Econ 6202, Fall 2007
Dmitry Shapiro
Midterm Exam
October 15, 2007
•
There are 3 questions in the midterm. You need to do all three of them.
•
The exam is 75 minutes long and has 75 points. Be sure to allocate your time in proportion
to the points.
•
The exam is
closedbook.
•
Please turn off your cellphones and other soundmaking devices.
Good luck!
1.
[25 points]
Let
u
(
x
1
, x
2
) = ln(
x
1
) + 2 ln(
x
2
).
(a)
[10 points]
Find the Marshallian demand.
(b)
[15 points]
Assume that prices are
p
1
=
p
2
= 1. Is the person with such utility function
a riskloving, riskneutral or riskaverse when offered gambles over income?
2.
[25 points]
The firm has a linear production function
y
=
∑
n
i
=1
a
i
x
i
and the input prices
are
w
1
, . . . , w
n
.
(a)
[15 points]
Find the combination of inputs that minimize the firm’s cost of producing a
particular amount of output
y
if input prices are such that there are no two goods
i
and
j
with
w
i
/w
j
=
a
i
/a
j
.
(b)
[10 points]
Find the cost function and conditional input demand functions for all values
of input prices.
3.
[25 points]
Suppose that Audrey Tautou is considering purchasing flood insurance for her
house. If Audrey does not buy flood insurance, her wealth will be
w
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 Fall '09
 SHAPIRO
 Utility, St. Petersburg paradox, Expected utility hypothesis, Audrey Tautou, wi /ai

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