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Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs Overview I. Production Analysis Total Product, Marginal Product, Average Product Isoquants Isocosts Cost Minimization II. Cost Analysis Total Cost, Variable Cost, Fixed Costs Cubic Cost Function

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managerial economics business strategy

Managerial Economics & Business Strategy

Chapter 5

The Production Process and Costs

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

overview
Overview

I. Production Analysis

  • Total Product, Marginal Product, Average Product
  • Isoquants
  • Isocosts
  • Cost Minimization

II. Cost Analysis

  • Total Cost, Variable Cost, Fixed Costs
  • Cubic Cost Function
  • Cost Relations

III. Multi-Product Cost Functions

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

production analysis
Production Analysis
  • Production Function
    • Q = F(K,L)
    • The maximum amount of output that can be produced with K units of capital and L units of labor.
  • Short-Run vs. Long-Run Decisions
  • Fixed vs. Variable Inputs

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

total product
Total Product
  • Cobb-Douglas Production Function
  • Example: Q = F(K,L) = K.5 L.5
    • K is fixed at 16 units.
    • Short run production function:

Q = (16).5 L.5 = 4 L.5

    • Production when 100 units of labor are used?

Q = 4 (100).5 = 4(10) = 40 units

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

marginal product of labor
Marginal Product of Labor
  • MPL = DQ/DL
  • Measures the output produced by the last worker.
  • Slope of the production function

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

average product of labor
Average Product of Labor
  • APL = Q/L
  • Measures the output of an “average” worker.

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide7

Q

AP

L

MP

Stages of Production

Increasing

Marginal

Returns

Diminishing

Marginal

Returns

Negative

Marginal

Returns

Q=F(K,L)

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

isoquant
Isoquant
  • The combinations of inputs (K, L) that yield the producer the same level of output.
  • The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.

L

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

linear isoquants

K

Increasing Output

Q2

Q3

Q1

L

Linear Isoquants
  • Capital and labor are perfect substitutes

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

leontief isoquants

Q3

K

Q2

Q1

Increasing Output

Leontief Isoquants
  • Capital and labor are perfect complements
  • Capital and labor are used in fixed-proportions

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

cobb douglas isoquants
Cobb-Douglas Isoquants
  • Inputs are not perfectly substitutable
  • Diminishing marginal rate of technical substitution
  • Most production processes have isoquants of this shape

K

Q3

Increasing Output

Q2

Q1

L

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

isocost
Isocost

K

  • The combinations of inputs that cost the producer the same amount of money
  • For given input prices, isocosts farther from the origin are associated with higher costs.
  • Changes in input prices change the slope of the isocost line

C0

C1

L

K

New Isocost Line for a decrease in the wage (price of labor).

L

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

cost minimization
Cost Minimization
  • Marginal product per dollar spent should be equal for all inputs:
  • Expressed differently

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

cost minimization14
Cost Minimization

K

Point of Cost Minimization

Slope of Isocost

=

Slope of Isoquant

Q

L

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

cost analysis
Cost Analysis

Types of Costs

Fixed costs (FC)

Variable costs (VC)

Total costs (TC)

Sunk costs

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide16

$

C(Q) =VC+FC

VC(Q)

FC

Q

Total and Variable Costs

  • C(Q): Minimum total cost of producing alternative levels of output:
    • C(Q) =VC+FC
  • VC(Q): Costs that vary with output
  • FC: Costs that do not vary with output

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide17

Fixed and Sunk Costs

$

FC: Costs that do not change as output changes

Sunk Cost: A cost that is forever lost after it has been paid

C(Q) = VC + FC

VC(Q)

FC

Q

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide18

MC

$

Q

Some Definitions

  • Average Total Cost
    • ATC = AVC + AFC
    • ATC = C(Q)/Q
  • Average Variable Cost
    • AVC = VC(Q)/Q
  • Average Fixed Cost
    • AFC = FC/Q
  • Marginal Cost
    • MC = DC/DQ

ATC

AVC

AFC

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide19

MC

$

ATC

AVC

Q

Fixed Cost

Q0(ATC-AVC)

= Q0 AFC

= Q0(FC/ Q0)

= FC

ATC

Fixed Cost

AFC

AVC

Q0

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide20

MC

$

ATC

AVC

Q

Variable Cost

Q0AVC

= Q0[VC(Q0)/ Q0]

= VC(Q0)

AVC

Variable Cost

Q0

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide21

MC

$

ATC

AVC

Q

Total Cost

Q0ATC

= Q0[C(Q0)/ Q0]

= C(Q0)

ATC

Total Cost

Q0

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

slide22

Economies of Scale

$

LRAC

Economies

of Scale

Diseconomies

of Scale

Output

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

cubic cost function
Cubic Cost Function
  • C(Q) = f + a Q + b Q2 + cQ3
  • Marginal Cost?
    • Memorize:

MC(Q) = a + 2bQ + 3cQ2

    • Calculus:

dC/dQ = a + 2bQ + 3cQ2

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

an example
An Example
  • Total Cost: C(Q) = 10 + Q + Q2
  • Variable cost function:

VC(Q) = Q + Q2

  • Variable cost of producing 2 units:

VC(2) = 2 + (2)2 = 6

  • Fixed costs:

FC = 10

  • Marginal cost function:

MC(Q) = 1 + 2Q

  • Marginal cost of producing 2 units:

MC(2) = 1 + 2(2) = 5

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

multi product cost function
Multi-Product Cost Function

C(Q1, Q2): Cost of producing two outputs jointly

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

economies of scope
Economies of Scope
  • C(Q1, Q2) < C(Q1, 0) + C(0, Q2)
  • It is cheaper to produce the two outputs jointly instead of separately.
  • Examples?

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

cost complementarity
Cost Complementarity
  • The marginal cost of producing good 1 declines as more of good two is produced:

DMC1/DQ2 < 0.

  • Examples?

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

quadratic multi product cost function
Quadratic Multi-Product Cost Function
  • C(Q1, Q2) = f + aQ1Q2 + (Q1 )2 + (Q2 )2
  • MC1(Q1, Q2) = aQ2 + 2Q1
  • MC2(Q1, Q2) = aQ1 + 2Q2
  • Cost complementarity: a < 0
  • Economies of scope: f > aQ1Q2

C(Q1 ,0) + C(0, Q2 ) = f + (Q1 )2 + f + (Q2)2

C(Q1, Q2) = f + aQ1Q2+ (Q1 )2 + (Q2 )2

f > aQ1Q2: Joint production is cheaper

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003

a numerical example
A Numerical Example:
  • C(Q1, Q2) = 90 - 2Q1Q2 + (Q1 )2 + (Q2 )2
  • Cost Complementarity?

Yes, since a = -2 < 0

MC1(Q1, Q2) = -2Q2 + 2Q1

  • Economies of Scope?

Yes, since 90 > -2Q1Q2

  • Implications for Merger?

Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2003