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Prof. Jay Bhattacharya
Spring 2001
Econ 11Lecture 12
1
Spring 2001
Econ 11Lecture 12
1
Theory of the Consumer
• Whatwehavedonesofar:
• Derived “downward” sloping demand
curves from underlying principles
– budgets
– preferences
– optimizing behavior
Spring 2001
Econ 11Lecture 12
2
Theory of the Firm
• We will derive “upward sloping” supply
curves from underlying principles
– Technology
– Firm objectives (profit maximization / cost
minimization)
– Firm optimization
Spring 2001
Econ 11Lecture 12
3
Technology
Inputs
(coal, steel)
Outputs
(cars)
Firm and
Technology
Spring 2001
Econ 11Lecture 12
4
Technology
We represent technology by a production
function:
)
,
(
L
K
f
y
=
β
α
L
AK
y
=
For example: CobbDouglass production function:
Spring 2001
Econ 11Lecture 12
5
Production Functions
Simple Case: 1 input, 1 output
)
(
x
f
y
=
y
x
Spring 2001
Econ 11Lecture 12
6
Properties of Production
Functions
1.Slope of the production function is equal to
the marginal product of the input
– The marginal physical product of the input
(MP
x
) is defined as the incremental increase in
output associated with an increase in the input.
x
MP
x
y
=
∂
∂
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View Full DocumentProf. Jay Bhattacharya
Spring 2001
Econ 11Lecture 12
2
Spring 2001
Econ 11Lecture 12
7
2.Marginal physical products of inputs are
positive
3.The average physical product of an input is
the ratio of output to the amount of input
used
0
>
X
MP
x
x
f
AP
X
)
(
=
Spring 2001
Econ 11Lecture 12
8
x
y
)
(
x
f
y
=
The average product at
any point x is the slope
of the line connecting
the origin and the total
product curve.
x
x
f
AP
X
)
(
=
Spring 2001
Econ 11Lecture 12
9
4. If MP
X
>AP
X
,thenAP
X
is increasing
– MP
x
x
means that the last unit of
input will produce more than the average
level of output up to that point.
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 Fall '07
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