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Winter 2011
Problem Set III
(for Friday, January 21)
A firm uses two inputs, capital and labor, to produce its output.
The production function is
ab
QKL
where
Q
,
K
, and
L
denote the firms output and its inputs of capital and labor, respectively, and
01
a
and
b
are constants.
Assume the firm is a price taker in all of its markets, and let
p
,
r
, and
w
denote the output price, and the prices of the capital and labor inputs, respectively.
1.
Show that this production function is homogeneous of degree
.
2.
Verify that both marginal products are decreasing,
i
.
e
, show that
22
/0
QK
and
QL
.
3.
What are the first and second order
necessary
conditions for choosing
K
and
L
to maximize
profit?
Show that the second order necessary conditions for a maximum of profit cannot be
satisfied if
1
.
4.
Show that the second order
sufficient
conditions for a maximum of profit are satisfied if
1
.
For problems 511 below assume that
1
.
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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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