Production Function Ppt - Repository UNIKOM

  

Managerial Economics

& Business Strategy

  

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

  

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

  

Total Product

• Cobb-Douglas Production Function

  .5 .5

• Example: Q = F(K,L) = K L _
_ K is fixed at 16 units.

  Short run production function: .5 .5 .5 _ Q = (16) L = 4 L

  Production when 100 units of labor are used? .5

  Q = 4 (100) = 4(10) = 40 units

  Marginal Product of

Labor

• MP

  L

  = Q/L

• Measures the output produced by the last worker.
• Slope of the production function

  Average Product of

Labor

• AP = Q/L

  L

• This is the accounting measure of productivity.

  Q L Q=F(K,L)

  Increasi ng Margina l

  Returns Diminishing Marginal

  Returns Negative Marginal

  Returns MP AP

  Stages of Production

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 Q ₃ Q ₂ Q ₁ Increasin g Output

  L K

  

Linear Isoquants

• Capital and labor are perfect substitutes

Leontief Isoquants

  Q

• Capital and labor

  K ₃ Q

  are perfect ₂ Q

  Increasi

  complements ₁

  ng

• Capital and labor

  Output

  are used in fixed- proportions

Cobb-Douglas Isoquants

  K

• Inputs are not

  Q

  perfectly

  3 Increasing Q

  substitutable

  Output

  2 Q

• Diminishing

  1

  marginal rate of technical substitution

• Most production processes have isoquants of

  L

  this shape

Isocost

• The combinations

  K

  of inputs that cost the producer the same amount of money

• For given input

  C C ₁

  prices, isocosts

  L

  farther from the

  K

  origin are

  New Isocost Line for a

  associated with

  decrease in the higher costs. wage (price of labor).

• Changes in input prices change the slope of the isocost line

  L

  r MP w MP

  

Cost Minimization

• Marginal product per dollar spent should be equal for all inputs:
• Expressed differently

  

K L

 r w

  MRTS KL 

  

Cost Minimization

K

  Point of Cost Slope of

  Minimizati Isocost on

   = Slope of Isoquant Q L

  

Cost Analysis

• Types of Costs _
_ Fixed costs (FC) Variable costs _ (VC) _ Total costs (TC) Sunk costs

  

Total and Variable Costs

C(Q): Minimum

  

$

total cost of

  C(Q) =

  VC producing

• FC

  alternative levels of

  VC( output:

  Q) C(Q) =

  VC FC +

  VC(Q): Costs that vary with output F C

  FC: Costs that do not vary with output Q

  Fixed and Sunk Costs $

  FC: Costs that do not change as C(Q) = VC

• FC

  output changes

  VC( Sunk Cost: A cost

  Q) that is forever lost after it has been paid

  F C 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

  $ Q ATC AVC AF C MC

Marginal Cost MC = C/Q

  

Fixed Cost

Q (ATC-AVC)

  MC = Q  AFC

  $ ATC

  = Q ) (FC/ Q AVC

  = FC ATC AFC

  Fixed Cost AVC Q Q

  Variable Cost Q AVC

  MC $ ATC

  = Q )/ [VC(Q Q ]

  AVC = VC(Q )

  AVC Variable Cost Q Q

  

Total Cost

Q

ATC

  MC $ = Q )/ Q ] [C(Q

  ATC = C(Q )

  AVC ATC Total Cost

  Q Q Economies of Scale LRAC $

  Output Economies of Scale

  Diseconomies of Scale

  An Example _ Total Cost: C(Q) = 10 + Q + Q

  2 _ Variable cost function:

  VC(Q) = Q + Q

  2 _ 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

  Multi-Product Cost

Function

• C(Q

  1

  , Q

  2

  ): Cost of producing two outputs jointly

  

Economies of Scope

• C(Q , Q ) < C(Q , 0) + C(0, Q )

  1

  2

  1

  2

• It is cheaper to produce the two outputs jointly instead of separately.
• Examples?

  

Cost Complementarity

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

  

  MC

  1

  /

  



  Q

  2 < 0.

• Examples?

  

Quadratic Multi-Product

Cost Function

  2

• C(Q ) = f + aQ + , Q Q + (Q )

  1

  2

  1

  2

  1

  2

  (Q )

  2

• MC

  1 (Q 1 , Q 2 ) = aQ 2 + 2Q

  1

• MC (Q , Q ) = aQ + 2Q

  2

  1

  2

  

1

  2

• Cost complementarity: a < 0
• Economies of scope: f > aQ Q

  1

  2

  1

  

2

  1

  2 C(Q ,0) + C(0, Q ) = f + (Q ) f +

  2

• (Q )

  2

  C(Q , Q ) = f + aQ Q + (Q )

• 2

  1

  2

  1

  2

  1

  2

  (Q )

  2 f > aQ Q : Joint production is

  1

  2

  cheaper

  

A Numerical Example:

  2

• C(Q , Q ) = 90 - 2Q Q + (Q )

  1

  2

  1

  2

  1

  2

• (Q )

  2

• Cost Complementarity?

  Yes, since a = -2 < 0

• MC (Q , Q ) = -2Q

  1

  1

  2

  2

  2Q

  1

• Economies of Scope?

  Yes, since 90 > -2Q Q

  1

  2

• Implications for Merger?