ECN 712
Fall 2007
Edward Schlee
Final Exam
1. (20 points)
Risk aversion and risk
.
Two consumers, A and B, satisfy the expected utility
hypothesis over money lotteries; consumer
t
’s preferences are represented by the strictly
increasing vNM utility
u
t
on
R
+
for
t
=
A, B
. Consumer
A
weakly prefers the sure wealth of
y >
0 to the lottery
L
with two equally likely outcomes,
z
1
or
z
2
, with 0
< z
1
< z
2
. Consumer
B
is
strictly
more risk averse than
A
:
u
B
(
z
) =
T
(
u
A
(
z
)), for some strictly increasing,
strictly
concave realvalued function
T
on
Range
(
u
A
).
(a) (10) Prove that consumer
B
strictly
prefers the sure wealth of
y
to the lottery
L
.
(b) (10) Suppose that
u
A
is strictly concave and differentiable everywhere (and that
A
still
weakly prefers the sure thing to the lottery
L
). Show that consumer
A
strictly
prefers
the sure wealth of
y
to a lottery with gives two equally likely outcomes,
z
1

ε
or
z
2
+
ε
,
where 0
< ε < z
1
.
2. (30 points)
Technology Choice
. A monopoly produces and sells a single output under constant
returns to scale.
Its technology, hence its unit production cost, depends on how much it
invests before production; if the firm spends
I
≥
0 dollars, then its
average
cost of production
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 Spring '10
 schlee
 Microeconomics, Game Theory, Utility, Bertrand, 0 dollars, Edward Schlee

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