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Winter 2011
Problem Set VII
(due Wednesday, February 23)
A firm uses two inputs, capital and labor, to produce its output.
The production function is
ab
QKL
where
0
K
and
0
L
denote the firm's inputs of capital and labor, respectively,
Q
denotes its output, and
0
a
and
0
b
are constants.
The firm is a price taker in both input markets; the prices of the capital and labor inputs are
r
and
w
, respectively.
The firm's objective is to minimize the cost of producing some specified level of output,
Q
.,
i
.
e
., the firm chooses
0
K
and
0
L
to minimize
rK
wL
subject to the constraint
.
1.
What are the first order conditions for this optimization problem?
2.
What is the (sufficient) second order condition?
(The second order condition is satisfied for all values of
0
a
and
0
b
.
You do not need to show this, but you may want to for your own satisfaction.
A fair bit
of algebra is involved.)
3.
Solve the first order conditions for the conditional factor demand functions,
ˆ
(, , )
KrwQ
and
ˆ
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This note was uploaded on 04/04/2011 for the course ECON 400 taught by Professor Ellis,g during the Spring '08 term at University of Washington.
 Spring '08
 Ellis,G

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