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Econ 51: Midterm
February 12, 2007
Instructions:
This is a closed book, closednotes exam. You are allowed to use a handheld calculator
(i.e. no laptop)
You have 110 minutes.
Please answer all 3 questions.
Please use a separate blue book for each question
.
Please write the name of your TA and section number on each blue book.
Always remember:
think before you do the math
!
Good luck!
1. Short questions (36 points, 6 points each)
(a) Let
x
and
y
be the consumption in two states of the world. Let
u
(
x; y
) =
±
10 +
2 log(
x
) + 6 log(
y
) + 21
y
3
+ 7
x
3
. Does
u
(
x; y
) represent vNM preferences? If yes,
express these preferences with a utility function that has the vNM form.
(b) There are apples (
a
) and bananas (
b
). Rob’s utility function is
u
R
(
a; b
) = log(
a
)+log(
b
).
Tom’s utility function is
u
T
(
a; b
) =
e
log(
a
)+log(
b
)
+
b
. There are 20 apples and 20 bananas
(c) There are apples (
a
) and bananas (
b
). Rob’s utility function is
u
R
(
a; b
) = log(
a
)+log(
b
).
Tom’s utility function is
u
T
(
a; b
) = 2 log(
a
)+2 log(
b
). There are 3 apples and 3 bananas
on the island. Derive the contract curve.
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 Winter '07
 Tendall,M

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