managerial economics and organizational architecture, 5e managerial economics and organizational...

Managerial Economics and Organizational Architecture, 5e

Managerial Economics and Organizational Architecture, 5e

Chapter 5: Production and Cost

Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.McGraw-Hill/Irwin

Managerial Economics and Organizational Architecture, 5e

Production FunctionsA production function specifies maximum output from given inputs:

),...,( 21 nxxxfQ

5-2

Managerial Economics and Organizational Architecture, 5e

Returns to Scale• The relation between output and a

proportional variation of all inputs together• Increasing returns to scale - if inputs

double, output more than doubles• Decreasing returns to scale - if inputs

double, output less than doubles• Constant returns to scale- if inputs double,

output doubles5-3

Managerial Economics and Organizational Architecture, 5e

Returns to a Factor• The relation between output and the

variation in only one input, holding all other inputs constant

• Total product - amount of output, Q, obtained when an input, L, increases

• Average product Q/L• Marginal product Q/L

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Managerial Economics and Organizational Architecture, 5e

Returns to a Factor

S A Q MPS APS

1 9 3.00 3.00 3.002 9 4.24 1.24 2.123 9 5.20 0.96 1.734 9 6.00 0.80 1.505 9 6.70 0.70 1.34

Production function: Q=S1/2A1/2

5-5

Managerial Economics and Organizational Architecture, 5e

Returns to a Factor:A Common Case

Law of diminishing returns – at somepoint, S1, the marginal product of a variable factor will decline as its use is increased

Quantity of steel

Total product

Average productMarginal

product

S1 S2

S

Qua

ntity

of a

uto

parts

pe

r uni

t of s

teel

Q/SS

Qua

ntity

of a

uto

parts

Q

5-6

Managerial Economics and Organizational Architecture, 5e

Illustrating Production Choices with Isoquants

• Isoquants show all combinations of two inputs that produce the same level of output, assuming efficient production

• Shape of isoquants indicates substitutability between inputs

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Managerial Economics and Organizational Architecture, 5e

Isoquants Isoquants• show all

combinations of two inputs that produce the same level of output

• Moving to the northeast implies greater output S

Qua

ntity

of A

lum

inum

Quantity of Steel

A

200

300

100

5-8

Managerial Economics and Organizational Architecture, 5e

Differing Input SubstitutabilityIsoquants

A

SQuantity of Steel

Qua

ntity

of A

lum

inum

Quantity of SteelQuantity of Steel

Fixed proportions Normal case Perfect substitutes

AA

SS

5-9

Managerial Economics and Organizational Architecture, 5e

Isocost Lines• Isocosts show all combinations of two

inputs that have the same cost• The slope of an isocost line changes as

input prices change

5-10

Managerial Economics and Organizational Architecture, 5e

Isocost LinesQ

uant

ity o

f al

umin

um

Quantity of steel

200

100

$100 line

200 400

$200 line

5-11

Managerial Economics and Organizational Architecture, 5e

Isocost LinesChanges in Input PricesQ

uant

ity o

f alu

min

um

100

Quantity of steel

200

PS = $1.00per pound

PS = $.50per pound

100

A

S

5-12

Managerial Economics and Organizational Architecture, 5e

Optimal Input Mix

• Equilibrium occurs when the isoprofit curve is tangent to the isocost curve

• If the price of one input increases, the firm will reduce its use and substitute relatively cheaper inputs in its place

5-13

Managerial Economics and Organizational Architecture, 5e

Cost MinimizationQ

uant

ity o

f alu

min

um

Quantity of steel

SS’ S*

A*

A’

Q*

5-14

Managerial Economics and Organizational Architecture, 5e

Optimal Input MixInput Price Changes

Qua

ntity

of a

lum

inum

High steelprice

Low steel price

Quantity of steel

SS2 S1

A2

A1

Q*

5-15

Managerial Economics and Organizational Architecture, 5e

Cost Concepts• Total cost

– relation between total cost and output• Marginal cost

– change in total cost when output rises one unit

• Average cost– total cost divided by total output

• Opportunity cost– value of a resource in it next best

alternative 5-16

Managerial Economics and Organizational Architecture, 5e

Cost Curves

Tota

l cos

ts (i

n do

llars

)

Total cost

Q

$

Quantity of output

Cos

t per

uni

t of

outp

ut (in

dol

lars

)

Marginal cost

Average cost

Q1 Q2

Q

$

5-17

Managerial Economics and Organizational Architecture, 5e

Short Run versus Long Run• Short run

– at least one input is fixed– cost curves are operating curves

• Long run– all inputs are variable– cost curves are planning curves

5-18

Managerial Economics and Organizational Architecture, 5e

Fixed versus Variable Costs

• Fixed costs– incurred even if firm produces nothing

• Variable costs– change with the level of output

5-19

Managerial Economics and Organizational Architecture, 5e

Short-Run Cost Curves

Quantity of output

Tota

l cos

ts (i

n do

llars

) Total cost

Total variable cost

$

Cos

t per

uni

t of o

utpu

t

(in d

olla

rs)

Average fixed cost

Q1 Q2 Q3

Marginal cost

Average total cost

Average variable cost

$

Q 5-20

Managerial Economics and Organizational Architecture, 5e

Long-Run Average Costenvelope of short-run average cost curves

$

Q

SRAC1

SRAC2SRAC3

SRAC4

SRAC5SRAC5

5-21

Managerial Economics and Organizational Architecture, 5e

Cost Concepts • Economies of scale

– Average costs fall as output expands• Economies of scope

– cost of producing a joint set of products is less than cost of producing separately in separate firms

5-22

Managerial Economics and Organizational Architecture, 5e

Additional Cost Concepts• Minimum efficient scale

– plant size at which long-run average cost first reaches its minimum point (Q*)

– Helps determine the number of firms in an industry and therefore the level of competition

• Learning curves– costs decline with production experience

5-23

Managerial Economics and Organizational Architecture, 5e

Learning Curve

Average cost of producing Q* units

$

Cos

t per

uni

t of o

utpu

t

(in d

olla

rs)

Cumulative quantity of output produced

Learning curve

ΣQ

5-24

Managerial Economics and Organizational Architecture, 5e

Economies of Scale versus Learning Effects

Quantity of output

Cos

t per

uni

t of o

utpu

t

(in d

olla

rs)

$

Learning effect

Average cost with low cumulative volume

Average cost with high cumulative volume

Q

5-25

Managerial Economics and Organizational Architecture, 5e

Profit Maximization

• A firm should increase output as long as marginal revenue exceeds marginal cost

• A firm should not increase output if marginal cost exceeds marginal revenue

• At the profit-maximizing level of output,

MR=MC

5-26

Managerial Economics and Organizational Architecture, 5e

Optimal Output and Changes in Marginal Cost

Cos

t/rev

enue

per

uni

t(in

dol

lars

)

Quantity of output

MR

MC1

MC0

QQ1Q0

$

5-27

Managerial Economics and Organizational Architecture, 5e

Factor DemandEfficient production requires that

MPi/Pi= MPj/Pj

From which we derive the demand curve (marginal revenue product) for input i

Pi=MRMPi

Marginal revenue product, MRP, is the addition to revenue from using one more unit of an input

5-28

Managerial Economics and Organizational Architecture, 5e

Factor Demand Curve

Quantity of input i

Cos

t/rev

enue

per

uni

t of

inpu

t

(in d

olla

rs)

Q*i

Qi

P*i

MRPi

$

5-29

Managerial Economics and Organizational Architecture, 5e

Cost Estimation• Effective management decisions should

incorporate estimates of short- and long-run costs

• Use regression analysis• Short-run costs may be approximately

linearVC = a + bQ

5-30