1

The Cost of Production

Chapter 7

2

Introduction

• The 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.

• The optimal, cost minimizing, level of inputs can be determined.

3

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.

●opportunity cost Cost associated with opportunities that are forgone when a firm’s resources are not put to their best alternative use.

●sunk cost Expenditure that has been made and cannot be recovered.

4

Fixed Costs and Variable Costs

total cost (TC or C) Total economic cost of production,consisting of fixed and variable costs.

fixed cost (FC) Cost that does not vary with the level of output

and that can be eliminated only by shutting down.variable cost (VC) Cost that varies as output varies.

Shutting down doesn’t necessarily mean going out of business.

By reducing the output of a factory to zero, the company could eliminate the costs of raw materials and much of the labor. The only way to eliminate fixed costs would be to close the doors, turn off the electricity, and perhaps even sell off or scrap the machinery.

Shutting Down

VC FC TC

5

Marginal and Average Cost

marginal cost (MC) Increase in cost resulting from the production of one extra unit of output.

Because fixed cost does not change as the firm’s level of output changes, marginal cost is equal to the increase in variable cost or the increase in total cost that results from an extra unit of output.

We can therefore write marginal cost as

6

Marginal and Average Cost

TABLE 7.1 A Firm’s Costs

Rate of Fixed Variable Total Marginal Average Average AverageOutput Cost Cost Cost Cost Fixed Cost Variable Cost Total Cost(Units (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars

per Year) per Year) per Year) per Year) per Unit) per Unit) per Unit) per Unit)

(FC) (VC) (TC) (MC) (AFC) (AVC) (ATC)(1) (2) (3) (4) (5) (6) (7)

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

7

Average Total Cost (ATC)

AVCAFC q

TC ATC

Cost per unit of outputAlso equals average fixed cost (AFC) plus average variable cost (AVC).

q

TVC

q

TFC

q

TC ATC

8

The Determinants of Short-Run Cost

The change in variable cost is the per-unit cost of the extra labor w times the amount of extra labor needed to produce the extra output ΔL. Because ΔVC = wΔL, it follows that

The extra labor needed to obtain an extra unit of output is ΔL/Δq = 1/MPL. As a result,

9

• 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

q

Lw

q

VC MC

10

L MPL

Q

LMP

1

Q

L Qunit 1 afor L

LMP MC

w

11

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

TC

VC

FC50

Total costis the vertical

sum of FC and VC.

Variable costincreases with production and

the rate varies withincreasing &

decreasing returns.

Fixed cost does notvary with output

12

Cost Curves

0

20

40

60

80

100

120

0 2 4 6 8 10 12

Output (units/yr)

Co

st (

$/u

nit

)

13

Cost Curves for a Firm

1 2 3 4 5 6 7 8 9 10 11 12 13

Output

P

100

200

300

400

FC

VC

TCThe line drawn from the origin to the variable cost curve:

Its slope equals AVCThe slope of a point on VC or TC equals MCTherefore, MC = AVC at 7 units of output (point A)

14

COST IN THE LONG RUN

●user cost of capital Annual cost of owning and using a capital asset, equal to economic depreciation plus forgone interest.

We can also express the user cost of capital as a rate per dollar of capital:

15

The Price of Capital

The price of capital is its user cost, given by r = Depreciation rate + Interest rate.

The Rental Rate of Capital

● rental rate : Cost per year of renting one unit of capital.

16

COST IN THE LONG RUN

●isocost line Graph showing all possible combinations of labor and capital that can be purchased for a given total cost.

To see what an isocost line looks like, recall that the total cost C of producing any particular output is given by the sum of the firm’s labor cost wL and its capital cost rK:

If we rewrite the total cost equation as an equation for a straight line, we get

It follows that the isocost line has a slope of ΔK/ΔL = −(w/r), which is the ratio of the wage rate to the rental cost of capital.

17

Cost Minimizing Input Choice

• Assumptions– Two Inputs: Labor (L) & capital (K)– Price of labor: wage rate (w)– The price of capital

• r = depreciation rate + interest rate• Or rental rate if not purchasing• These are equal in a competitive capital

market

18

Producing a Given Output at Minimum Cost

C2C1C0

Q1

AK1

L1

K3

L3

K2

L2

Capitalper

year

Labor per year

Q1 is an isoquant for output Q1.

There are three isocost lines, of which 2 are possible choices

in which to produce Q1

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

are higher cost combinationsthan K1L1.

19

C1C2

Q1

K2

L2

B

K1

L1

A

Capitalper

year

Labor per year

If the price of laborrises, the isocost curve

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

The new combination of K and L is used to

produce Q1.Combination B is used in place of combination

A.

20

Cost in the Long Run

It follows that when a firm minimizes the cost of producing a particular output, the following condition holds:

We can rewrite this condition slightly as follows:

21

Cost in the Long Run

rwKL MPMP

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

22

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

23

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

24

A Firm’s Expansion Path

$3000

300 Units

C

$2000

200 Units

B

A

Capitalper

year

25

50

75

100

150

Labor per year100 150 300200

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

Long-Run Versus Short-Run Cost Curves

• In the short run some costs are fixed• In 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

26

The Inflexibility of Short-Run Production

L2

Q2

K2

D

C

F

E

Long-RunExpansion Path

Q1

A

BL1

K1

L3

PShort-RunExpansion Path

Capital is fixed at K1To produce q1, min cost at K1,L1If increase output to Q2, min cost

is K1 and L3 in short run

In LR, can change

capital and min costs falls to K2

and L2

27

Long-Run Versus Short-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 min cost

1. Constant Returns to Scale– If input is doubled, output will double– AC cost is constant at all levels of output.

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

28

Economies and Diseconomies of Scale

• As output increases, the firm’s average cost of producing that output is likely to decline, at least to a point.

• This can happen for the following reasons:

– If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive.

– Scale can provide flexibility. By varying the combination of inputs utilized to produce the firm’s output, managers can organize the production process more effectively.

29

Economies and Diseconomies of Scale

● economies of scale Situation in which output can be doubled for less than a doubling of cost.

● diseconomies of scale Situation in which a doubling of output requires more than a doubling of cost.

Increasing Returns to Scale: Output more than doubles when the quantities of all inputs are

doubled.

Economies of Scale: A doubling of output requires less than a doubling of cost.

30

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

31

Long-Run Cost with Economiesand Diseconomies of Scale

32

Cont’

• Advantages1. Both use capital and labor.2. The firms share management resources.3. Both use the same labor skills and type of

machine4. 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

33

1 and 0between is and positive are

constants are and

output ofunit per input labor

producedoutput of units cumulative

B & A

BA,

L

N

The learning curve in the figure is based on the relationship:

BNAL

34

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

• 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.