Chapter 7
Slide 1
Measuring Cost: Which Costs Matter?
nExplicit costs: Costs that involve a direct monetary outlay (e.g. fuel, salaries of an aeroplane)
nImplicit Costs: Costs that do not involve outlays of cash (income it forgoes by not leasing this
aeroplane)
nSacrificed costs=sum of explicit and implicit costs associated with the decision
Explicit Costs vs. Implicit Costs

Chapter 7
Slide 2
Opportunity costs
nThe value of the next best alternative that is forgone when another alternative is chosen.
nThe forward-looking nature of opportunity costs
nTwo options – to run own business (costs 100 000 workers wages + 80 000 for supplies)  or to be
employed (income 75 000) => the opportunity cost of continuing in business over the next year is
$255,000
nopportunity cost differs from the original expense incurred by the firm (there are different
opportunity costs for different decisions under different circumstances)
n
n

Chapter 7
Slide 3
Measuring Cost: Which Costs Matter?
nAccounting Cost: costs that would appear on accounting statements (explicit costs that have been
incurred in the past)
nEconomic Cost: The sum of the firm’s explicit costs and implicit costs. Cost to a firm of
utilizing economic resources in production, including opportunity cost (synonymous with opportunity
costs)
Economic Cost vs. Accounting Cost

Chapter 7
Slide 4
nOpportunity cost: Cost associated with opportunities that are foregone when a firm’s resources are
not put to their highest-value use.
nE.g.: A firm owns its own building and pays no rent for office space.
lDoes this mean the cost of office space is zero?
Measuring Cost: Which Costs Matter?

Chapter 7
Slide 5
SUNK (UNAVOIDABLE) VERSUS NONSUNK
(AVOIDABLE) COSTS
nsunk costs: costs that have already been incurred and cannot be recovered
nnonsunk costs: Costs that are incurred only if a particular decision is made, so they are avoided
if the decision is not made > avoidable costs)
Economic Cost vs. Accounting Cost

Chapter 7
Slide 6
The cost minimization problem
nHow to choose a combination of inputs to minimize the cost of producing a given quantity of
output?
na firm that seeks to minimize the cost of producing a given amount of output is called a
cost-minimizing firm
nLong run= The period of time that is long enough for the firm to vary the quantities of all of its
inputs as much as it desires (so all costs are nonsunk).
nShort run= The period of time in which at least one of the firm’s input quantities cannot be
changed.

Chapter 7
Slide 7
Short-run cost minimization
nA firm uses just two inputs (capital and labor)
nfirm is unable to alter its quantity of capital, even if it produces zero output
ncan alter its quantity of labor L (e.g., by hiring or firing workers).
nfirm’s total costs are wL + rK
nThe firm’s labor cost thus constitutes its total variable cost (the
noutput-sensitive component of its costs) => total variable cost
nBy contrast, the firm’s capital cost will not go up or down as the firm produces more or less
output => total fixed cost
n

Chapter 7
Slide 8
Short-run cost minimization
nShould the firm produce no output, or should it produce some positive level of output?
nthe firm’s total expenditure on labor is a nonsunk cost (since variable costs are completely
avoidable)
nBy contrast, the firm’s fixed capital cost may be sunk or nonsunk (the fixed cost will be sunk if
there are no alternative uses for and nonsunk if e.g. we find somebody who will rent our factory so
we can cover our payments to bank)
n

Chapter 7
Slide 9


Chapter 7
Slide 10
Short-run cost minimization
nthe firm’s problem when it seeks to produce a quantity of output Q0 but is unable to change the
quantity of capital from its fixed level
nThe firm’s only technically efficient combination of inputs occurs at point F

Chapter 7
Slide 11
Short-run cost minimization
nfirm cannot substitute between capital and labor => the determination of the optimal amount of
labor does not involve a tangency condition
nin the short run, the firm will typically operate with higher total costs than it would if it
could adjust all of its inputs freely
n

Chapter 7
Slide 12


Chapter 7
Slide 13
nTotal output is a function of variable inputs and fixed inputs.
nTherefore, the total cost of production equals the fixed cost plus the variable cost
Measuring Cost: Which Costs Matter?
Fixed and Variable Costs

Chapter 7
Slide 14
Cost in the Short Run
nMarginal Cost (MC)  is the cost of expanding output by one unit.  Since fixed cost has no impact
on marginal cost, it can be written as:

Chapter 7
Slide 15
Cost in the Short Run
nAverage Total Cost (ATC) is the cost per unit of output, or average fixed cost (AFC) plus average
variable cost (AVC). This can be written:

Chapter 7
Slide 16
Cost in the Short Run
nAssume the wage rate (w) is fixed relative to the number of workers hired. Then:
n
nContinuing:

A Firm’s Short-Run Costs ($)
n 0 50 0 50 --- --- --- ---
n 1 50 50 100
n 2 50 78 128
n 3 50 98 148
n 4 50 112 162
n 5 50 130 180
n 6 50 150 200
n 7 50 175 225
n 8 50 204 254
n 9 50 242 292
n 10 50 300 350
n 11 50 385 435
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 18
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 19
Cost Curves for a Firm
nUnit Costs
lAFC falls continuously
lWhen MC < AVC or MC < ATC, AVC & ATC decrease
lWhen 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 20
Long-run cost minimization
nEach input has a price
nThe price of a unit of labor services—also called the wage rate - is w. This price per unit of
capital services is r.
nBoth prices could be explicit or implicit cost
nThe firm has decided to produce Q0 units of output (now this amount is exogenous => the question
for managers is how to produce that amount in the cost-minimizing way)
nthe manager must choose a quantity of capital K and a quantity of labor L that minimize the total
cost TC= wL + rK of producing Q0 units of output (TC is sum of all the economic costs when uses
labour and capital services to produce output)

Chapter 7
Slide 21
Isocost lines
n= The set of combinations of labor and capital that yield the same total cost for the firm
(analogous to a BL)
n

Chapter 7
Slide 22
Long-run cost minimization
nConsider, for example, a case in which w=10 per labor-hour,
nr=20 per machine-hour, and TC=$1 million per year.
n
nGraphical illustration of isocost?
nWhat happen when TC will be $2 million and $3 million

Chapter 7
Slide 23
Isocost lines
nPoint G is off the Q0 isoquant altogether. Although this input combination could produce Q0 units
of output, in using it the firm would be wasting inputs (i.e., point G is technically inefficient)
nPoints E and F are technically efficient, but they are not cost-minimizing because they are on an
isocost line that corresponds to a higher level of cost than the isocost line passing through the
cost-minimizing point A. By moving from point E to A or from F to A, the firm can produce the same
amount of output, but at a lower total cost

Chapter 7
Slide 24
Long-run cost minimization
nSuppose that the firm’s production function is of the form
n
n
nMPL and MPK?
nw = 5 and r = 20
nWhat is the cost-minimizing input combination if the firm wants to produce 1,000 units per year?

Chapter 7
Slide 25
Corner point solution
nThe cost-minimizing input combination for producing Q0 units of output occurs at point A, where
the firm uses no capital.
nthe marginal product per dollar spent on labor exceeds the marginal product per dollar spent on
capital services:
n
n
n
nevery additional dollar spent on labor yields more output than every additional dollar spent on
capital. In this situation, the firm should substitute labor for capital until it uses no capital
at all,
n

Chapter 7
Slide 26
Corner point solution

Chapter 7
Slide 27
Long-run cost minimization
nSuppose that we have the linear production function:
n Q = 10L + 2K
nMPL and MPK?
nw = 5 and r = 2
nWhat is the cost-minimizing input combination if the firm wants to produce 200 units?

Chapter 7
Slide 28
Comparative statics analysis of changes in input prices
n= how changes in input prices and output affect the firm’s cost-minimization problem
nSuppose price of labor w changes, with the price of capital r held constant at 1 and the quantity
of output held constant at Q0
nIf w increases from 1 to 2 => it causes substitution capital for labor (the isocost lines is
steeper)
nIt causes changes the position of the tangency point between the isocost line and the isoquant

n
Chapter 7
Slide 29

Chapter 7
Slide 30
Comparative statics analysis of changes in output
n= changes in output quantity Q, with the prices of inputs (capital and labor) held constant.
nExpansion path= A line that connects the cost-minimizing input combinations as the quantity of
output, Q, varies, holding input prices constant.
nas quantity of output increases, the quantity of each input also increases => both labor and
capital are normal inputs => the expansion path is upward sloping
nWhen one of inputs is inferior (e.g. To increase output firm uses using more capital but less
labor)  => the expansion path is downward sloping
n

Normal inputs
Chapter 7
Slide 31

One input is inferior (labour)
Chapter 7
Slide 32

Chapter 7
Slide 33
The input demand curves

Chapter 7
Slide 34
Deriving the input demand curves form a production function
nSuppose that a firm faces the production function:
n
n
n What are the demand curves for labor and capital?

Chapter 7
Slide 35
Cost in the Long Run
nAssumptions
lTwo Inputs: Labor (L) & capital (K)
lPrice of labor: wage rate (w)
lThe price of capital: r = depreciation rate + interest rate
nQuestion
lIf capital was rented, would it change the value of r ?
u
The Cost Minimizing Input Choice

Chapter 7
Slide 36
Cost in the Long Run
nThe Isocost Line: shows all combinations of L & K that can be purchased for the same cost
lC = wL + rK
nRewriting C as linear: K = C/r - (w/r)L
nThe slope of the isocost line:
nis the ratio of the wage rate to the rental cost of capital. This shows the rate at which capital
can be substituted for labor with no change in cost.
l
The User Cost of Capital
The Cost Minimizing Input Choice

Chapter 7
Slide 37
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 cost C0.
C0
C1
C2
CO  C1  C2  are
three
isocost lines
A
K1
L1
K3
L3
K2
L2

Chapter 7
Slide 38
Input Substitution with 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 39
Cost in the Long Run
nIsoquants and Isocosts and the Production Function

Chapter 7
Slide 40
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 41
A Firm’s Long-Run Total Cost Curve
Output, Units/yr
Cost
per
Year

1000
100
300
200
2000
3000
D
E
F

Chapter 7
Slide 42
Long-Run
Expansion Path
The long-run expansion
path is drawn as before..
LR Versus SR Cost Curves: The Inflexibility of SR 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 43
nLong-Run Average Cost (LRAC)
lConstant Returns to Scale: If input is doubled, output will double; average cost is constant at
all levels of output.
lIncreasing Returns to Scale: If input is doubled, output will more than double; average cost
decreases at all levels of output.
lDecreasing Returns to Scale: If input is doubled, the increase in output is less than doubled;
average cost increases with output.
l
LR Versus SR Cost Curves

Chapter 7
Slide 44
nLong-Run Average Cost (LRAC)
lIn the long-run: firms experience increasing and decreasing returns to scale and therefore
long-run average cost is “U” shaped.
lLong-run marginal cost leads long-run average cost:
uIf LRMC < LRAC, LRAC will fall
uIf LRMC > LRAC, LRAC will rise
uTherefore, LRMC = LRAC at the minimum of LRAC
LR Versus SR Cost Curves

Chapter 7
Slide 45
Long-Run Average and Marginal Cost
Output
Cost
($ per unit
of output
LRAC
LRMC
A

Chapter 7
Slide 46
nEconomies & Diseconomies of Scale
lEconomies of Scale: Increase in output is greater than the increase in inputs.
lDiseconomies of Scale: Increase in output is less than the increase in inputs.
nMeasuring Economies of Scale
lEc = % change in cost from a 1% increase in Q
LR Versus SR Cost Curves

Chapter 7
Slide 47
LR Cost with Constant Returns to Scale
Output
Cost
($ per unit
of output)
Q3
SRAC3
SRMC3
Q2
SRAC2
SRMC2
Q1
SRAC1
SRMC1
LRAC =
LRMC
With many plant sizes with minimum SRAC = $10
the LRAC = LRMC and is a straight line
$10

Chapter 7
Slide 48
LR Cost with Economies and Diseconomies of Scale
Output
Cost
($ per unit
of output
SRMC1
SRAC1
SRAC2
SRMC2
LRMC
If the output is Q1 a manager
would chose the small plant
SRAC1 and SRAC $8.
Point B is on the LRAC because
it is a least cost plant for a
given output.
$10
Q1
$8
B
A
LRAC
SRAC3
SRMC3

Chapter 7
Slide 49
nEconomies 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.
nWhat are the advantages of joint production?
lConsider an automobile company producing cars and tractors:  both use capital and labor; the firms
share management resources; both use the same labor skills and type of machinery.
Production with Two Outputs: Economies of Scope

Chapter 7
Slide 50
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.
O1
Each curve shows
combinations of output
with a given combination
of L & K.

Chapter 7
Slide 51
nThere is no direct relationship between economies of scope and economies of scale.
nThe degree of economies of scope measures the savings in cost and can be written:
l
lC(Q1) is the cost of producing Q1
lC(Q2) is the cost of producing Q2
lC(Q1Q2) is the joint cost of producing both products
Production with Two Outputs: Economies of Scope

Chapter 7
Slide 52
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
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 53
Economies of Scale Versus Learning
Output
Cost
($ per unit
of output)
AC1
B
Economies of Scale
A
AC2
Learning
C

Chapter 7
Slide 54
nScenario: A new firm enters the chemical processing industry.
nDo they:
l1) 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?
nHow would the learning curve influence your decision?
l
The Learning Curve in Practice

Chapter 7
Slide 55
nStudy of 37 chemical products
uAverage cost fell 5.5% per year
uFor each doubling of plant size, average production costs fall by 11%
uFor each doubling of cumulative output, the average cost of production falls by 27%
nSemiconductors: a study of 7 generations of DRAM semiconductors from 1974-1992 found learning
rates averaged 20%.
nIn the aircraft industry, learning rates are as high as 40%.
The Learning Curve in Practice: Empirical Results