--
Economies of Scope
? Dynamic Changes in Costs--The
Learning Curve
? Estimating and Predicting Cost
Chapter 7 Slide 4
Introduction
? The production technology measures
the relationship between input and
output,
? Given the production technology,
managers must choose how to
produce,
Chapter 7 Slide 5
Introduction
? 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 6
Measuring Cost,
Which Costs Matter?
? Accounting Cost
? Actual expenses plus depreciation
charges for capital equipment
? Economic Cost
? Cost to a firm of utilizing economic
resources in production,including
opportunity cost
Economic Cost vs,Accounting Cost
Chapter 7 Slide 7
? Opportunity cost,
? Cost associated with opportunities that
are foregone when a firm’s resources
are not put to their highest-value use,
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 8
? 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?
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 9
? Sunk Cost
? Expenditure that has been made and
cannot be recovered
? Should not influence a firm’s decisions,
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 10
? An Example
? A firm pays $500,000 for an option to buy a
building,
? The cost of the building is $5 million or a total of
$5.5 million,
? The firm finds another building for $5.25 million,
? Which building should the firm buy?
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 11
Choosing the Location
for a New Law School Building
? Northwestern University Law School
1) Current location in downtown
Chicago
2) Alternative location in Evanston
with the main campus
Chapter 7 Slide 12
? Northwestern University Law School
3) Choosing a Site
?Land owned in Chicago
?Must purchase land in Evanston
?Chicago location might appear
cheaper without considering the
opportunity cost of the downtown land
(i.e,what it could be sold for)
Choosing the Location
for a New Law School Building
Chapter 7 Slide 13
? Northwestern University Law School
3) Choosing a Site
?Chicago location chosen--very costly
?Justified only if there is some intrinsic
values associated with being in
Chicago
?If not,it was an inefficient decision if it
was based on the assumption that the
downtown land was,free”
Choosing the Location
for a New Law School Building
Chapter 7 Slide 14
? Total output is a function of variable
inputs and fixed inputs,
? Therefore,the total cost of production
equals the fixed cost (the cost of the
fixed inputs) plus the variable cost
(the cost of the variable inputs),or…
V C FC TC ??
Measuring Cost,
Which Costs Matter?
Fixed and Variable Costs
Chapter 7 Slide 15
? Fixed Cost
?Does not vary with the level of output
? Variable Cost
?Cost that varies as output varies
Measuring Cost,
Which Costs Matter?
Fixed and Variable Costs
Chapter 7 Slide 16
? Fixed Cost
?Cost paid by a firm that is in business
regardless of the level of output
? Sunk Cost
?Cost that have been incurred and cannot
be recovered
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 17
?Personal Computers,most costs
are variable
?Components,labor
?Software,most costs are sunk
?Cost of developing the software
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 18
?Pizza
?Largest cost component is fixed
Measuring Cost,
Which Costs Matter?
A Firm’s Short-Run Costs ($)
0 50 0 50 --- --- --- ---
1 50 50 100 50 50 50 100
2 50 78 128 28 25 39 64
3 50 98 148 20 16.7 32.7 49.3
4 50 112 162 14 12.5 28 40.5
5 50 130 180 18 10 26 36
6 50 150 200 20 8.3 25 33.3
7 50 175 225 25 7.1 25 32.1
8 50 204 254 29 6.3 25.5 31.8
9 50 242 292 38 5.6 26.9 32.4
10 50 300 350 58 5 30 35
11 50 385 435 85 4.5 35 39.5
Rate of Fixed Variable Total Marginal Average Average Average Output Cost Cost Cost Cost Fixed Variable Total
(FC) (VC) (TC) (MC) Cost Cost Cost
(AFC) (AVC) (ATC)
Chapter 7 Slide 20
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,
Q
TC
Q
VC
MC
?
?
?
?
?
?
Chapter 7 Slide 21
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,
Q
T VC
Q
T F C A T C ??
Chapter 7 Slide 22
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,
Q
TCor A VC A F C A T C ??
Chapter 7 Slide 23
Cost in the Short Run
? The Determinants of Short-Run Cost
? The relationship between the production
function and cost can be exemplified by
either increasing returns and cost or
decreasing returns and cost,
Chapter 7 Slide 24
Cost in the Short Run
? The Determinants of Short-Run 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 25
Cost in the Short Run
? For Example,Assume the wage rate
(w) is fixed relative to the number of
workers hired,Then,
Q
VC
MC
?
?
?
L VC w?
Chapter 7 Slide 26
Cost in the Short Run
? Continuing,
L VC ??? w
Q
L
MC
?
?
?
w
Chapter 7 Slide 27
Cost in the Short Run
? Continuing,
L
MP L
?
??? Q
LMP
1
Q
L
Qu n i t 1 af o r L
?
?
?
?
???
Chapter 7 Slide 28
Cost in the Short Run
? In conclusion,
? …and a low marginal product (MP)
leads to a high marginal cost (MC)
and vise versa,
LMP
MC
w
?
Chapter 7 Slide 29
Cost in the Short Run
? Consequently (from the table),
? MC decreases initially with increasing
returns
?0 through 4 units of output
? MC increases with decreasing returns
?5 through 11 units of output
A Firm’s Short-Run Costs ($)
0 50 0 50 --- --- --- ---
1 50 50 100 50 50 50 100
2 50 78 128 28 25 39 64
3 50 98 148 20 16.7 32.7 49.3
4 50 112 162 14 12.5 28 40.5
5 50 130 180 18 10 26 36
6 50 150 200 20 8.3 25 33.3
7 50 175 225 25 7.1 25 32.1
8 50 204 254 29 6.3 25.5 31.8
9 50 242 292 38 5.6 26.9 32.4
10 50 300 350 58 5 30 35
11 50 385 435 85 4.5 35 39.5
Rate of Fixed Variable Total Marginal Average Average Average Output Cost Cost Cost Cost Fixed Variable Total
(FC) (VC) (TC) (MC) Cost Cost Cost
(AFC) (AVC) (ATC)
Chapter 7 Slide 31
Cost Curves for a Firm
Output
Cost
($ per
year)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VC
Variable cost
increases with
production and
the rate varies with
increasing &
decreasing returns,
TC Total cost is the vertical
sum of FC
and VC,
FC 50
Fixed cost does not
vary with output
Chapter 7 Slide 32
Cost Curves for a Firm
Output (units/yr.)
Cost
($ per
unit)
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
MC
ATC
AVC
AFC
Chapter 7 Slide 33
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)
Output
P
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
FC
VC
A
TC
Chapter 7 Slide 34
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 Output (units/yr.)
Cost
($ per
unit)
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
MC
ATC
AVC
AFC
Chapter 7 Slide 35
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
Output (units/yr.)
Cost
($ per
unit)
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
MC
ATC
AVC
AFC
Chapter 7 Slide 36
Operating Costs for Aluminum Smelting
($/Ton - based on an output of 600 tons/day)
Variable costs that are constant at all output levels
Electricity $316
Alumina 369
Other raw materials 125
Plant power and fuel 10
Subtotal $820
Chapter 7 Slide 37
Operating Costs for Aluminum Smelting
($/Ton - based on an output of 600 tons/day)
Variable costs that increase when output exceeds 600 tons/day
Labor $150
Maintenance 120
Freight 50
Subtotal $320
Total operating costs $1140
Chapter 7 Slide 38
The Short-Run Variable
Costs of Aluminum Smelting
Output (tons/day)
Cost
($ per ton)
1100
1200
1300
300 600 900
1140
MC
AVC
Chapter 7 Slide 39
Cost in the Long Run
? User Cost of Capital = Economic
Depreciation + (Interest Rate)(Value
of Capital)
The User Cost of Capital
Chapter 7 Slide 40
Cost in the Long Run
? Example
?Delta buys a Boeing 737 for $150 million
with an expected life of 30 years
?Annual economic depreciation =
$150 million/30 = $5 million
?Interest rate = 10%
The User Cost of Capital
Chapter 7 Slide 41
Cost in the Long Run
? Example
?User Cost of Capital = $5 million +
(.10)($150 million – depreciation)
?Year 1 = $5 million +
(.10)($150 million) = $20 million
?Year 10 = $5 million +
(.10)($100 million) = $15 million
The User Cost of Capital
Chapter 7 Slide 42
Cost in the Long Run
? Rate per dollar of capital
?r = Depreciation Rate + Interest Rate
The User Cost of Capital
Chapter 7 Slide 43
Cost in the Long Run
? Airline Example
?Depreciation Rate = 1/30 = 3.33/yr
?Rate of Return = 10%/yr
? User Cost of Capital
?r = 3.33 + 10 = 13.33%/yr
The User Cost of Capital
Chapter 7 Slide 44
Cost in the Long Run
? Assumptions
? Two Inputs,Labor (L) & capital (K)
? Price of labor,wage rate (w)
? The price of capital
?R = depreciation rate + interest rate
The Cost Minimizing Input Choice
Chapter 7 Slide 45
Cost in the Long Run
? Question
? If capital was rented,would it change the
value of r?
The User Cost of Capital The Co t Minimizing Input Choice
Chapter 7 Slide 46
Cost in the Long Run
? The Isocost Line
? C = wL + rK
? Isocost,A line showing all combinations
of L & K that can be purchased for the
same cost
The User Cost of Capital The Co t Minimizing Input Choice
Chapter 7 Slide 47
Cost in the Long Run
? Rewriting C as linear,
? K = C/r - (w/r)L
? Slope of the isocost,
? 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,
? ?rwLK ????
The Isocost Line
Chapter 7 Slide 48
Choosing Inputs
? We will address how to minimize cost
for a given level of output,
? We will do so by combining isocosts with
isoquants
Chapter 7 Slide 49
Producing a Given
Output at Minimum Cost
Labor per year
Capital
per
year
Isocost C2 shows quantity
Q1 can be produced with
combination K2L2 or K3L3,
However,both of these
are higher cost combinations
than K1L1,
Q1
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,
C0 C1 C2
CO C1 C2 are
three
isocost lines
A
K1
L1
K3
L3
K2
L2
Chapter 7 Slide 50
Input Substitution When
an Input Price Change
C2
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,
K2
L2
B
C1
K1
L1
A
Q1
If the price of labor
changes,the isocost curve
becomes steeper due to
the change in the slope -(w/L),
Labor per year
Capital
per
year
Chapter 7 Slide 51
Cost in the Long Run
? Isoquants and Isocosts and the
Production Function
K
L MPMP- M R T S ???? LK
rwLK ????? l i n ei s o c o s t of S l o p e
rwMP
MP
K
L ?? a n d
Chapter 7 Slide 52
Cost in the Long Run
? The minimum cost combination can
then be written as,
? 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,
rw
KL MPMP ?
Chapter 7 Slide 53
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 54
The Effect of Effluent
Fees on Firms’ Input Choices
? Firms that have a by-product to
production produce an effluent,
? An effluent fee is a per-unit fee that
firms must pay for the effluent that
they emit,
? How would a producer respond to an
effluent fee on production?
Chapter 7 Slide 55
? The Scenario,Steel Producer
1) Located on a river,Low cost
transportation and emission
disposal (effluent),
2) EPA imposes a per unit effluent
fee to reduce the environmentally
harmful effluent,
The Effect of Effluent
Fees on Firms’ Input Choices
Chapter 7 Slide 56
? The Scenario,Steel Producer
3) How should the firm respond?
The Effect of Effluent
Fees on Firms’ Input Choices
Chapter 7 Slide 57
The Cost-Minimizing
Response to an Effluent Fee
Waste Water
(gal./month)
Capital
(machine
hours per
month)
Output of 2,000
Tons of Steel per Month
A
10,000 18,000 20,000 0 12,000
Slope of
isocost = -10/40
= -0.25
2,000
1,000
4,000
3,000
5,000
5,000
Chapter 7 Slide 58
The Cost-Minimizing
Response to an Effluent Fee
Output of 2,000
Tons of Steel per Month
2,000
1,000
4,000
3,000
5,000
10,000 18,000 20,000 0 12,000
Capital
(machine
hours per
month)
E
5,000
3,500
Slope of
isocost = -20/40
= -0.50
B Following the imposition
of the effluent fee of $10/gallon
the slope of the isocost changes
which the higher cost of water to
capital so now combination B
is selected,A
Prior to regulation the
firm chooses to produce
an output using 10,000
gallons of water and 2,000
machine-hours of capital at A,
C
F
Waste Water
(gal./month)
Chapter 7 Slide 59
? Observations,
? The more easily factors can be
substituted,the more effective the fee is
in reducing the effluent,
? The greater the degree of substitutes,
the less the firm will have to pay (for
example,$50,000 with combination B
instead of $100,000 with combination A)
The Effect of Effluent
Fees on Firms’ Input Choices
Chapter 7 Slide 60
? Cost minimization with Varying Output
Levels
? A firm’s expansion path shows the
minimum cost combinations of labor and
capital at each level of output,
Cost in the Long Run
Chapter 7 Slide 61
A Firm’s Expansion Path
Labor per year
Capital
per
year
Expansion Path
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,
25
50
75
100
150
100 50 150 300 200
A
$2000
Isocost Line
200 Unit
Isoquant
B
$3000 Isocost Line
300 Unit Isoquant
C
Chapter 7 Slide 62
A Firm’s Long-Run Total Cost Curve
Output,Units/yr
Cost
per
Year
Expansion Path
1000
100 300 200
2000
3000
D
E
F
Chapter 7 Slide 63
Long-Run Versus
Short-Run Cost Curves
? What happens to average costs when
both inputs are variable (long run)
versus only having one input that is
variable (short run)?
Chapter 7 Slide 64
Long-Run
Expansion Path
The long-run expansion
path is drawn as before.,
The Inflexibility of
Short-Run Production
Labor per year
Capital
per
year
L2
Q2
K2
D
C
F
E
Q1
A
B L1
K1
L3
P
Short-Run
Expansion Path
Chapter 7 Slide 65
? Long-Run Average Cost (LAC)
? Constant Returns to Scale
?If input is doubled,output will double
and average cost is constant at all
levels of output,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 66
? Long-Run Average Cost (LAC)
? Increasing Returns to Scale
?If input is doubled,output will more
than double and average cost
decreases at all levels of output,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 67
? Long-Run Average Cost (LAC)
? Decreasing Returns to Scale
?If input is doubled,the increase in
output is less than twice as large and
average cost increases with output,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 68
? Long-Run Average Cost (LAC)
? In the long-run,
?Firms experience increasing and
decreasing returns to scale and
therefore long-run average cost is,U”
shaped,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 69
? Long-Run Average Cost (LAC)
? Long-run marginal cost leads long-run
average cost,
?If LMC < LAC,LAC will fall
?If LMC > LAC,LAC will rise
?Therefore,LMC = LAC at the
minimum of LAC
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 70
Long-Run Average
and Marginal Cost
Output
Cost
($ per unit
of output
LAC
LMC
A
Chapter 7 Slide 71
? Question
? What is the relationship between long-
run average cost and long-run marginal
cost when long-run average cost is
constant?
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 72
? Economies and Diseconomies of
Scale
? Economies of Scale
?Increase in output is greater than the
increase in inputs,
? Diseconomies of Scale
?Increase in output is less than the
increase in inputs,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 73
? Measuring Economies of Scale
output in
i nc r eas e 1% a f r om c os t in % Δ
el as ti c i ty output C os tE c
?
??
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 74
? Measuring Economies of Scale
)//()/( QQCCE c ???
M C / A C)//()/( ???? QCQCE c
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 75
? Therefore,the following is true,
? EC < 1,MC < AC
? Average cost indicate decreasing economies
of scale
? EC = 1,MC = AC
? Average cost indicate constant economies of
scale
? EC > 1,MC > AC
? Average cost indicate increasing
diseconomies of scale
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 76
? The Relationship Between Short-Run
and Long-Run Cost
? We will use short and long-run cost to
determine the optimal plant size
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 77
Long-Run Cost with
Constant Returns to Scale
Output
Cost
($ per unit
of output
Q3
SAC3
SMC3
Q2
SAC2
SMC2
LAC =
LMC
With many plant sizes with SAC = $10
the LAC = LMC and is a straight line
Q1
SAC1
SMC1
Chapter 7 Slide 78
? Observation
? The optimal plant size will depend on the
anticipated output (e.g,Q1 choose SAC1,etc),
? The long-run average cost curve is the
envelope of the firm’s short-run average cost
curves,
? Question
? What would happen to average cost if an output
level other than that shown is chosen?
Long-Run Cost with
Constant Returns to Scale
Chapter 7 Slide 79
Long-Run Cost with Economies
and Diseconomies of Scale
Output
Cost
($ per unit
of output
SMC1
SAC1
SAC2
SMC2 LMC
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
LAC SAC3
SMC3
Chapter 7 Slide 80
? 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,
Long-Run Cost with
Constant Returns to Scale
Chapter 7 Slide 81
? Observations
? The LAC does not include the minimum
points of small and large size plants?
Why not?
? LMC is not the envelope of the short-run
marginal cost,Why not?
Long-Run Cost with
Constant Returns to Scale
Chapter 7 Slide 82
Production with Two
Outputs--Economies of Scope
? Examples,
? Chicken farm--poultry and eggs
? Automobile company--cars and trucks
? University--Teaching and research
Chapter 7 Slide 83
? 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,
? What are the advantages of joint
production?
? Consider an automobile company producing
cars and tractors
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 84
? Advantages
1) Both use capital and labor,
2) The firms share management
resources,
3) Both use the same labor skills and
type of machinery,
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 85
? Production,
? Firms must choose how much of each to
produce,
? The alternative quantities can be
illustrated using product transformation
curves,
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 86
Product Transformation Curve
Number of cars
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,O
1
Each curve shows
combinations of output
with a given combination
of L & K,
Chapter 7 Slide 87
? Observations
? Product transformation curves are
negatively sloped
? Constant returns exist in this example
? Since the production transformation
curve is concave is joint production
desirable?
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 88
? Observations
? There is no direct relationship between
economies of scope and economies of
scale,
?May experience economies of scope
and diseconomies of scale
?May have economies of scale and not
have economies of scope
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 89
? 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
)(
)()()C( SC
2,1
2,121
QQC
QQCQCQ ???
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 90
? Interpretation,
? If SC > 0 -- Economies of scope
? If SC < 0 -- Diseconomies of scope
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 91
Economies of Scope
in the Trucking Industry
? Issues
? Truckload versus less than truck load
? Direct versus indirect routing
? Length of haul
Chapter 7 Slide 92
? Questions,
? Economies of Scale
?Are large-scale,direct hauls cheaper
and more profitable than individual
hauls by small trucks?
?Are there cost advantages from
operating both direct and indirect
hauls?
Economies of Scope
in the Trucking Industry
Chapter 7 Slide 93
? Empirical Findings
? An analysis of 105 trucking firms
examined four distinct outputs,
?Short hauls with partial loads
?Intermediate hauls with partial loads
?Long hauls with partial loads
?Hauls with total loads
Economies of Scope
in the Trucking Industry
Chapter 7 Slide 94
? Empirical Findings
? Results
? SC = 1.576 for reasonably large firm
? SC = 0.104 for very large firms
? Interpretation
? Combining partial loads at an intermediate
location lowers cost management difficulties
with very large firms,
Economies of Scope
in the Trucking Industry
Chapter 7 Slide 95
Dynamic Changes in
Costs--The Learning Curve
? 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,
Chapter 7 Slide 96
The Learning Curve
Cumulative number of
machine lots produced
Hours of labor
per machine lot
10 20 30 40 50 0
2
4
6
8
10
Chapter 7 Slide 97
The Learning Curve
Hours of labor
per machine lot
10 20 30 40 50 0
2
4
6
8
10
? The horizontal axis
measures the
cumulative number of
hours of machine
tools the firm has
produced
? The vertical axis
measures the number
of hours of labor
needed to produce
each lot,
Chapter 7 Slide 98
? The learning curve in the figure is based
on the relationship,
??? BNL
1 a n d 0b e t w e e n is a n d p o s i t i v e a r e
c o n s t a n t s a r e a n d
o u t p u t ofu n i t p e r i n p u t l a b o r
p r o d u c e do u t p u t of u n i t s c u m u l a t i v e
?
?
B & A
BA,
L
N
?
?
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 99
?
? 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
:0??If
:1?NIf
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 100
?
? L approaches A,and A represent minimum
labor input/unit of output after all learning
has taken place,
?
? The more important the learning effect,
:in c r e a s e s a n d 0 NIf ??
:la r g e r T h e ?
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 101
The Learning Curve
Cumulative number of
machine lots produced
Hours of labor
per machine lot
10 20 30 40 50 0
2
4
6
8
10
31.0??
The chart shows a sharp drop
in lots to a cumulative amount of
20,then small savings at
higher levels,
Doubling cumulative output causes
a 20% reduction in the difference
between the input required and
minimum attainable input requirement,
Chapter 7 Slide 102
? Observations
1) New firms may experience a learning
curve,not economies of scale,
2) Older firms have relatively small
gains from learning,
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 103
Economies of
Scale Versus Learning
Output
Cost
($ per unit
of output)
AC1 B
Economies of Scale
A
AC2
Learning C
Predicting the Labor
Requirements of Producing a Given Output
10 1.00 10.0
20,80 18.0 (10.0 + 8.0)
30,70 25.0 (18.0 + 7.0)
40,64 31.4 (25.0 + 6.4)
50,60 37.4 (31.4 + 6.0)
60,56 43.0 (37.4 + 5.6)
70,53 48.3 (43.0 + 5.3)
80 and over,51 53.4 (48.3 + 5.1)
Cumulative Output Per-Unit Labor Requirement Total Labor
(N) for each 10 units of Output (L) Requirement
Chapter 7 Slide 105
? The learning curve implies,
1) The labor requirement falls per unit,
2) Costs will be high at first and then will
fall with learning,
3) After 8 years the labor requirement will be
0.51 and per unit cost will be half
what it was in the first year of production,
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 106
? Scenario
? A new firm enters the chemical processing
industry,
? Do they,
1) Produce a low level of output and sell at a
high price?
2) Produce a high level of output and sell at a
low price?
The Learning Curve in Practice
Chapter 7 Slide 107
The Learning Curve in Practice
? How would the learning curve
influence your decision?
Chapter 7 Slide 108
? The Empirical Findings
? Study of 37 chemical products
? Average cost fell 5.5% per year
? For each doubling of plant size,average
production costs fall by 11%
? For each doubling of cumulative output,the
average cost of production falls by 27%
? Which is more important,the economies of
scale or learning effects?
The Learning Curve in Practice
Chapter 7 Slide 109
? Other Empirical Findings
? In the semi-conductor industry a study of
seven generations of DRAM
semiconductors from 1974-1992 found
learning rates averaged 20%,
? In the aircraft industry the learning rates
are as high as 40%,
The Learning Curve in Practice
Chapter 7 Slide 110
? Applying Learning Curves
1) To determine if it is profitable to
enter an industry,
2) To determine when profits will
occur based on plant size and
cumulative output,
The Learning Curve in Practice
Chapter 7 Slide 111
Estimating and Predicting Cost
? Estimates of future costs can be
obtained from a cost function,which
relates the cost of production to the
level of output and other variables
that the firm can control,
? Suppose we wanted to derive the
total cost curve for automobile
production,
Chapter 7 Slide 112
Total Cost Curve
for the Automobile Industry
Quantity of Cars
Variable
cost General Motors
Toyota
Ford
Chrysler
Volvo
Honda
Nissan
Chapter 7 Slide 113
? A linear cost function (does not show
the U-shaped characteristics) might
be,
? The linear cost function is applicable
only if marginal cost is constant,
? Marginal cost is represented by,
Q?? VC
?
Estimating and Predicting Cost
Chapter 7 Slide 114
? If we wish to allow for a U-shaped
average cost curve and a marginal
cost that is not constant,we might
use the quadratic cost function,
2 VC QQ ?? ??
Estimating and Predicting Cost
Chapter 7 Slide 115
? If the marginal cost curve is not linear,
we might use a cubic cost function,
32 VC QQQ ??? ???
Estimating and Predicting Cost
Chapter 7 Slide 116
Cubic Cost Function
Output
(per time period)
Cost
($ per unit)
2QQAVC ??? ???
2QQM ??? 32 ???C
Chapter 7 Slide 117
? Difficulties in Measuring Cost
1) Output data may represent an
aggregate of different type of products,
2) Cost data may not include opportunity
cost,
3) Allocating cost to a particular product
may be difficult when there is more than
one product line,
Estimating and Predicting Cost
Chapter 7 Slide 118
? Cost Functions and the Measurement of
Scale Economies
? Scale Economy Index (SCI)
? EC = 1,SCI = 0,no economies or
diseconomies of scale
? EC > 1,SCI is negative,diseconomies of
scale
? EC < 1,SCI is positive,economies of scale
Estimating and Predicting Cost
Chapter 7 Slide 119
Cost Functions for Electric Power
Scale Economies in the Electric Power Industry
Output (million kwh) 43 338 1109 2226 5819
Value of SCI,1955,41,26,16,10,04
Chapter 7 Slide 120
Average Cost of Production
in the Electric Power Industry
Output (billions of kwh)
Average
Cost
(dollar/1000 kwh)
5.0
5.5
6.0
6.5
6 12 18 24 30 36
1955
1970
A
Chapter 7 Slide 121
Cost Functions for Electric Power
? Findings
?Decline in cost
?Not due to economies of scale
?Was caused by,
? Lower input cost (coal & oil)
? Improvements in technology
Chapter 7 Slide 122
A Cost Function for the
Savings and Loan Industry
? The empirical estimation of a long-run
cost function can be useful in the
restructuring of the savings and loan
industry in the wake of the savings
and loan collapse in the 1980s,
Chapter 7 Slide 123
? Data for 86 savings and loans for
1975 & 1976 in six western states
? Q = total assets of each S&L
? LAC = average operating expense
? Q & TC are measured in hundreds of
millions of dollars
? Average operating cost are measured as
a percentage of total assets,
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 124
? A quadratic long-run average cost function
was estimated for 1975,
? Minimum long-run average cost reaches its
point of minimum average total cost when
total assets of the savings and loan reach
$574 million,
20, 0 5 3 6 Q 0, 6 1 5 3 Q - 2, 3 8 L A C ??
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 125
? Average operating expenses are
0.61% of total assets,
? Almost all of the savings and loans in
the region being studied had
substantially less than $574 million in
assets,
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 126
? Questions
1) What are the implications of the
analysis for expansion and
mergers?
2) What are the limitations of using
these results?
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 127
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 128
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 129
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,
Chapter 7 Slide 130
Summary
? A firm enjoys economies of scale
when it can double its output at less
than twice the cost,
? Economies of scope arise when the
firm can produce any combination of
the two outputs more cheaply than
could two independent firms that each
produced a single product,
Chapter 7 Slide 131
Summary
? A firm’s average cost of production
can fall over time if the firm,learns”
how to produce more effectively,
? Cost functions relate the cost of
production to the level of output of the
firm,
End of Chapter 7
The Cost of
Production
The Cost of
Production
Chapter 7 Slide 2
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 3
Topics to be Discussed
? Production with Two Outputs--
Economies of Scope
? Dynamic Changes in Costs--The
Learning Curve
? Estimating and Predicting Cost
Chapter 7 Slide 4
Introduction
? The production technology measures
the relationship between input and
output,
? Given the production technology,
managers must choose how to
produce,
Chapter 7 Slide 5
Introduction
? 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 6
Measuring Cost,
Which Costs Matter?
? Accounting Cost
? Actual expenses plus depreciation
charges for capital equipment
? Economic Cost
? Cost to a firm of utilizing economic
resources in production,including
opportunity cost
Economic Cost vs,Accounting Cost
Chapter 7 Slide 7
? Opportunity cost,
? Cost associated with opportunities that
are foregone when a firm’s resources
are not put to their highest-value use,
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 8
? 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?
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 9
? Sunk Cost
? Expenditure that has been made and
cannot be recovered
? Should not influence a firm’s decisions,
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 10
? An Example
? A firm pays $500,000 for an option to buy a
building,
? The cost of the building is $5 million or a total of
$5.5 million,
? The firm finds another building for $5.25 million,
? Which building should the firm buy?
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 11
Choosing the Location
for a New Law School Building
? Northwestern University Law School
1) Current location in downtown
Chicago
2) Alternative location in Evanston
with the main campus
Chapter 7 Slide 12
? Northwestern University Law School
3) Choosing a Site
?Land owned in Chicago
?Must purchase land in Evanston
?Chicago location might appear
cheaper without considering the
opportunity cost of the downtown land
(i.e,what it could be sold for)
Choosing the Location
for a New Law School Building
Chapter 7 Slide 13
? Northwestern University Law School
3) Choosing a Site
?Chicago location chosen--very costly
?Justified only if there is some intrinsic
values associated with being in
Chicago
?If not,it was an inefficient decision if it
was based on the assumption that the
downtown land was,free”
Choosing the Location
for a New Law School Building
Chapter 7 Slide 14
? Total output is a function of variable
inputs and fixed inputs,
? Therefore,the total cost of production
equals the fixed cost (the cost of the
fixed inputs) plus the variable cost
(the cost of the variable inputs),or…
V C FC TC ??
Measuring Cost,
Which Costs Matter?
Fixed and Variable Costs
Chapter 7 Slide 15
? Fixed Cost
?Does not vary with the level of output
? Variable Cost
?Cost that varies as output varies
Measuring Cost,
Which Costs Matter?
Fixed and Variable Costs
Chapter 7 Slide 16
? Fixed Cost
?Cost paid by a firm that is in business
regardless of the level of output
? Sunk Cost
?Cost that have been incurred and cannot
be recovered
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 17
?Personal Computers,most costs
are variable
?Components,labor
?Software,most costs are sunk
?Cost of developing the software
Measuring Cost,
Which Costs Matter?
Chapter 7 Slide 18
?Pizza
?Largest cost component is fixed
Measuring Cost,
Which Costs Matter?
A Firm’s Short-Run Costs ($)
0 50 0 50 --- --- --- ---
1 50 50 100 50 50 50 100
2 50 78 128 28 25 39 64
3 50 98 148 20 16.7 32.7 49.3
4 50 112 162 14 12.5 28 40.5
5 50 130 180 18 10 26 36
6 50 150 200 20 8.3 25 33.3
7 50 175 225 25 7.1 25 32.1
8 50 204 254 29 6.3 25.5 31.8
9 50 242 292 38 5.6 26.9 32.4
10 50 300 350 58 5 30 35
11 50 385 435 85 4.5 35 39.5
Rate of Fixed Variable Total Marginal Average Average Average Output Cost Cost Cost Cost Fixed Variable Total
(FC) (VC) (TC) (MC) Cost Cost Cost
(AFC) (AVC) (ATC)
Chapter 7 Slide 20
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,
Q
TC
Q
VC
MC
?
?
?
?
?
?
Chapter 7 Slide 21
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,
Q
T VC
Q
T F C A T C ??
Chapter 7 Slide 22
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,
Q
TCor A VC A F C A T C ??
Chapter 7 Slide 23
Cost in the Short Run
? The Determinants of Short-Run Cost
? The relationship between the production
function and cost can be exemplified by
either increasing returns and cost or
decreasing returns and cost,
Chapter 7 Slide 24
Cost in the Short Run
? The Determinants of Short-Run 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 25
Cost in the Short Run
? For Example,Assume the wage rate
(w) is fixed relative to the number of
workers hired,Then,
Q
VC
MC
?
?
?
L VC w?
Chapter 7 Slide 26
Cost in the Short Run
? Continuing,
L VC ??? w
Q
L
MC
?
?
?
w
Chapter 7 Slide 27
Cost in the Short Run
? Continuing,
L
MP L
?
??? Q
LMP
1
Q
L
Qu n i t 1 af o r L
?
?
?
?
???
Chapter 7 Slide 28
Cost in the Short Run
? In conclusion,
? …and a low marginal product (MP)
leads to a high marginal cost (MC)
and vise versa,
LMP
MC
w
?
Chapter 7 Slide 29
Cost in the Short Run
? Consequently (from the table),
? MC decreases initially with increasing
returns
?0 through 4 units of output
? MC increases with decreasing returns
?5 through 11 units of output
A Firm’s Short-Run Costs ($)
0 50 0 50 --- --- --- ---
1 50 50 100 50 50 50 100
2 50 78 128 28 25 39 64
3 50 98 148 20 16.7 32.7 49.3
4 50 112 162 14 12.5 28 40.5
5 50 130 180 18 10 26 36
6 50 150 200 20 8.3 25 33.3
7 50 175 225 25 7.1 25 32.1
8 50 204 254 29 6.3 25.5 31.8
9 50 242 292 38 5.6 26.9 32.4
10 50 300 350 58 5 30 35
11 50 385 435 85 4.5 35 39.5
Rate of Fixed Variable Total Marginal Average Average Average Output Cost Cost Cost Cost Fixed Variable Total
(FC) (VC) (TC) (MC) Cost Cost Cost
(AFC) (AVC) (ATC)
Chapter 7 Slide 31
Cost Curves for a Firm
Output
Cost
($ per
year)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VC
Variable cost
increases with
production and
the rate varies with
increasing &
decreasing returns,
TC Total cost is the vertical
sum of FC
and VC,
FC 50
Fixed cost does not
vary with output
Chapter 7 Slide 32
Cost Curves for a Firm
Output (units/yr.)
Cost
($ per
unit)
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
MC
ATC
AVC
AFC
Chapter 7 Slide 33
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)
Output
P
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
FC
VC
A
TC
Chapter 7 Slide 34
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 Output (units/yr.)
Cost
($ per
unit)
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
MC
ATC
AVC
AFC
Chapter 7 Slide 35
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
Output (units/yr.)
Cost
($ per
unit)
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
MC
ATC
AVC
AFC
Chapter 7 Slide 36
Operating Costs for Aluminum Smelting
($/Ton - based on an output of 600 tons/day)
Variable costs that are constant at all output levels
Electricity $316
Alumina 369
Other raw materials 125
Plant power and fuel 10
Subtotal $820
Chapter 7 Slide 37
Operating Costs for Aluminum Smelting
($/Ton - based on an output of 600 tons/day)
Variable costs that increase when output exceeds 600 tons/day
Labor $150
Maintenance 120
Freight 50
Subtotal $320
Total operating costs $1140
Chapter 7 Slide 38
The Short-Run Variable
Costs of Aluminum Smelting
Output (tons/day)
Cost
($ per ton)
1100
1200
1300
300 600 900
1140
MC
AVC
Chapter 7 Slide 39
Cost in the Long Run
? User Cost of Capital = Economic
Depreciation + (Interest Rate)(Value
of Capital)
The User Cost of Capital
Chapter 7 Slide 40
Cost in the Long Run
? Example
?Delta buys a Boeing 737 for $150 million
with an expected life of 30 years
?Annual economic depreciation =
$150 million/30 = $5 million
?Interest rate = 10%
The User Cost of Capital
Chapter 7 Slide 41
Cost in the Long Run
? Example
?User Cost of Capital = $5 million +
(.10)($150 million – depreciation)
?Year 1 = $5 million +
(.10)($150 million) = $20 million
?Year 10 = $5 million +
(.10)($100 million) = $15 million
The User Cost of Capital
Chapter 7 Slide 42
Cost in the Long Run
? Rate per dollar of capital
?r = Depreciation Rate + Interest Rate
The User Cost of Capital
Chapter 7 Slide 43
Cost in the Long Run
? Airline Example
?Depreciation Rate = 1/30 = 3.33/yr
?Rate of Return = 10%/yr
? User Cost of Capital
?r = 3.33 + 10 = 13.33%/yr
The User Cost of Capital
Chapter 7 Slide 44
Cost in the Long Run
? Assumptions
? Two Inputs,Labor (L) & capital (K)
? Price of labor,wage rate (w)
? The price of capital
?R = depreciation rate + interest rate
The Cost Minimizing Input Choice
Chapter 7 Slide 45
Cost in the Long Run
? Question
? If capital was rented,would it change the
value of r?
The User Cost of Capital The Co t Minimizing Input Choice
Chapter 7 Slide 46
Cost in the Long Run
? The Isocost Line
? C = wL + rK
? Isocost,A line showing all combinations
of L & K that can be purchased for the
same cost
The User Cost of Capital The Co t Minimizing Input Choice
Chapter 7 Slide 47
Cost in the Long Run
? Rewriting C as linear,
? K = C/r - (w/r)L
? Slope of the isocost,
? 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,
? ?rwLK ????
The Isocost Line
Chapter 7 Slide 48
Choosing Inputs
? We will address how to minimize cost
for a given level of output,
? We will do so by combining isocosts with
isoquants
Chapter 7 Slide 49
Producing a Given
Output at Minimum Cost
Labor per year
Capital
per
year
Isocost C2 shows quantity
Q1 can be produced with
combination K2L2 or K3L3,
However,both of these
are higher cost combinations
than K1L1,
Q1
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,
C0 C1 C2
CO C1 C2 are
three
isocost lines
A
K1
L1
K3
L3
K2
L2
Chapter 7 Slide 50
Input Substitution When
an Input Price Change
C2
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,
K2
L2
B
C1
K1
L1
A
Q1
If the price of labor
changes,the isocost curve
becomes steeper due to
the change in the slope -(w/L),
Labor per year
Capital
per
year
Chapter 7 Slide 51
Cost in the Long Run
? Isoquants and Isocosts and the
Production Function
K
L MPMP- M R T S ???? LK
rwLK ????? l i n ei s o c o s t of S l o p e
rwMP
MP
K
L ?? a n d
Chapter 7 Slide 52
Cost in the Long Run
? The minimum cost combination can
then be written as,
? 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,
rw
KL MPMP ?
Chapter 7 Slide 53
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 54
The Effect of Effluent
Fees on Firms’ Input Choices
? Firms that have a by-product to
production produce an effluent,
? An effluent fee is a per-unit fee that
firms must pay for the effluent that
they emit,
? How would a producer respond to an
effluent fee on production?
Chapter 7 Slide 55
? The Scenario,Steel Producer
1) Located on a river,Low cost
transportation and emission
disposal (effluent),
2) EPA imposes a per unit effluent
fee to reduce the environmentally
harmful effluent,
The Effect of Effluent
Fees on Firms’ Input Choices
Chapter 7 Slide 56
? The Scenario,Steel Producer
3) How should the firm respond?
The Effect of Effluent
Fees on Firms’ Input Choices
Chapter 7 Slide 57
The Cost-Minimizing
Response to an Effluent Fee
Waste Water
(gal./month)
Capital
(machine
hours per
month)
Output of 2,000
Tons of Steel per Month
A
10,000 18,000 20,000 0 12,000
Slope of
isocost = -10/40
= -0.25
2,000
1,000
4,000
3,000
5,000
5,000
Chapter 7 Slide 58
The Cost-Minimizing
Response to an Effluent Fee
Output of 2,000
Tons of Steel per Month
2,000
1,000
4,000
3,000
5,000
10,000 18,000 20,000 0 12,000
Capital
(machine
hours per
month)
E
5,000
3,500
Slope of
isocost = -20/40
= -0.50
B Following the imposition
of the effluent fee of $10/gallon
the slope of the isocost changes
which the higher cost of water to
capital so now combination B
is selected,A
Prior to regulation the
firm chooses to produce
an output using 10,000
gallons of water and 2,000
machine-hours of capital at A,
C
F
Waste Water
(gal./month)
Chapter 7 Slide 59
? Observations,
? The more easily factors can be
substituted,the more effective the fee is
in reducing the effluent,
? The greater the degree of substitutes,
the less the firm will have to pay (for
example,$50,000 with combination B
instead of $100,000 with combination A)
The Effect of Effluent
Fees on Firms’ Input Choices
Chapter 7 Slide 60
? Cost minimization with Varying Output
Levels
? A firm’s expansion path shows the
minimum cost combinations of labor and
capital at each level of output,
Cost in the Long Run
Chapter 7 Slide 61
A Firm’s Expansion Path
Labor per year
Capital
per
year
Expansion Path
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,
25
50
75
100
150
100 50 150 300 200
A
$2000
Isocost Line
200 Unit
Isoquant
B
$3000 Isocost Line
300 Unit Isoquant
C
Chapter 7 Slide 62
A Firm’s Long-Run Total Cost Curve
Output,Units/yr
Cost
per
Year
Expansion Path
1000
100 300 200
2000
3000
D
E
F
Chapter 7 Slide 63
Long-Run Versus
Short-Run Cost Curves
? What happens to average costs when
both inputs are variable (long run)
versus only having one input that is
variable (short run)?
Chapter 7 Slide 64
Long-Run
Expansion Path
The long-run expansion
path is drawn as before.,
The Inflexibility of
Short-Run Production
Labor per year
Capital
per
year
L2
Q2
K2
D
C
F
E
Q1
A
B L1
K1
L3
P
Short-Run
Expansion Path
Chapter 7 Slide 65
? Long-Run Average Cost (LAC)
? Constant Returns to Scale
?If input is doubled,output will double
and average cost is constant at all
levels of output,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 66
? Long-Run Average Cost (LAC)
? Increasing Returns to Scale
?If input is doubled,output will more
than double and average cost
decreases at all levels of output,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 67
? Long-Run Average Cost (LAC)
? Decreasing Returns to Scale
?If input is doubled,the increase in
output is less than twice as large and
average cost increases with output,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 68
? Long-Run Average Cost (LAC)
? In the long-run,
?Firms experience increasing and
decreasing returns to scale and
therefore long-run average cost is,U”
shaped,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 69
? Long-Run Average Cost (LAC)
? Long-run marginal cost leads long-run
average cost,
?If LMC < LAC,LAC will fall
?If LMC > LAC,LAC will rise
?Therefore,LMC = LAC at the
minimum of LAC
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 70
Long-Run Average
and Marginal Cost
Output
Cost
($ per unit
of output
LAC
LMC
A
Chapter 7 Slide 71
? Question
? What is the relationship between long-
run average cost and long-run marginal
cost when long-run average cost is
constant?
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 72
? Economies and Diseconomies of
Scale
? Economies of Scale
?Increase in output is greater than the
increase in inputs,
? Diseconomies of Scale
?Increase in output is less than the
increase in inputs,
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 73
? Measuring Economies of Scale
output in
i nc r eas e 1% a f r om c os t in % Δ
el as ti c i ty output C os tE c
?
??
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 74
? Measuring Economies of Scale
)//()/( QQCCE c ???
M C / A C)//()/( ???? QCQCE c
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 75
? Therefore,the following is true,
? EC < 1,MC < AC
? Average cost indicate decreasing economies
of scale
? EC = 1,MC = AC
? Average cost indicate constant economies of
scale
? EC > 1,MC > AC
? Average cost indicate increasing
diseconomies of scale
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 76
? The Relationship Between Short-Run
and Long-Run Cost
? We will use short and long-run cost to
determine the optimal plant size
Long-Run Versus
Short-Run Cost Curves
Chapter 7 Slide 77
Long-Run Cost with
Constant Returns to Scale
Output
Cost
($ per unit
of output
Q3
SAC3
SMC3
Q2
SAC2
SMC2
LAC =
LMC
With many plant sizes with SAC = $10
the LAC = LMC and is a straight line
Q1
SAC1
SMC1
Chapter 7 Slide 78
? Observation
? The optimal plant size will depend on the
anticipated output (e.g,Q1 choose SAC1,etc),
? The long-run average cost curve is the
envelope of the firm’s short-run average cost
curves,
? Question
? What would happen to average cost if an output
level other than that shown is chosen?
Long-Run Cost with
Constant Returns to Scale
Chapter 7 Slide 79
Long-Run Cost with Economies
and Diseconomies of Scale
Output
Cost
($ per unit
of output
SMC1
SAC1
SAC2
SMC2 LMC
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
LAC SAC3
SMC3
Chapter 7 Slide 80
? 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,
Long-Run Cost with
Constant Returns to Scale
Chapter 7 Slide 81
? Observations
? The LAC does not include the minimum
points of small and large size plants?
Why not?
? LMC is not the envelope of the short-run
marginal cost,Why not?
Long-Run Cost with
Constant Returns to Scale
Chapter 7 Slide 82
Production with Two
Outputs--Economies of Scope
? Examples,
? Chicken farm--poultry and eggs
? Automobile company--cars and trucks
? University--Teaching and research
Chapter 7 Slide 83
? 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,
? What are the advantages of joint
production?
? Consider an automobile company producing
cars and tractors
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 84
? Advantages
1) Both use capital and labor,
2) The firms share management
resources,
3) Both use the same labor skills and
type of machinery,
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 85
? Production,
? Firms must choose how much of each to
produce,
? The alternative quantities can be
illustrated using product transformation
curves,
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 86
Product Transformation Curve
Number of cars
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,O
1
Each curve shows
combinations of output
with a given combination
of L & K,
Chapter 7 Slide 87
? Observations
? Product transformation curves are
negatively sloped
? Constant returns exist in this example
? Since the production transformation
curve is concave is joint production
desirable?
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 88
? Observations
? There is no direct relationship between
economies of scope and economies of
scale,
?May experience economies of scope
and diseconomies of scale
?May have economies of scale and not
have economies of scope
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 89
? 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
)(
)()()C( SC
2,1
2,121
QQC
QQCQCQ ???
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 90
? Interpretation,
? If SC > 0 -- Economies of scope
? If SC < 0 -- Diseconomies of scope
Production with Two
Outputs--Economies of Scope
Chapter 7 Slide 91
Economies of Scope
in the Trucking Industry
? Issues
? Truckload versus less than truck load
? Direct versus indirect routing
? Length of haul
Chapter 7 Slide 92
? Questions,
? Economies of Scale
?Are large-scale,direct hauls cheaper
and more profitable than individual
hauls by small trucks?
?Are there cost advantages from
operating both direct and indirect
hauls?
Economies of Scope
in the Trucking Industry
Chapter 7 Slide 93
? Empirical Findings
? An analysis of 105 trucking firms
examined four distinct outputs,
?Short hauls with partial loads
?Intermediate hauls with partial loads
?Long hauls with partial loads
?Hauls with total loads
Economies of Scope
in the Trucking Industry
Chapter 7 Slide 94
? Empirical Findings
? Results
? SC = 1.576 for reasonably large firm
? SC = 0.104 for very large firms
? Interpretation
? Combining partial loads at an intermediate
location lowers cost management difficulties
with very large firms,
Economies of Scope
in the Trucking Industry
Chapter 7 Slide 95
Dynamic Changes in
Costs--The Learning Curve
? 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,
Chapter 7 Slide 96
The Learning Curve
Cumulative number of
machine lots produced
Hours of labor
per machine lot
10 20 30 40 50 0
2
4
6
8
10
Chapter 7 Slide 97
The Learning Curve
Hours of labor
per machine lot
10 20 30 40 50 0
2
4
6
8
10
? The horizontal axis
measures the
cumulative number of
hours of machine
tools the firm has
produced
? The vertical axis
measures the number
of hours of labor
needed to produce
each lot,
Chapter 7 Slide 98
? The learning curve in the figure is based
on the relationship,
??? BNL
1 a n d 0b e t w e e n is a n d p o s i t i v e a r e
c o n s t a n t s a r e a n d
o u t p u t ofu n i t p e r i n p u t l a b o r
p r o d u c e do u t p u t of u n i t s c u m u l a t i v e
?
?
B & A
BA,
L
N
?
?
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 99
?
? 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
:0??If
:1?NIf
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 100
?
? L approaches A,and A represent minimum
labor input/unit of output after all learning
has taken place,
?
? The more important the learning effect,
:in c r e a s e s a n d 0 NIf ??
:la r g e r T h e ?
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 101
The Learning Curve
Cumulative number of
machine lots produced
Hours of labor
per machine lot
10 20 30 40 50 0
2
4
6
8
10
31.0??
The chart shows a sharp drop
in lots to a cumulative amount of
20,then small savings at
higher levels,
Doubling cumulative output causes
a 20% reduction in the difference
between the input required and
minimum attainable input requirement,
Chapter 7 Slide 102
? Observations
1) New firms may experience a learning
curve,not economies of scale,
2) Older firms have relatively small
gains from learning,
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 103
Economies of
Scale Versus Learning
Output
Cost
($ per unit
of output)
AC1 B
Economies of Scale
A
AC2
Learning C
Predicting the Labor
Requirements of Producing a Given Output
10 1.00 10.0
20,80 18.0 (10.0 + 8.0)
30,70 25.0 (18.0 + 7.0)
40,64 31.4 (25.0 + 6.4)
50,60 37.4 (31.4 + 6.0)
60,56 43.0 (37.4 + 5.6)
70,53 48.3 (43.0 + 5.3)
80 and over,51 53.4 (48.3 + 5.1)
Cumulative Output Per-Unit Labor Requirement Total Labor
(N) for each 10 units of Output (L) Requirement
Chapter 7 Slide 105
? The learning curve implies,
1) The labor requirement falls per unit,
2) Costs will be high at first and then will
fall with learning,
3) After 8 years the labor requirement will be
0.51 and per unit cost will be half
what it was in the first year of production,
Dynamic Changes in
Costs--The Learning Curve
Chapter 7 Slide 106
? Scenario
? A new firm enters the chemical processing
industry,
? Do they,
1) Produce a low level of output and sell at a
high price?
2) Produce a high level of output and sell at a
low price?
The Learning Curve in Practice
Chapter 7 Slide 107
The Learning Curve in Practice
? How would the learning curve
influence your decision?
Chapter 7 Slide 108
? The Empirical Findings
? Study of 37 chemical products
? Average cost fell 5.5% per year
? For each doubling of plant size,average
production costs fall by 11%
? For each doubling of cumulative output,the
average cost of production falls by 27%
? Which is more important,the economies of
scale or learning effects?
The Learning Curve in Practice
Chapter 7 Slide 109
? Other Empirical Findings
? In the semi-conductor industry a study of
seven generations of DRAM
semiconductors from 1974-1992 found
learning rates averaged 20%,
? In the aircraft industry the learning rates
are as high as 40%,
The Learning Curve in Practice
Chapter 7 Slide 110
? Applying Learning Curves
1) To determine if it is profitable to
enter an industry,
2) To determine when profits will
occur based on plant size and
cumulative output,
The Learning Curve in Practice
Chapter 7 Slide 111
Estimating and Predicting Cost
? Estimates of future costs can be
obtained from a cost function,which
relates the cost of production to the
level of output and other variables
that the firm can control,
? Suppose we wanted to derive the
total cost curve for automobile
production,
Chapter 7 Slide 112
Total Cost Curve
for the Automobile Industry
Quantity of Cars
Variable
cost General Motors
Toyota
Ford
Chrysler
Volvo
Honda
Nissan
Chapter 7 Slide 113
? A linear cost function (does not show
the U-shaped characteristics) might
be,
? The linear cost function is applicable
only if marginal cost is constant,
? Marginal cost is represented by,
Q?? VC
?
Estimating and Predicting Cost
Chapter 7 Slide 114
? If we wish to allow for a U-shaped
average cost curve and a marginal
cost that is not constant,we might
use the quadratic cost function,
2 VC QQ ?? ??
Estimating and Predicting Cost
Chapter 7 Slide 115
? If the marginal cost curve is not linear,
we might use a cubic cost function,
32 VC QQQ ??? ???
Estimating and Predicting Cost
Chapter 7 Slide 116
Cubic Cost Function
Output
(per time period)
Cost
($ per unit)
2QQAVC ??? ???
2QQM ??? 32 ???C
Chapter 7 Slide 117
? Difficulties in Measuring Cost
1) Output data may represent an
aggregate of different type of products,
2) Cost data may not include opportunity
cost,
3) Allocating cost to a particular product
may be difficult when there is more than
one product line,
Estimating and Predicting Cost
Chapter 7 Slide 118
? Cost Functions and the Measurement of
Scale Economies
? Scale Economy Index (SCI)
? EC = 1,SCI = 0,no economies or
diseconomies of scale
? EC > 1,SCI is negative,diseconomies of
scale
? EC < 1,SCI is positive,economies of scale
Estimating and Predicting Cost
Chapter 7 Slide 119
Cost Functions for Electric Power
Scale Economies in the Electric Power Industry
Output (million kwh) 43 338 1109 2226 5819
Value of SCI,1955,41,26,16,10,04
Chapter 7 Slide 120
Average Cost of Production
in the Electric Power Industry
Output (billions of kwh)
Average
Cost
(dollar/1000 kwh)
5.0
5.5
6.0
6.5
6 12 18 24 30 36
1955
1970
A
Chapter 7 Slide 121
Cost Functions for Electric Power
? Findings
?Decline in cost
?Not due to economies of scale
?Was caused by,
? Lower input cost (coal & oil)
? Improvements in technology
Chapter 7 Slide 122
A Cost Function for the
Savings and Loan Industry
? The empirical estimation of a long-run
cost function can be useful in the
restructuring of the savings and loan
industry in the wake of the savings
and loan collapse in the 1980s,
Chapter 7 Slide 123
? Data for 86 savings and loans for
1975 & 1976 in six western states
? Q = total assets of each S&L
? LAC = average operating expense
? Q & TC are measured in hundreds of
millions of dollars
? Average operating cost are measured as
a percentage of total assets,
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 124
? A quadratic long-run average cost function
was estimated for 1975,
? Minimum long-run average cost reaches its
point of minimum average total cost when
total assets of the savings and loan reach
$574 million,
20, 0 5 3 6 Q 0, 6 1 5 3 Q - 2, 3 8 L A C ??
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 125
? Average operating expenses are
0.61% of total assets,
? Almost all of the savings and loans in
the region being studied had
substantially less than $574 million in
assets,
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 126
? Questions
1) What are the implications of the
analysis for expansion and
mergers?
2) What are the limitations of using
these results?
A Cost Function for the
Savings and Loan Industry
Chapter 7 Slide 127
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 128
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 129
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,
Chapter 7 Slide 130
Summary
? A firm enjoys economies of scale
when it can double its output at less
than twice the cost,
? Economies of scope arise when the
firm can produce any combination of
the two outputs more cheaply than
could two independent firms that each
produced a single product,
Chapter 7 Slide 131
Summary
? A firm’s average cost of production
can fall over time if the firm,learns”
how to produce more effectively,
? Cost functions relate the cost of
production to the level of output of the
firm,
End of Chapter 7
The Cost of
Production
