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F
E
500, 8:00
December 12, 2007
Name:
Email:
@uiuc.edu
All questions must be answered on this test form!
For each question you must show your work and (or) provide a clear argument.
If you need scratch paper, use the last two pages or the back of the form.
Question 1
A production function is given by
f
(
z
)
=
2 min
{
z
1
,
z
2
}
+
z
3
. Then the cost
function is given by
10 points
c
(
w,
q
)
=
1
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Suppose a production function
f
(
z
1
,
z
2
) has the following properties.
1. The marginal product of input
i
only depends on the level of input
i
, not on
that of the other input.
2. Changing both inputs by a factor of
α
≥
0 changes output by
α
2
.
The general form of a production function that satisfies both conditions is
10 points
f
(
z
1
,
z
2
)
=
Use a, b, .
. . to denote general parameters.
The parameters must satisfy the following conditions:
No detailed proof needed.
2
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