Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Managerial Economics &
Business Strategy
Chapter 5
The Production Process and Costs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
Average Product of Labor
? APL = Q/L
? Measures the output of an,average”
worker,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Q
L
Q=F(K,L)
Increasing
Marginal
Returns
Diminishing
Marginal
Returns
Negative
Marginal
Returns
MP
AP
Stages of Production
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
Linear Isoquants
? Capital and labor are
perfect substitutes
Q3 Q2 Q1
Increasing
Output
L
K
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Leontief Isoquants
? Capital and labor are
perfect complements
? Capital and labor are
used in fixed-proportions
Q3
Q2
Q1
K
Increasing
Output
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cobb-Douglas Isoquants
? Inputs are not
perfectly substitutable
? Diminishing marginal
rate of technical
substitution
? Most production
processes have
isoquants of this shape
Q1
Q2
Q3 K
L
Increasing
Output
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Isocost
? 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
K
L C
1 C0
L
K
New Isocost Line for
a decrease in the
wage (price of
labor),
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cost Minimization
? Marginal product per dollar spent should be
equal for all inputs,
? Expressed differently
r
MP
w
MP KL ?
r
wM R T S
KL ?
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cost Minimization
Q
L
K
Point of Cost
Minimization Slope of Isocost
=
Slope of Isoquant
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cost Analysis
? Types of Costs
? Fixed costs (FC)
? Variable costs (VC)
? Total costs (TC)
? Sunk costs
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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
$
Q
C(Q) = VC + FC
VC(Q)
FC
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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
$
Q
FC
C(Q) = VC + FC
VC(Q)
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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
$
Q
ATC
AVC
AFC
MC
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Fixed Cost
$
Q
ATC
AVC
MC
ATC
AVC
Q0
AFC Fixed Cost
Q0?(ATC-AVC)
= Q0? AFC
= Q0?(FC/ Q0)
= FC
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Variable Cost
$
Q
ATC
AVC
MC
AVC
Variable Cost
Q0
Q0?AVC
= Q0?[VC(Q0)/ Q0]
= VC(Q0)
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
$
Q
ATC
AVC
MC
ATC
Total Cost
Q0
Q0?ATC
= Q0?[C(Q0)/ Q0]
= C(Q0)
Total Cost
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Economies of Scale
LRAC
$
Output
Economies
of Scale
Diseconomies
of Scale
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
Multi-Product Cost Function
? C(Q1,Q2),Cost of producing two outputs
jointly
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
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,3e,?The McGraw-Hill Companies,Inc.,1999
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?