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ECON 400
Hartman
Winter 2010
MIDTERM EXAMINATION
1.
A firm uses two inputs, labor and capital, to produce its output.
The production function is
1/4
1/4
8
QL
K
where
Q
,
L
, and
K
denote the firms output and its inputs of labor and capital,
respectively.
The firm is a price taker in all of its markets and and it chooses
L
and
K
to maximizes
its profit,
1/4
1/4
8
pLK
w
L r
K
, where
p
,
w
, and
r
denote the output price, and the prices of the labor
and capital inputs, respectively.
a.
What are the first order conditions for profit maximization?
b.
What are the (sufficient) second order conditions?
Are the second order conditions satisfied?
c.
Solve for the profitmaximizing factor demand functions,
*
(,,)
Lwrp
and
*
Kw
rp
.
d.
Find the firm's supply function,
*
Qw
.
e. Are
*
,
*
, and
*
homogeneous of degree zero in
w
,
r
, and
p
?
Does
this imply that the production function is homogeneous of degree one?
f.
What is the elasticity of labor demand with respect to the price of the capital input,
i
.
e
., what is
Lr
?
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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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