Cost and production
•Firms maximize profits
•Types of costs and their
relevance for decision
making.
•Long run vs. short run
•Optimal choice between the
inputs
Marginal product of labor
• MPL = DQ/DL
• Increase in total output associated
with increase in labor
NOTE: not the output produced by
the last worker
2,500
2,000
1,500
1,000
500
0
1 2 3 4 5 6 7 8 9 10 11
(500)
Labor
Output MP
Average Product of Labor
• APL = Q/L
• Measures the output of an
“average” worker.
350
300
250
200
150
100
50
0
1 2 3 4 5 6 7 8 9 10 11
-50
-100
MP AP
Stages of Production
Q Increasing Diminishing Negative
Marginal Marginal Marginal
Returns Returns Returns
TP
AP
L
MP
Value of marginal product
of labor
• Market value of the marginal
product of labor
• Optimal input employment rule:
marginal benefit equals marginal
cost. Value of marginal product of
labor equals wage
What is the value of marginal
product of a place-kicker?
Labor demand
1200
1000
800
600
Wage
400
200
0
1 2 3 4 5 6
-200
Labor
Short run vs. Long run
• In the short run, some costs do
not change. Some costs are fixed.
• In the long run, all costs change.
There are no fixed costs.
• How long is the long run
– For a hot dog stand?
– For a nuclear power plant?
– For a coffee shop on the corner?
Average Cost
• Total cost per unit
• Sum of average variable cost and average
fixed cost
Marginal Cost
• The cost of producing an additional unit of
output
• Increase in cost divided by the increase in
output
Relation between the cost
curves
$
MC ATC
TFC A AVC
D
B
C
AFC
1 Q
Sunk cost
• Sunk cost is irrelevant
• My laptop was $1,400 when I bought it
in 2000. I have never used it. I should
be able to sell it for $1,200
• When you drive a car off the dealer’s
lot, how much cost do you “sink”?
Short-Run Costs of Four
Different Plants
Long-Run Average Cost
Curve
Legally imposed decreasing
returns to scale
• Tanker companies and unlimited liability
• From 1967 to 1980 the number of firms in
hazardous sectors has increased.
• Single-engine airplane producers Cessna
and Piper Aircraft stopped production in
90’s. At the same time, it is legal to fly a
non-certified plane if you built at least half
of it yourself.
Learning by doing vs. increasing
returns to scale:
after producing 15 million cars the cost of one
Model T fell from $3,000 to $300
Cost
Economies of scale
ATC
Learning by doing
Output
Capital and labor:
optimal choice between two inputs
Are we in long or short run?
• Isoquants
• Isocosts
Isoquant
(production indifference curves)
• 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 L
output.
Linear Isoquants
• Capital and labor
are perfect
K
substitutes Increasing
Output
Q1 Q2 Q3
L
Leontief Isoquants
• Capital and labor K
Q2
Q3
are perfect Q1 Increasing
complements Output
• Capital and labor
are used in fixed-
proportions
Isoquants in a “normal” case
• Inputs are not K
Q3
perfectly Increasing
substitutable Q2
Output
Q1
• Diminishing marginal
rate of technical
substitution
• Most production
processes have
isoquants of this
shape
L
Concave indifference curves can be thought
of as an approximation to a set of fixed-
proportions technologies: there are three
isoquants for 10 units of output.
K
6
3
2 4 L
How do you get to the point A.
K
6
A
3
B
2 4 L
At what relative price of capital production
will use combination of inputs given by B.
Isocost
(production budget line)
K
• The combinations of
inputs that cost the C0 C1
producer the same L
amount of money K
• For given input prices, New Isocost Line for
a decrease in the
isocosts farther from the wage (price of
origin are associated labor).
with higher costs.
• Changes in input prices
change the slope of the L
isocost line
Cost Minimization
K
Point of Cost
Minimization
Slope of Isocost
=
Slope of Isoquant
Q
L
Cost Minimization
• Marginal product per dollar spent
should be equal for all inputs:
MPL MPK
w r
• Expressed differently
w
MRTSKL
r
The firm is using inputs at point C and uses the inputs
efficiently. The price of capital is 5. What is the price of
labor?
Inputs substitution in production
of parking
• There are two inputs: Land and Concrete.
• How is the choice of inputs affected by the
price (relative scarcity) of land?
Downtown
C Chicago
Q = 200 parking spots
Oxford, Ohio. L
Multi-Product Cost
Function
• C(Q1, Q2): Cost of producing two
outputs jointly
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?
• How is it different from economies
of scale?
Mergers. Economies of scope or
economies of scale?
• Daimler-Chrysler
• AOL-Time Warner
• Cingular – AT&T
Cost Complementarity
• The marginal cost of producing
good 1 declines as more of good
two is produced:
DMC1/DQ2 < 0.
• Examples?
Functional forms of cost
functions 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