Chapter 7 Slide 1

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 CostEconomic Cost vs. Accounting Cost

Chapter 7 Slide 2

Opportunity cost: Cost associated with opportunities that are foregone when a firm’s resources are not put to their highest-value use.

E.g.: 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 3

Sunk Cost: Expenditure that has been made and cannot be recovered - should not influence a firm’s decisions.

E.g.: 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 4

Total output is a function of variable inputs and fixed inputs.

Therefore, the total cost of production equals the fixed cost plus the variable cost

VC FC TC

Measuring Cost: Which Costs Matter?

Fixed and Variable CostsFixed and Variable Costs

Chapter 7 Slide 5

Cost in the Short Run

Marginal 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:

Q

TC

Q

VC MC

Chapter 7 Slide 6

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:

QTVC

QTFC

QTC ATC

Chapter 7 Slide 7

Cost in the Short Run

Assume the wage rate (w) is fixed relative to the number of workers hired. Then:

Continuing: L VC w

Q

VC MC

L VC w

LMPww

QL

MC

A Firm’s Short-Run Costs ($)

0 50 0 50 --- --- --- ---

1 50 50 1002 50 78 1283 50 98 1484 50 112 1625 50 130 1806 50 150 2007 50 175 2258 50 204 2549 50 242 292

10 50 300 35011 50 385 435

Rate of Fixed Variable Total Marginal Average Average AverageOutput Cost Cost Cost Cost Fixed Variable Total

(FC) (VC) (TC) (MC) Cost Cost Cost(AFC) (AVC) (ATC)

Chapter 7 Slide 9

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

VCVariable cost

increases with production and

the rate varies withincreasing &

decreasing returns.

TCTotal cost

is the verticalsum of FC

and VC.

FC50

Fixed cost does notvary with output

Chapter 7 Slide 10

Cost Curves for a Firm

Unit CostsAFC 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 11

Cost in the Long Run

AssumptionsTwo Inputs: Labor (L) & capital (K)Price of labor: wage rate (w)The price of capital: r = depreciation rate +

interest rate

Question If capital was rented, would it change the value

of r ?

The Cost Minimizing Input ChoiceThe Cost Minimizing Input Choice

Chapter 7 Slide 12

Cost in the Long Run

The Isocost Line: shows all combinations of L & K that can be purchased for the same costC = wL + rK

Rewriting C as linear: K = C/r - (w/r)L

The slope of the isocost line:

is 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.

The User Cost of CapitalThe User Cost of CapitalThe Cost Minimizing Input ChoiceThe Cost Minimizing Input Choice

rwLK

Chapter 7 Slide 13

Producing a Given Output at Minimum Cost

Labor per year

Capitalper

year

Isocost C2 shows quantity Q1 can be produced withcombination K2L2 or K3L3.However, both of these

are higher cost combinationsthan K1L1.

Q1

Q1 is an isoquantfor output Q1.

Isocost curve C0 showsall combinations of K and L

that cost C0.

C0 C1 C2

CO C1 C2 arethree

isocost lines

AK1

L1

K3

L3

K2

L2

Chapter 7 Slide 14

Input Substitution with an Input Price Change

C2

This yields a new combinationof K and L to produce Q1.

Combination B is used in placeof combination A.

The new combination represents the higher cost of labor relativeto capital and therefore capital

is substituted for labor.

K2

L2

B

C1

K1

L1

A

Q1

If the price of laborchanges, the isocost curve

becomes steeper due to the change in the slope -(w/L).

Labor per year

Capitalper

year

Chapter 7 Slide 15

Cost in the Long Run

Isoquants and Isocosts and the Production Function

KL

MPMP- MRTS

LK

rw

LK

lineisocost of Slope

rw

MPMP

K

L

Chapter 7 Slide 16

A Firm’s Expansion Path

Labor per year

Capitalper

year

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.

25

50

75

100

150

10050 150 300200

A

$2000Isocost Line

200 UnitIsoquant

B

$3000 Isocost Line

300 Unit Isoquant

C

Chapter 7 Slide 17

A Firm’s Long-Run Total Cost Curve

Output, Units/yr

Costper

Year

1000

100 300200

2000

3000

D

E

F

Chapter 7 Slide 18

Long-RunExpansion Path

The long-run expansionpath is drawn as before..

LR Versus SR Cost Curves: The Inflexibility of SR Production

Labor per year

Capitalper

year

L2

Q2

K2

D

C

F

E

Q1

A

BL1

K1

L3

PShort-RunExpansion Path

Chapter 7 Slide 19

Long-Run Average Cost (LRAC)Constant Returns to Scale: If input is doubled,

output will double; average cost is constant at all levels of output.

Increasing Returns to Scale: If input is doubled, output will more than double; average cost decreases at all levels of output.

Decreasing Returns to Scale: If input is doubled, the increase in output is less than doubled; average cost increases with output.

LR Versus SR Cost Curves

Chapter 7 Slide 20

Long-Run Average Cost (LRAC) In the long-run: firms experience increasing and

decreasing returns to scale and therefore long-run average cost is “U” shaped.

Long-run marginal cost leads long-run average cost:

If LRMC < LRAC, LRAC will fall If LRMC > LRAC, LRAC will rise Therefore, LRMC = LRAC at the minimum of

LRAC

LR Versus SR Cost Curves

Chapter 7 Slide 21

Long-Run Average and Marginal Cost

Output

Cost($ per unitof output

LRAC

LRMC

A

Chapter 7 Slide 22

Economies & Diseconomies of ScaleEconomies 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.

Measuring Economies of Scale

Ec = % change in cost from a 1% increase in Q

LR Versus SR Cost Curves

Chapter 7 Slide 23

LR Cost with Constant Returns to Scale

Output

Cost($ per unitof output)

Q3

SRAC3

SRMC3

Q2

SRAC2

SRMC2

Q1

SRAC1

SRMC1

LRAC =LRMC

With many plant sizes with minimum SRAC = $10the LRAC = LRMC and is a straight line

$10

Chapter 7 Slide 24

LR Cost with Economies and Diseconomies of Scale

Output

Cost($ per unitof output

SRMC1

SRAC1

SRAC2

SRMC2LRMC

If the output is Q1 a managerwould 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

$8B

A

LRAC SRAC3

SRMC3

Chapter 7 Slide 25

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: 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 26

Product Transformation Curve

Number of cars

Numberof tractors

O2 O1 illustrates a low levelof output. O2 illustrates

a higher level of output withtwo times as much labor

and capital.O1

Each curve showscombinations of output

with a given combination of L & K.

Chapter 7 Slide 27

There is no direct relationship between economies of scope and economies of scale.

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 28

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.

Chapter 7 Slide 29

Economies of Scale Versus Learning

Output

Cost($ per unitof output)

AC1

B

Economies of Scale

A

AC2

LearningC

Chapter 7 Slide 30

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?

How would the learning curve influence your decision?

The Learning Curve in Practice

Chapter 7 Slide 31

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%

Semiconductors: a study of 7 generations of DRAM semiconductors from 1974-1992 found learning rates averaged 20%.

In the aircraft industry, learning rates are as high as 40%.

The Learning Curve in Practice: Empirical Results