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

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


Production FunctionsA production function specifies maximum output from given inputs:

),...,( 21 nxxxfQ

5-2


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


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

5-4


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


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


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

5-7


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


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


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


Isocost LinesQ

uant

ity o

f al

umin

um

Quantity of steel

200

100

$100 line

200 400

$200 line

5-11


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


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


Cost MinimizationQ

uant

ity o

f alu

min

um

Quantity of steel

SS’ S*

A*

A’

Q*

5-14


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


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


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


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


Fixed versus Variable Costs

• Fixed costs– incurred even if firm produces nothing

• Variable costs– change with the level of output

5-19


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


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

$

Q

SRAC1

SRAC2SRAC3

SRAC4

SRAC5SRAC5

5-21


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


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


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


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


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


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


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


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


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

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