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Econ 51: Midterm Exam
Tuesday, February 8, 2011
Instructions
Please make sure to follow the instructions below. Failure to follow them can result in
getting a score of zero, so please follow them very carefully.
(1) This is a closed book, closed notes exam.
(2) Please write your answers with
a pen (black or blue), not a pencil.
(3) You are allowed to use a simple handheld calculator.
Do NOT use any other
device
such as a laptop, a tablet computer, a smartphone etc (the list is not ex
haustive).
(4) You have 110 minutes (910:50).
(5) Please answer all three questions.
Please use a separate blue book for each
question.
Please, never forget to write your name as well as the question you are
answering, on each blue book.
(6) Write your answers clearly.
I retain the right not to grade answers that are
illegible to me. Also, incorrect grading due to illegible answers is not a
ground for regrading.
(7) When I write log(
x
), I mean the natural logarithm.
(8) Good luck!
1
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Short Questions (28 points)
(1) Let there be two states of the world
s
= 1
,
2, and let
x
and
y
be the consumptions
in two states 1 and 2, respectively. Does the utility function
u
(
x,y
) = 6 + 5
x
2
+
7
y
2
+14
y
+10
x
represent a vNM preferences? Why or why not? If it does represent
a vNM preferences, what are the implied probabilities of each state?
(2) There are two states
s
= 1
,
2 with probabilities
π
and 1

π
. The agent’s vNM utility
function is
u
(
x,y
) =
π
(

x

3
) + (1

π
)(

y

3
), where
x
and
y
are consumptions in
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This note was uploaded on 03/19/2011 for the course ECON 51 taught by Professor Tendall,m during the Winter '07 term at Stanford.
 Winter '07
 Tendall,M

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