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Managerial Economics and Organizational Architecture, 5e
Managerial Economics and
Organizational Architecture, 5e
Chapter 5:
Production and Cost
McGraw-Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Managerial Economics and Organizational Architecture, 5e
Production Functions
A production function specifies maximum
output from given inputs:
Q  f ( x1, x2 ,...xn )
5-2
Managerial Economics and Organizational Architecture, 5e
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 doubles
5-3
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Returns to a Factor
Production function: Q=S1/2A1/2
S
1
2
3
4
5
A
9
9
9
9
9
Q
3.00
4.24
5.20
6.00
6.70
MPS
3.00
1.24
0.96
0.80
0.70
APS
3.00
2.12
1.73
1.50
1.34
5-5
Managerial Economics and Organizational Architecture, 5e
Returns to a Factor:
A Common Case
Total
product
S
Q/S
Quantity of auto parts
per unit of steel
Law of diminishing
returns – at some
point, S1, the
marginal
product of a variable
factor will decline as
its use is increased
Quantity of auto parts
Q
Average
product
Marginal
product
S1
Quantity of steel
S2
S
5-6
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Isoquants
Isoquants
Quantity of Aluminum
• show all
combinations of
two inputs that
produce the same
level of output
• Moving to the
northeast implies
greater output
A
300
200
100
S
Quantity of Steel
5-8
Managerial Economics and Organizational Architecture, 5e
Differing Input Substitutability
Isoquants
A
A
Quantity of Aluminum
A
S
Quantity of Steel
Fixed proportions
S
Quantity of Steel
Normal case
S
Quantity of Steel
Perfect substitutes
5-9
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Quantity of aluminum
Isocost Lines
200
100
$100 line
200
Quantity of steel
$200 line
400
5-11
Managerial Economics and Organizational Architecture, 5e
Isocost Lines
Changes in Input Prices
A
Quantity of aluminum
100
PS = $1.00
per pound
PS = $.50
per pound
S
100
Quantity of steel
200
5-12
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Cost Minimization
Quantity of aluminum
A’
A*
Q*
S
S’
S*
5-14
Quantity of steel
Managerial Economics and Organizational Architecture, 5e
Quantity of aluminum
Optimal Input Mix
Input Price Changes
A2
A1
Q*
High steel
price
Low steel
price
S
S2
S1
Quantity of steel
5-15
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Cost Curves
Total costs (in dollars)
$
Total cost
Q
Marginal cost
(in dollars)
Cost per unit of output
$
Average cost
Q1
Q2
Quantity of output
Q
5-17
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Fixed versus Variable Costs
• Fixed costs
– incurred even if firm produces nothing
• Variable costs
– change with the level of output
5-19
Managerial Economics and Organizational Architecture, 5e
Short-Run Cost Curves
$
Total costs (in dollars)
Total
cost
Total variable
cost
Average
total cost
Marginal
cost
Average
variable cost
(in dollars)
Cost per unit of output
$
Average
fixed cost
Q1
Q 2 Q3
Quantity of output
Q
5-20
Managerial Economics and Organizational Architecture, 5e
Long-Run Average Cost
envelope of short-run average cost curves
$
SRAC5
SRAC1
SRAC5
SRAC2
SRAC3
SRAC4
Q
5-21
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Learning Curve
$
(in dollars)
Cost per unit of output
Average cost
of producing
Q* units
Learning curve
ΣQ
Cumulative quantity of output produced
5-24
Managerial Economics and Organizational Architecture, 5e
Economies of Scale versus
Learning Effects
(in dollars)
Cost per unit of output
$
Learning effect
Average cost with low
cumulative volume
Average cost with high
cumulative volume
Q
Quantity of output
5-25
Managerial Economics and Organizational Architecture, 5e
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
Managerial Economics and Organizational Architecture, 5e
Optimal Output and Changes in
Marginal Cost
$
MC
0
Cost/revenue per unit
(in dollars)
MC1
MR
Q0
Q1
Quantity of output
Q
5-27
Managerial Economics and Organizational Architecture, 5e
Factor Demand
Efficient production requires that
MPi/Pi= MPj/Pj
From which we derive the demand curve
(marginal revenue product) for input i
Pi=MRMPi
Marginal revenue product, MRP, is the
addition to revenue from using one
more unit of an input
5-28
Managerial Economics and Organizational Architecture, 5e
Factor Demand Curve
(in dollars)
Cost/revenue per unit of input
$
P*i
MRPi
Q*i
Quantity of input i
Qi
5-29
Managerial Economics and Organizational Architecture, 5e
Cost Estimation
• Effective management decisions should
incorporate estimates of short- and longrun costs
• Use regression analysis
• Short-run costs may be approximately
linear
VC = a + bQ
5-30