Managerial economics and organizational architecture 5e ch005

Returns to Scaleproportional variation of all inputs together double, output more than doubles double, output less than doubles... Returns to a Factor• The relation between output and t

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 Functions

A production function specifies

maximum output from given inputs:

) ,

, ( x 1 x 2 x n f

5-2

Returns to Scale

proportional variation of all inputs

together

double, output more than doubles

double, output less than doubles

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

factor will decline as

its use is increased

Quantity of steel

Total product

Average product

Marginal product

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

• show all

combinations of

two inputs that

produce the same

Differing Input Substitutability

A A

S S

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 Lines Changes in Input Prices

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

Optimal Input Mix

Input Price Changes

Low steel price

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

Short-Run Cost Curves

Q1 Q2 Q3

Marginal cost

Average total cost

Average variable cost

$

Long-Run Average Cost

envelope of short-run average cost curves

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

Economies of Scale versus

Profit Maximization

as marginal revenue exceeds marginal

cost

marginal cost exceeds marginal

revenue

Optimal Output and Changes in

Factor Demand

Efficient production requires that

From which we derive the demand curve

(marginal revenue product) for input i

Marginal revenue product, MRP, is the

addition to revenue from using one

more unit of an input

5-28

Factor Demand Curve

Cost Estimation

• Effective management decisions

should incorporate estimates of

short- and long-run costs

• Use regression analysis

• Short-run costs may be

approximately linear

VC = a + bQ

5-30