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PPA 723: Managerial Economics Lecture 11: Costs

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PPA 723: Managerial Economics

Lecture 11:

Costs

Managerial Economics, Lecture 11: Costs

Outline

Short-Run Cost Curves

The Input Mix Decision

Long-Run Cost Curves

Managerial Economics, Lecture 11: Costs

Review

Short run production concepts:Total, average, and marginal products.MPL=APL at maximum APL

Law of Diminishing Marginal Returns

Long-run production conceptsIsoquantMRTS = MPL/MPK

Returns to Scale

Managerial Economics, Lecture 10: Production

Managerial Economics, Lecture 11: Costs

From Production to CostProduction concepts examine the

amount of input(s) needed to produce a given output.

Cost concepts examine the cost of the inputs needed to produce a given output.

Thus cost concepts combine production concepts with input prices.

Managerial Economics, Lecture 11: Costs

Short-Run Cost MeasuresFixed cost (F): production expense that

does not vary with output.

Variable cost (VC): production expense that changes with quantity of output produced.

Total cost (C):

C = VC + F

Managerial Economics, Lecture 11: Costs

Average Cost Concepts

Average fixed cost:

AFC = F /q

Average variable cost:

AVC = VC /q

Average (total) cost:

AC = C/q = AFC + AVC

Managerial Economics, Lecture 11: Costs

Marginal CostMarginal cost, MC, is the cost of

producing the last unit

MC is the change in cost, C, when output changes by q

That is, MC = C/q

Managerial Economics, Lecture 11: Costs

Sunk Fixed Cost We usually assume fixed cost is sunk, i.e.,

expenditure that cannot be recovered. The opportunity cost of capital is zerobecause you can't get this expenditure back no

matter what you do.So ignore it when making decisions

Example: walk out of a bad movie early, regardless of what you paid to attend

Otherwise, fixed cost is called avoidable.

Managerial Economics, Lecture 11: Costs

Managerial Economics,Lecture 11: Costs

Figure 7.1 Short-Run Cost Curves 120

216

400

48

0 6 10

10

42 8Quantity, q, Units per day

Quantity, q, Units per day6

b

a

B

A

42 8

C

F

1

1

27

20

VC

MC

AC

AVC

AFC

Cost, $

Cost per unit, $

(a)

(b)

60

2827

20

8

0

Managerial Economics, Lecture 11: Costs

MC, AC, and AVC Curves

AC and AVC curves fall when MC is below them, and rise when MC is above them.

Therefore, the MC curve intersects the AC and AVC curves at their minimum points.

Managerial Economics, Lecture 11: Costs

Example

• Suppose the short-run cost function is C = 125 + 2q + q2

• What are the:fixed costvariable costaverage costaverage fixed costaverage variable cost?

Managerial Economics, Lecture 11: Costs

Answer

If C = 125 + 2q + q2

Fixed cost = F = 125

Variable cost = VC = 2q + q2

Average cost = AC = C/q = 125/q + 2 + q

Average fixed cost = AFC = 125/q

Average variable cost = AVC = 2 + q

Note: marginal cost = MC = 2 + 2q

Managerial Economics, Lecture 11: Costs

Production Functions & Cost Curves

A production function shows the inputs needed to produce a given output.

A firm's cost is found by multiplying the quantity of each input by its price and summing across inputs.

Higher average or marginal productivity implies lower average or marginal cost, so cost curves are U-shaped—the inverse of product curves.

Managerial Economics, Lecture 11: Costs

ApplicationShort-Run Cost Curves for a Printing Firm(with continually rising AVC)

Cost, kroner

100 200 300q, Units per year

AFC

AVCAC

MC

0

20

30

40

50

10

Managerial Economics, Lecture 11: Costs

Cost Effects of $10 Tax This tax affects variable but not fixed cost

After-tax (a) cost = before-tax (b) cost + 10q:

Ca = Cb + 10q

At every quantity, AVC, AC, and MC curves shift up by $10:

AVCa = AVCb + $10

ACa = ACb + $10

MCa = MCb + $10

Managerial Economics, Lecture 11: Costs

Figure 7.3 Effects of a Specific Tax on Cost CurvesCosts per

unit, $

155 8 100q, Units per day

80

37

27

$10

AC a = AC b + 10

AC b

MC b

MCa = MCb + 10

$10

Managerial Economics, Lecture 11: Costs

Long-Run Costs

A firm adjusts all its inputs so its cost of production is as low as possible.

If capital and other variable costs can be varied, LR fixed costs equal zero (F = 0).

Thus LR total cost = LR variable cost:

C = VC

Managerial Economics, Lecture 11: Costs

Input Choice

To understand LR cost curves, we must examine a firm’s input mix decision.

A firm chooses from all technologically efficient combinations of inputs, the economically efficient combination of inputs.

Managerial Economics, Lecture 11: Costs

The Iso-Cost LineIsocost line: all combinations of inputs

that require the same (iso) total expenditure (cost).

If cost is C = wL + rKthen isocost iswhere is a fixed level of cost

An isocost line is analogous to a budget constraint.

,C wL rK C

Managerial Economics, Lecture 11: Costs

Figure 7.4 A Family of Isocost LinesK, Units of

capital per year

a

b

d

e

c

$150 isocost$100 isocost$50 isocost

$100———

$5= 20

$150———

$5= 30

$50———$5

= 10

$100———$10

10 =

$50———$10

5 =

$150———$10

15 =

L, Units of labor per year

Managerial Economics, Lecture 11: Costs

Properties of Isocost Lines The intercepts depend on factor prices.

intersects capital axis at intersects labor axis at

Isocosts farther from origin involve higher costs.

The slope of each isocost line is the same.As with a budget line, the slope is the price of the

factor on the horizontal axis divided by the price of the factor on the vertical axis.

That is, slope = K/L = -w/r

/C r

/C w

Managerial Economics, Lecture 11: Costs

Minimizing Costs To pick lowest-cost combination of inputs to

produce a given level of output when isoquants are smooth:

Pick the lowest possible isocost line that touches the relevant isoquant.

The isocost and isoquant lines are tangent at this point, that is,

MRTS = w/r

Managerial Economics, Lecture 11: Costs

Figure 7.5 Cost minimization for Norwegian printing firm

K, Units ofcapital per year

y

x

z

11650240L , Units of labor per year

100

303

28

q = 100 isoquant

3,000-krisocost

2,000-krisocost

1,000-krisocost

Managerial Economics, Lecture 11: Costs

Last Dollar Rule

L

K

MP wMRTS

MP r

L KMP MP

w r

As in the case of utility maximization, this analysis leads to a last dollar rule: make sure the last dollar spent on one input produces as much extra output as last dollar spent on any other input

Managerial Economics, Lecture 11: Costs

Cost Minimizing vs. Output Maximizing

With smooth isoquants: firm determines best factor proportions by either

Minimizing cost: what is the lowest cost, C*, at which the firm can produce output q*?

Maximizing output: What is the most output, q*, that can be produced at cost C*?

Managerial Economics, Lecture 11: Costs

Long-Run Cost Examine the lowest-cost factor combination

for various levels of output Define the expansion path:

Defined by cost-minimizing combination of labor and capital for each output level

The curve through tangency points is LR expansion path

The expansion path shows same relationship between LR cost and output as the LR cost curve.

Managerial Economics, Lecture 11: Costs

Figure 7.7a Expansion Path and Long-Run cost CurveK, Units of

capital per year

x

y

z

10075500 L, Workers per year

150

200

100

Expansion path

(a) Expansion Path

3,000-krisocost

2,000-krisocost

4,000-kr isocost

100 isoquant150 isoquant

200 isoquant

Managerial Economics, Lecture 11: Costs

Figure 7.7b Expansion Path and Long-Run cost Curve

C, Cost, kroner

X

Y

Z

0 q, Units per year

4,000

3,000

2,000

Long-run cost curve

(b) Long-Run Cost Curve

200100 150

Managerial Economics, Lecture 11: Costs

Shape of LR Cost Curves Short-run:

SR AC initially downward sloping because AFC is downward sloping

SR AC later upward sloping because of diminishing returns

Long-runNo fixed cost in LR (usually)Shape of cost curves determined by production

function returns to scale.

Managerial Economics, Lecture 11: Costs

Figure 7.8 Long-Run Cost Curves

Cost, $

q* q, Quantity per day

(a) Cost Curve

C

Cost perunit, $

q* q, Quantity per day

MC

AC

(b) Marginal and Average Cost Curves

Managerial Economics, Lecture 11: Costs

Economies of Scale

economies of scale AC falls as output expands

no economies of scale

AC does not change as output increases

diseconomies of scale

AC rises when output increases

Managerial Economics, Lecture 11: Costs

Long-Run & Short-Run Cost Curves

In LR, firm chooses optimal plant size to minimize its LR cost for a given q

Because the firm cannot vary its capital in SR but can in LRSR cost LR cost SR cost > LR cost if the "wrong" level of

capital is used in SR

Managerial Economics, Lecture 11: Costs

Figure 7.9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves

Average cost, $

a

bd

e

SRAC1 SRAC 2SRAC3

SRAC 3LRAC

c

q2q1 q, Output per day

10

0

12

Managerial Economics, Lecture 11: Costs

Long-Run Cost Curves in Printing

Cost, kroner

200 600 1,200

q, Output per year

0

20

30

40

10

SRAC 1

SRMC 1

SRAC 2

SRMC 2

LRAC = LRMC

Managerial Economics, Lecture 11: Costs

Long-Run Cost Curves Oil Pipelines

2000100040020010 20 40 1000Thousand barrels per day

Cost per barrel-mile

150

100

50

10

8" SRAC

10" SRAC

16" SRAC

12" SRAC

26" SRAC20" SRAC

40" SRAC

LRAC