John Riley
Econ 200 Diagnostic Quiz
Fall 2011
1
Attempt all three questions. Time allowed: 10 minutes reading and 100 minutes writing. To test
out you need to show some progress on all three questions so manage your time carefully. As
long as you are enrolled in the class I will let you know via email whether or not you must
continue in Econ 200 or have completed the requirements of the course. Please keep this email as
your official record as your grade will not be posted till the end of the Fall quarter.
1.
Consumer Choice
(a)
Solve the following consumer problem. You should assume that income and prices are all
strictly positive.
3
1
{
( )
ln

}
j
x
j
Max U x
x
p x
I
=
=
⋅
≤
∑
.
State any theorems that you use to obtain your answer.
(b)
Suppose instead that
1
2
3
( )
ln(
)
ln
U x
x
x
x
=
+
+
,
(1,2,3)
p
=
and
100
I
=
. Solve for the utility
maximizing consumption bundle.
2.
Supporting Hyperplanes
(a)
A firm has a production function
1/2
,
0
q
z
z
=
≥
where
z
is the single input and
q
the single
output. What is the production set of the firm? Is it convex?
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 Fall '10
 riley
 Derivative, Convex function, John Riley, strictly quasiconcave functions, following consumer problem

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