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ECO3553 Microeconomic Theory III
ECO3153B Microeconomic Theory III
Online partial exam
– Winter
2024
Winter
2015
Paul Makdissi
Professor: Paul Makdissi
Office: FSS9008
Office hours: Tuesday 3:00 to 6:00
Phone:
562-5800
Period(613)
allocated
to extension
take the4897
exam: From Monday February 26 at 8:30 a.m. to Friday March 1
Email:
at 11:59 [email protected]
p.m.
Web: http://aix1.uottawa.ca/~pmakdiss/
Estimated time for the partial exam: Approximately 3 hours of intensive work if you are
Description:
well prepared. Don’t wait until the last minute.
This course develops a mathematical approach to microeconomics, which gives students the preparation
necessary to understand the literature of modern economics and serves as an important stepping-stone for
graduate studies. The course represents a significant advancement from Micro I and II in terms of the level
Instructions: The exam is online, so you are entitled to all the documentation.
of abstraction and technique.
However, as mentioned in the commitment you signed, you must not communicate with other students or
Textbook:
receive help from anyone for the exam. The exam
is scheduled to be completed in 3 hours. The system gives you until March 1 at 11:59 p.m.
Cowell, Frank (2006), Microeconomics. Principles and Analysis, Oxford University Press, Oxford. This book
to submit it. After this time, the exam can no longer be submitted.
is available at the university’s bookstore.
Assessment:
1. Write your handwritten answer on white paper.
Homework 20% (Two homeworks will be assigned and marked. The first is due at
2. Take a photo or scan of each page of your answers and create a file containing all of these pages.
Name this file as follows: ExamenPartiel- beginning of the lecture on
April 13.)
Student
number-ECO3553.
Midterm 30%
(February
26)
Final 50%
3. Download (upload) your answer file before the deadline, ie before the 1st
March at 11:59 p.m.
A student may be granted a deferred exam for a religious reason if he informs the professor of any religious
restriction before January 30, 2015. A deferred exam may also be granted for health reasons. In this case,
the students should consult a healthcare professional PRIOR TO the exam. As a general note, only
a SERIOUS ILLNESS qualifies for a deferred exam. Examples of illnesses that qualify include high-grade fever or admission to a hospital
at the time of the exam. Colds, diarrhea, headaches, menstrual cramps, insomnia and caffeine are NOT acceptable reasons to defer an
exam. Feeling unewell a day or two prior to THE REVIEW STARTS ON THE NEXT PAGE
an exam, leaving you inadequate “cramming time”, is also NOT an acceptable reason to defer an exam. For more information, consult
http://uottawa.ca/health/services/certificates.html
Academic Fraud
Academic fraud is neither accepted nor tolerated by the University. Anyone found guilty of academic fraud is
liable to severe academic sanctions. Students can refer to http://www.uottawa.ca/plagiarism.pdf for more information.
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Problem 1 (20 points)
State whether each of the following statements is true, false or uncertain and justify your answer.
a) If there is no monetary illusion, we can calculate the income elasticity of demand for a good
once we know all the price elasticities. (5 points)
b) If the income elasticities of Walrasian demands for all goods are constant and equal to each
other, then they are necessarily equal to 1. (5 points)
c) In a two-good world, if one good is a Giffen good then the other is a luxury good. (5 points)
d) A risk-phobic consumer initially has 0. If he is offered two lotteries from which he must choose:
L1 = (10, 50, 100; 0.2, 0.5, 0.3)
L2 = (10, 40, 60, 100; 0.2, 0.25, 0.25, 0.3)
then, he chooses L1. (5 points)
Problem 2 (20 points)
A consumer has preferences defined over n goods, xi can be
represented by the utility function u (x) =
, i = 1, 2, …,
not. These preferences
not
not
i=1 ÿi ln xi where
i=1 ÿi = 1.
a) Calculate Walrasian demands if consumer income is I and prices n. (5 points) of the goods
2, …,
are pi , i = 1,
b) Find the indirect utility function and the expenditure function associated with this utility
function. (5 points)
c) Verify Roy’s identities by calculating the Marshallian demand directly from the indirect utility
function and comparing your answer with that obtained in (a). (5 points)
d) Find the Hicksian demands for each of the goods using the lemma of
Sheppard. (5 points)
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Problem 3 (30 points)
Suppose a consumer with Von-Neumann Morgenstern preferences is faced with two risks and
can only eliminate one of them. Let ÿ˜ = ÿ1 with probability p and ÿ˜ = ÿ2 with probability (1 ÿ p).
Suppose ÿ˜ = 0 if ÿ˜ = ÿ2. If ÿ˜ = ÿ1, ÿ˜ = ÿÿ with probability 0.5 and ÿ˜ = ÿ with probability 0.5.
Let us now define a risk premium ÿu for ÿ˜ as follows:
E [u (˜ÿ ÿ ÿu)] = E [u (˜ÿ + ˜ÿ)]
Show that it is possible to approximate this risk premium by
ÿu ÿ
ÿ0.5p · u (ÿ1) · ÿ 2
p · u (ÿ1) + (1 ÿ p) · u (ÿ2)
Problem 4 (20 points)
Consider two lotteries each having an exponential distribution. The cumulative distribution
function of an exponential distribution is:
F(x; ÿ) = 1 ÿ e
ÿÿx
ÿx ÿ +.
The expected gain given by this distribution is E[X] = 1/ÿ. Suppose that the first lottery, F1 has a
parameter ÿ1 and the second, F2 has a parameter ÿ2. Suppose ÿ1 < ÿ2. Which of these two
lotteries will a consumer with Von-Neumann Morgenstern preferences choose?
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Problem 5 (10 points)
Consider the following 5 games represented in normal form. For each of these games, ).
sÿ
find the Nash equilibria(s), (s ÿ
i1 , i2
a) Games A: (2 points)
Player 2
RIGHT
LEFT
1
80
High
73
50
85
reyalP
15
Down
20
50
77
b) Games B: (2 points)
Player 2
RIGHT
LEFT
1
80
High
97
30
88
reyalP
45
Down
72
46
33
c) Games C: (2 points)
Player 2
RIGHT
LEFT
1
68
High
90
22
90
reyalP
44
68
Down
94
31
PROBLEM 5 CONTINUES ON THE NEXT PAGE
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Problem 5 (continued)
d) Games D: (2 points)
Player 2
RIGHT
LEFT
47
High
4
40
54
reyalP
64
Down
6
21
89
e) Games E: (2 points)
Player 2
RIGHT
LEFT
97
High
82
81
72
reyalP
81
Down
94
34
45
END OF PARTIAL EXAM.
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