Chapter 9 su1

Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/IrwinManagerial Economics, 9e

Managerial Economics ThomasMauriceninth edition

Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/IrwinManagerial Economics, 9e

Managerial Economics ThomasMauriceninth edition

Chapter 9

Production & Cost in the Long Run

Managerial EconomicsManagerial Economics

9-2

Production Isoquants

• In the long run, all inputs are variable & isoquants are used to study production decisions• An isoquant is a curve showing all

possible input combinations capable of producing a given level of output

• Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output


9-3

Marginal Rate of Technical Substitution• The MRTS is the slope of an isoquant

& measures the rate at which the two inputs can be substituted for one another while maintaining a constant level of output

K

MRTSL

MRTS

K LThe minus sign is added to make a positivenumber since , the slope of the isoquant, isnegative


9-4

Marginal Rate of Technical Substitution• The MRTS can also be expressed as

the ratio of two marginal products:

L

K

MPMRTS

MP

L

K

MPMP MRTSAs labor is substituted f or capital, declines &

rises causing to diminish

L

K

MPKMRTS

L MP


9-5

Isocost Curves

• Represents amount of capital that may be purchased if zero labor is purchased

( C ) ( w, r )

Show various combinations of inputs thatmay be purchased for given level ofexpenditure at given input prices

•

• K C r-intercept is

C w

K Lr r

•( w r )

Slope of an isocost curve is the negativeof the input price ratio


9-6

Optimal Combination of Inputs

• Two slopes are equal in equilibrium• Implies marginal product per dollar spent on

last unit of each input is the same

Q

Q

Minimize total cost of producing bychoosing the input combination on the

isoquant for which is just tangent to anisocost curve

•

L L K

K

MP MP MPw

MP r w ror


9-7

Optimization & Cost

• Expansion path gives the efficient (least-cost) input combinations for every level of output• Derived for a specific set of input

prices• Along expansion path, input-price

ratio is constant & equal to the marginal rate of technical substitution


9-8

Expansion Path (Figure 9.6)


9-9

Returns to Scale

• If all inputs are increased by a factor of c & output goes up by a factor of z then, in general, a producer experiences:• Increasing returns to scale if z > c; output goes up

proportionately more than the increase in input usage

• Decreasing returns to scale if z < c; output goes up proportionately less than the increase in input usage

• Constant returns to scale if z = c; output goes up by the same proportion as the increase in input usage

f(cL, cK) = zQ


9-10

Long-Run Costs

• Long-run total cost (LTC) for a given level of output is given by: LTC = wL* + rK* Where w & r are prices of labor & capital,

respectively, & (L*, K*) is the input combination on the expansion path that minimizes the total cost of producing that output


9-11

Long-Run Costs• Long-run average cost (LAC) measures the

cost per unit of output when production can be adjusted so that the optimal amount of each input is employed• LAC is U-shaped

• Falling LAC indicates economies of scale

• Rising LAC indicates diseconomies of scale

LTC

LACQ


9-12

Long-Run Costs• Long-run marginal cost (LMC) measures

the rate of change in long-run total cost as output changes along expansion path• LMC is U-shaped

• LMC lies below LAC when LAC is falling

• LMC lies above LAC when LAC is rising

• LMC = LAC at the minimum value of LAC

LTC

LMCQ


9-13

Derivation of a Long-Run Cost Schedule (Table 9.1)

Least-cost combination of

Output Labor (units)

Capital (units)

Total cost

(w = $5, r = $10)

LAC LMC

100

500

600

200

300

400

700

LMC

10

4052

1220

30

60

7

2230

8

10

15

42

$120

420

560

140

200

300

720

$1.20

0.840.93

0.700.67

0.75

1.03

$1.20

1.201.40

0.200.60

1.00

1.60


9-14

Long-Run Total, Average, & Marginal Cost (Figure 9.9)


9-15

Constant Long-Run Costs

• When constant returns to scale occur over entire range of output• Firm experiences constant costs in

the long run• LAC curve is flat & equal to LMC at

all output levels


9-16

Long-Run Average Cost as the Planning Horizon (Figure 9.13)


9-17

Restructuring Short-Run Costs (Figure 9.14)

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Chapter 9 su1