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Chapter 7
The Cost of Production
Chapter 7 2©2005 Pearson Education, Inc.
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 3©2005 Pearson Education, Inc.
Topics to be Discussed
Production with Two Outputs: Economies of Scope
Dynamic Changes in Costs: The Learning Curve
Estimating and Predicting Cost
Chapter 7 4©2005 Pearson Education, Inc.
Introduction
Production technology measures the relationship between input and output
Production technology, together with prices of factor inputs, determine the firm’s cost of production
Given the production technology, managers must choose how to produce
Chapter 7 5©2005 Pearson Education, Inc.
Introduction
The optimal, cost minimizing, level of inputs can be determined
A firm’s costs depend on the rate of output and we will show how these costs are likely to change over time
The characteristics of the firm’s production technology can affect costs in the long run and short run
Chapter 7 6©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
For a firm to minimize costs, we must clarify what is meant by costs and how to measure them It is clear that if a firm has to rent equipment
or buildings, the rent they pay is a cost What if a firm owns its own equipment or
building?How are costs calculated here?
Chapter 7 7©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Accountants tend to take a retrospective view of firms’ costs, whereas economists tend to take a forward-looking view
Accounting Cost Actual expenses plus depreciation charges
for capital equipmentEconomic Cost
Cost to a firm of utilizing economic resources in production, including opportunity cost
Chapter 7 8©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Economic costs distinguish between costs the firm can control and those it cannot Concept of opportunity cost plays an
important role
Opportunity cost Cost associated with opportunities that are
foregone when a firm’s resources are not put to their highest-value use
Chapter 7 9©2005 Pearson Education, Inc.
Opportunity Cost
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? The building could have been rented instead Foregone rent is the opportunity cost of using
the building for production and should be included in the economic costs of doing business
Chapter 7 10©2005 Pearson Education, Inc.
Opportunity Cost
A person starting their own business must take into account the opportunity cost of their time Could have worked elsewhere making a
competitive salary
Accountants and economists often treat depreciation differently as well
Chapter 7 11©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Although opportunity costs are hidden and should be taken into account, sunk costs should not
Sunk Cost Expenditure that has been made and cannot
be recovered Should not influence a firm’s future economic
decisions
Chapter 7 12©2005 Pearson Education, Inc.
Sunk Cost
Firm buys a piece of equipment that cannot be converted to another use
Expenditure on the equipment is a sunk cost Has no alternative use so cost cannot be
recovered – opportunity cost is zero Decision to buy the equipment might have
been good or bad, but now does not matter
Chapter 7 13©2005 Pearson Education, Inc.
Prospective Sunk Cost
An Example Firm is considering moving its headquarters A firm paid $500,000 for an option to buy a
building The cost of the building is $5 million for a
total of $5.5 million The firm finds another building for $5.25
million Which building should the firm buy?
Chapter 7 14©2005 Pearson Education, Inc.
Prospective Sunk Cost
Example (cont.)The first building should be purchasedThe $500,000 is a sunk cost and should
not be considered in the decision to buyWhat should be considered is
Spending an additional $5,250,000 or Spending an additional $5,000,000
Chapter 7 15©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Some costs vary with output, while some remain the same no matter the amount of output
Total cost can be divided into:
1. Fixed Cost Does not vary with the level of output
2. Variable Cost Cost that varies as output varies
Chapter 7 16©2005 Pearson Education, Inc.
Fixed and Variable Costs
Total output is a function of variable inputs and fixed inputs
Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or…
VC FC TC
Chapter 7 17©2005 Pearson Education, Inc.
Fixed and Variable Costs
Which costs are variable and which are fixed depends on the time horizon
Short time horizon – most costs are fixedLong time horizon – many costs become
variableIn determining how changes in
production will affect costs, must consider if fixed or variable costs are affected.
Chapter 7 18©2005 Pearson Education, Inc.
Fixed Cost Versus Sunk Cost
Fixed cost and sunk cost are often confused
Fixed Cost Cost paid by a firm that is in business
regardless of the level of output
Sunk Cost Cost that has been incurred and cannot be
recovered
Chapter 7 19©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Personal Computers Most costs are variable Largest component: labor
Software Most costs are sunk Initial cost of developing the software
Chapter 7 20©2005 Pearson Education, Inc.
Marginal and Average Cost
In completing a discussion of costs, must also distinguish between Average Cost Marginal Cost
After definition of costs is complete, one can consider the analysis between short-run and long-run costs
Chapter 7 21©2005 Pearson Education, Inc.
Measuring Costs
Marginal Cost (MC): The cost of expanding output by one unit Fixed costs have no impact on marginal cost,
so it can be written as:
Δq
ΔTC
Δq
ΔVC MC
Chapter 7 22©2005 Pearson Education, Inc.
Measuring Costs
Average Total Cost (ATC) Cost per unit of output Also equals average fixed cost (AFC) plus
average variable cost (AVC)
q
TVC
q
TFC
q
TC ATC
AVCAFC q
TC ATC
Chapter 7 23©2005 Pearson Education, Inc.
Measuring Costs
All the types of costs relevant to production have now been discussed
Can now discuss how they differ in the long and short run
Costs that are fixed in the short run may not be fixed in the long run
Typically in the long run, most if not all costs are variable
Chapter 7 24©2005 Pearson Education, Inc.
A Firm’s Short Run Costs
Chapter 7 25©2005 Pearson Education, Inc.
Determinants of Short Run Costs
The rate at which these costs increase depends on the nature of the production process The extent to which production involves
diminishing returns to variable factors
Diminishing returns to labor When marginal product of labor is decreasing
Chapter 7 26©2005 Pearson Education, Inc.
Determinants of Short Run Costs
If marginal product of labor decreases significantly as more labor is hired Costs of production increase rapidly Greater and greater expenditures must be
made to produce more output
If marginal product of labor decreases only slightly as increase labor Costs will not rise very fast when output is
increased
Chapter 7 27©2005 Pearson Education, Inc.
Determinants of Short Run Costs – An Example
Assume the wage rate (w) is fixed relative to the number of workers hired
Variable costs is the per unit cost of extra labor times the amount of extra labor: wL
q
Lw
q
VC MC
Chapter 7 28©2005 Pearson Education, Inc.
Determinants of Short Run Costs – An Example
Remembering that
L MPL
Q
LMP
1
Q
L Qunit 1 afor L
And rearranging
Chapter 7 29©2005 Pearson Education, Inc.
Determinants of Short Run Costs – An Example
We can conclude:
LMP MC
w
…and a low marginal product (MPL) leads to a high marginal cost (MC) and vice versa
Chapter 7 30©2005 Pearson Education, Inc.
Determinants of Short Run Costs
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
Chapter 7 31©2005 Pearson Education, Inc.
Cost Curves
The following figures illustrate how various cost measures change as outputs change
Curves based on the information in table 7.1 discussed earlier
Chapter 7 32©2005 Pearson Education, Inc.
Cost Curves for a Firm
Output
Cost($ peryear)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VC
Variable costincreases with production and
the rate varies withincreasing and
decreasing returns.
TC
Total costis the vertical
sum of FC and VC.
FC50
Fixed cost does notvary with output
Chapter 7 33©2005 Pearson Education, Inc.
Cost Curves
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Output (units/yr)
Co
st (
$/u
nit
)
MC
ATC
AVC
AFC
Chapter 7 34©2005 Pearson Education, Inc.
Cost Curves
When MC is below AVC, AVC is fallingWhen MC is above AVC, AVC is risingWhen MC is below ATC, ATC is fallingWhen MC is above ATC, ATC is risingTherefore, MC crosses AVC and ATC at
the minimums The Average – Marginal relationship
Chapter 7 35©2005 Pearson Education, Inc.
Cost Curves for a FirmThe line drawn from
the origin to the variable cost curve: Its slope equals AVC The slope of a point
on VC or TC equals MC
Therefore, MC = AVC at 7 units of output (point A)
1 2 3 4 5 6 7 8 9 10 11 12 13
Output
P
100
200
300
400
FC
VC
TC
A
Chapter 7 36©2005 Pearson Education, Inc.
Cost in the Long Run
In the long run a firm can change all of its inputs
In making cost minimizing choices, must look at the cost of using capital and labor in production decisions
Chapter 7 37©2005 Pearson Education, Inc.
Cost in the Long Run
Capital is either rented/leased or purchased We will consider capital rented as if it were
purchased
Assume Delta is considering purchasing an airplane for $150 million Plane lasts for 30 years $5 million per year – economic depreciation
for the plane
Chapter 7 38©2005 Pearson Education, Inc.
Cost in the Long Run
Delta needs to compare its revenues and costs on an annual basis
If the firm had not purchased the plane, it would have earned interest on the $150 million
Forgone interest is an opportunity cost that must be considered
Chapter 7 39©2005 Pearson Education, Inc.
User Cost of Capital
The user cost of capital must be considered The annual cost of owning and using the
airplane instead of selling or never buying it Sum of the economic depreciation and the
interest (the financial return) that could have been earned had the money been invested elsewhere
Chapter 7 40©2005 Pearson Education, Inc.
Cost in the Long Run
User Cost of Capital = Economic Depreciation + (Interest Rate)*(Value of Capital)
= $5 mil + (.10)($150 mil – depreciation) Year 1 = $5 million + (.10)($150 million) =
$20 million Year 10 = $5 million +(.10)($100 million) =
$15 million
Chapter 7 41©2005 Pearson Education, Inc.
Cost in the Long Run
User cost can also be described as: Rate per dollar of capital, r r = Depreciation Rate + Interest Rate
In our example, depreciation rate was 3.33% and interest was 10%, so r = 3.33% + 10% = 13.33%
Chapter 7 42©2005 Pearson Education, Inc.
Cost Minimizing Input Choice
How do we put all this together to select inputs to produce a given output at minimum cost?
Assumptions Two Inputs: Labor (L) and capital (K) Price of labor: wage rate (w) The price of capital
r = depreciation rate + interest rateOr rental rate if not purchasingThese are equal in a competitive
capital market
Chapter 7 43©2005 Pearson Education, Inc.
Cost in the Long Run
The Isocost Line A line showing all combinations of L & K that
can be purchased for the same cost Total cost of production is sum of firm’s labor
cost, wL, and its capital cost, rK:
C = wL + rK For each different level of cost, the equation
shows another isocost line
Chapter 7 44©2005 Pearson Education, Inc.
Cost in the Long Run
Rewriting C as an equation for a straight line: K = C/r - (w/r)L Slope of the isocost:
-(w/r) is the ratio of the wage rate to rental cost of capital.
This shows the rate at which capital can be substituted for labor with no change in cost
rw
LK
Chapter 7 45©2005 Pearson Education, Inc.
Choosing Inputs
We will address how to minimize cost for a given level of output by combining isocosts with isoquants
We choose the output we wish to produce and then determine how to do that at minimum cost Isoquant is the quantity we wish to produce Isocost is the combination of K and L that
gives a set cost
Chapter 7 46©2005 Pearson Education, Inc.
Producing a Given Output at Minimum Cost
Labor per year
Capitalper
year
Isocost C2 shows quantity Q1 can be produced with
combination K2,L2 or K3,L3.However, both of these
are higher cost combinationsthan K1,L1.
Q1
Q1 is an isoquant for output Q1.
There are three isocost lines, of which 2 are possible choices in
which to produce Q1.
C0 C1 C2
AK1
L1
K3
L3
K2
L2
Chapter 7 47©2005 Pearson Education, Inc.
Input Substitution When an Input Price Change
If the price of labor changes, then the slope of the isocost line changes, -(w/r)
It now takes a new quantity of labor and capital to produce the output
If price of labor increases relative to price of capital, and capital is substituted for labor
Chapter 7 48©2005 Pearson Education, Inc.
Input Substitution When an Input Price Change
C2
The new combination of K and L is used to produce Q1.
Combination B is used in place of combination A.K2
L2
B
C1
K1
L1
A
Q1
If the price of laborrises, the isocost curve
becomes steeper due to the change in the slope -(w/L).
Labor per year
Capitalper
year
Chapter 7 49©2005 Pearson Education, Inc.
Cost in the Long Run
How does the isocost line relate to the firm’s production process?
K
LMP
MP- MRTS L
K
rw
LK
lineisocost of Slope
costminimizesfirmwhenrw
MPMP
K
L
Chapter 7 50©2005 Pearson Education, Inc.
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.
rwKL MPMP
Chapter 7 51©2005 Pearson Education, Inc.
Cost in the Long Run
If w = $10, r = $2, and MPL = MPK, which input would the producer use more of? Labor because it is cheaper Increasing labor lowers MPL
Decreasing capital raises MPK
Substitute labor for capital until
r
MP
w
MP KL
Chapter 7 52©2005 Pearson Education, Inc.
Cost in the Long Run
Cost minimization with Varying Output Levels For each level of output, there is an isocost
curve showing minimum cost for that output level
A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output
Slope equals K/L
Chapter 7 53©2005 Pearson Education, Inc.
A Firm’s Expansion Path
Expansion Path
The expansion path illustratesthe least-cost combinations oflabor and capital that can be used to produce each level of
output in the long-run.
Capitalper
year
25
50
75
100
150
50Labor per year
100 150 300200
A
$2000
200 Units
B
$3000
300 Units
C
Chapter 7 54©2005 Pearson Education, Inc.
Expansion Path and Long Run Costs
Firm’s expansion path has same information as long-run total cost curve
To move from expansion path to LR cost curve Find tangency with isoquant and isocost Determine min cost of producing the output
level selected Graph output-cost combination
Chapter 7 55©2005 Pearson Education, Inc.
A Firm’s Long Run Total Cost Curve
Long Run Total Cost
Output, Units/yr100 300200
Cost/ Year
1000
2000
3000
D
E
F
Chapter 7 56©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
In the short run, some costs are fixedIn the long run, firm can change anything
including plant size Can produce at a lower average cost in long
run than in short run Capital and labor are both flexible
We can show this by holding capital fixed in the short run and flexible in long run
Chapter 7 57©2005 Pearson Education, Inc.
Capital is fixed at K1.To produce q1, min cost at K1,L1.If increase output to Q2, min cost
is K1 and L3 in short run.
The Inflexibility of Short Run Production
Long-RunExpansion Path
Labor per year
Capitalper
year
L2
Q2
K2
D
C
F
E
Q1
A
BL1
K1
L3
PShort-RunExpansion Path
In LR, can change capital and min costs falls to K2 and L2.
Chapter 7 58©2005 Pearson Education, Inc.
Long Run VersusShort Run Cost Curves
Long-Run Average Cost (LAC) Most important determinant of the shape of
the LR AC and MC curves is relationship between scale of the firm’s operation and inputs required to minimize cost
1. Constant Returns to Scale If input is doubled, output will double AC cost is constant at all levels of output
Chapter 7 59©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
2. Increasing Returns to Scale If input is doubled, output will more than
double AC decreases at all levels of output
3. Decreasing Returns to Scale If input is doubled, output will less than
double AC increases at all levels of output
Chapter 7 60©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
In the long run: Firms experience increasing and decreasing
returns to scale and therefore long-run average cost is “U” shaped.
Source of U-shape is due to returns to scale instead of decreasing returns to scale like the short-run curve
Long-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit
Chapter 7 61©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
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
In special case where LAC is constant, LAC and LMC are equal
Chapter 7 62©2005 Pearson Education, Inc.
Long Run Average and Marginal Cost
Output
Cost($ per unitof output
LAC
LMC
A
Chapter 7 63©2005 Pearson Education, Inc.
Long Run Costs
As output increases, firm’s AC of producing is likely to decline to a point
1. On a larger scale, workers can better specialize
2. Scale can provide flexibility – managers can organize production more effectively
3. Firm may be able to get inputs at lower cost if can get quantity discounts. Lower prices might lead to different input mix.
Chapter 7 64©2005 Pearson Education, Inc.
Long Run Costs
At some point, AC will begin to increase1. Factory space and machinery may make it
more difficult for workers to do their jobs efficiently
2. Managing a larger firm may become more complex and inefficient as the number of tasks increase
3. Bulk discounts can no longer be utilized. Limited availability of inputs may cause price to rise.
Chapter 7 65©2005 Pearson Education, Inc.
Long Run Costs
When input proportions change, the firm’s expansion path is no longer a straight line Concept of return to scale no longer applies
Economies of scale reflects input proportions that change as the firm changes its level of production
Chapter 7 66©2005 Pearson Education, Inc.
Economies and Diseconomies of Scale
Economies of Scale Increase in output is greater than the
increase in inputsDiseconomies of Scale
Increase in output is less than the increase in inputs
U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels
Chapter 7 67©2005 Pearson Education, Inc.
Long Run Costs
Increasing Returns to Scale Output more than doubles when the
quantities of all inputs are doubled
Economies of Scale Doubling of output requires less than a
doubling of cost
Chapter 7 68©2005 Pearson Education, Inc.
Long Run Costs
Economies of scale are measured in terms of cost-output elasticity, EC
EC is the percentage change in the cost of production resulting from a 1-percent increase in output
ACMC
QQCCEC
Chapter 7 69©2005 Pearson Education, Inc.
Long Run Costs
EC is equal to 1, MC = AC Costs increase proportionately with output Neither economies nor diseconomies of scale
EC < 1 when MC < AC Economies of scale Both MC and AC are declining
EC > 1 when MC > AC Diseconomies of scale Both MC and AC are rising
Chapter 7 70©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
We will use short and long run costs to determine the optimal plant size
We can show the short run average costs for 3 different plant sizes
This decision is important because once built, the firm may not be able to change plant size for a while
Chapter 7 71©2005 Pearson Education, Inc.
Long Run Cost withConstant Returns to Scale
The optimal plant size will depend on the anticipated output If expect to produce q0, then should build
smallest plant: AC = $8 If produce more, like q1, AC rises
If expect to produce q2, middle plant is least cost
If expect to produce q3, largest plant is best
Chapter 7 72©2005 Pearson Education, Inc.
Long Run Cost with Economiesand Diseconomies of Scale
Chapter 7 73©2005 Pearson Education, Inc.
Long Run Cost withConstant Returns to Scale
What is the firm’s 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
Firm will always choose plant that minimizes the average cost of production
Chapter 7 74©2005 Pearson Education, Inc.
Long Run Cost withConstant Returns to Scale
The long-run average cost curve envelops the short-run average cost curves
The LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels
Chapter 7 75©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
Many firms produce more than one product and those products are closely linked
Examples: Chicken farm--poultry and eggs Automobile company--cars and trucks University--teaching and research
Chapter 7 76©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
Advantages
1. Both use capital and labor
2. The firms share management resources
3. Both use the same labor skills and types of machinery
Chapter 7 77©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
Firms must choose how much of each to produce
The alternative quantities can be illustrated using product transformation curves Curves showing the various combinations of
two different outputs (products) that can be produced with a given set of inputs
Chapter 7 78©2005 Pearson Education, Inc.
Product Transformation Curve
Number of cars
Numberof tractors
O1 illustrates a low levelof output. O2 illustrates
a higher level of output withtwo times as much labor
and capital.
Each curve showscombinations of output
with a given combination of L & K.
O2
O1
Chapter 7 79©2005 Pearson Education, Inc.
Product Transformation Curve
Product transformation curves are negatively sloped To get more of one output, must give up
some of the other outputConstant returns exist in this example
Second curve lies twice as far from origin as the first curve
Curve is concave Joint production has its advantages
Chapter 7 80©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
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
Chapter 7 81©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
The degree of economies of scope (SC) can be measured by percentage of cost saved producing two or more products jointly:
C(q1) is the cost of producing q1
C(q2) is the cost of producing q2
C(q1,q2) is the joint cost of producing both products
)qC(q
)qC(q)C(q)C(q SC
,
,
21
2121
Chapter 7 82©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
With economies of scope, the joint cost is less than the sum of the individual costs
Interpretation: If SC > 0 Economies of scope If SC < 0 Diseconomies of scope The greater the value of SC, the greater the
economies of scope
Chapter 7 83©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
Firms may lower their costs not only due to economies of scope, but also due to managers and workers becoming more experienced at their jobs
As management and labor gain experience with production, the firm’s marginal and average costs may fall
Chapter 7 84©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
Reasons1. Speed of work increases with experience
2. Managers learn to schedule production processes more efficiently
3. More flexibility is allowed with experience; may include more specialized tools and plant organization
4. Suppliers become more efficient, passing savings to company
Chapter 7 85©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
The learning curve measures the impact of workers’ experience on the costs of production
It describes the relationship between a firm’s cumulative output and the amount of inputs needed to produce a unit of output
Chapter 7 86©2005 Pearson Education, Inc.
The Learning Curve
Cumulative number of machine lots produced
Hours of laborper machine lot
10 20 30 40 500
2
4
6
8
10
Chapter 7 87©2005 Pearson Education, Inc.
The Learning Curve
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 88©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
The learning curve in the figure is based on the relationship:
BNAL
1 and 0between is and positive are
constants are and
output ofunit per input labor
producedoutput of units cumulative
B & A
BA,
L
N
Chapter 7 89©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
If N = 1 L equals A + B and this measures labor input
to produce the first unit of output
If = 0 Labor input per unit of output remains
constant as the cumulative level of output increases, so there is no learning
Chapter 7 90©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
If > 0 and N increases, L approaches A, and A represents minimum
labor input/unit of output after all learning has taken place
The larger , The more important the learning effect
Chapter 7 91©2005 Pearson Education, Inc.
The Learning Curve
Cumulative number ofmachine lots produced
Hours of laborper machine lot
10 20 30 40 500
2
4
6
8
10
The chart shows a sharp dropin lots to a cumulative amount of
20, then small savings at higher levels.
Doubling cumulative output causesa 20% reduction in the difference between the input required and
minimum attainable input requirement.
31.0
Chapter 7 92©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
Observations1. New firms may experience a learning curve,
not economies of scale Should increase production of many lots
regardless of individual lot size
2. Older firms have relatively small gains from learning Should produce their machines in very large
lots to take advantage of lower costs associated with size
Chapter 7 93©2005 Pearson Education, Inc.
Economies of Scale Versus Learning
Output
Cost($ per unitof output)
AC1
B
Economies of Scale
A
AC2
Learning C
Chapter 7 94©2005 Pearson Education, Inc.
Predicting Labor Requirements of Producing a Given Output
Chapter 7 95©2005 Pearson Education, Inc.
Dynamic Changes in Costs – The Learning Curve
From the table, 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
Chapter 7 96©2005 Pearson Education, Inc.
The Learning Curve in Practice
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?
Chapter 7 97©2005 Pearson Education, Inc.
The Learning Curve in Practice
The Empirical Findings Study of 37 chemical products
Average cost fell 5.5% per yearFor 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?
Chapter 7 98©2005 Pearson Education, Inc.
The Learning Curve in Practice
Other Empirical Findings In the semiconductor 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%
Chapter 7 99©2005 Pearson Education, Inc.
The Learning Curve in Practice
Applying Learning Curves1. To determine if it is profitable to enter an
industry
2. To determine when profits will occur based on plant size and cumulative output
Chapter 7 100©2005 Pearson Education, Inc.
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 7 101©2005 Pearson Education, Inc.
Total Cost Curve for the Automobile Industry
Quantity of Cars
Variablecost General Motors
Toyota
Ford
Chrysler
Volvo
Honda
Nissan
Chapter 7 102©2005 Pearson Education, Inc.
Estimating and Predicting Cost
A linear cost function might be:
The linear cost function is applicable only if marginal cost is constant Marginal cost is represented by
Q VC
Chapter 7 103©2005 Pearson Education, Inc.
Estimating and Predicting Cost
If we wish to allow for a U-shaped average cost curve and a marginal cost that is not constant, we might use a quadratic cost function:
2 VC QQ
Chapter 7 104©2005 Pearson Education, Inc.
Estimating and Predicting Cost
If the marginal cost curve is also not linear, we might use a cubic cost function:
32 VC QQQ
Chapter 7 105©2005 Pearson Education, Inc.
Cubic Cost Function
Output(per time period)
Cost($ per unit)
2δQγQβAVC
232 δQγQβMC
Chapter 7 106©2005 Pearson Education, Inc.
Estimating and Predicting Cost
Difficulties in Measuring Cost1. Output data may represent an aggregate of
different types 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
Chapter 7 107©2005 Pearson Education, Inc.
Cost Functions & 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
Chapter 7 108©2005 Pearson Education, Inc.
Scale Economies in Electric Power Industry
Chapter 7 109©2005 Pearson Education, Inc.
Average Cost of Productionin the Electric Power Industry
Chapter 7 110©2005 Pearson Education, Inc.
Cost Functions for Electric Power
FindingsDecline in cost
Not due to economies of scale Was caused by:
Lower input cost (coal and oil)Improvements in technology