Jorgen Harris
October 9, 2014
Econ 6090
First Practice Exam Solutions
Part I (30 points):
1. We can calculate Walrasian demand from indirect utility using Roys identity:
(
)
(
)
(
)
(
)
2. No, is not a rational preference relation, because it is not compl
Economics 6090
Professor David Easley
Fall 2015
Cornell University
Problem Set 5
Due Friday, Nov 20 in TA Section
1. Suppose an individual's Bernoulli utility function, u(m), is twice continuously differentiable on
with u'(m) > 0 for all m > 0. The indiv
ECON 6090: Section II
TA: Nahim Bin Zahur
September 11, 2015
1. Optimization
Mary goes to the grocery store to buy tomatoes (x) and pineapples (y). She needs to buy at least
20 tomatoes. Their prices are $3 per pound and $1 per pound respectively. Marys g
ECON 6090: Section XII
TA: Nahim Bin Zahur
December 02, 2015
1. SEU and Ambuguity Aversion (Final 2013)
At date t an individual has to decide how to allocate wealth w across assets that payoff in the
next period, date t + 1. There are S possible states of
ECON 6090: Section XII
TA: Nahim Bin Zahur
December 02, 2015
1. Nash Equilibria (Final 2013)
Players A and B will play a normal form game. As strategy set is cfw_U, M, D and Bs strategy set
is cfw_W, X, Y, Z. In the payoff matrix below the rows correspond
Professor Easley
October 26, 2015
ECON 6090
Practice Second Exam
Part I (30 points) Provide a brief answer for each of the following questions.
1. A firm produces output y 0 from inputs x1 0 and x2 0 using
the production function y = mincfw_ax1 , bx2 for
Professor Easley
September 23, 2015
Econ 6090
First Practice Exam
Part I (30 points) Provide a brief answer for each of the following questions.
1. A consumer has indirect utility function V (p1 , p2 , w) = wp1 p2 where
p1 and p2 are prices of the two goo
Problem Set 2 Solutions
ECON 6090
September 25, 2015
Question 1
Proposition 1.D.2 in the textbook (MWG) says that we need choices from all subsets upto three
elements in order to have a rational preference relation representing the choices. This result do
ECON 6090: Section V
TA: Nahim Bin Zahur
October 02, 2015
1. Effect of price changes (Aug 2009 Qualifying Exams, Part I)
An individual has preferences over consumption goods in <l+ represented by the utility function
u : <l+ <1 . This utility function is
Problem Set 5 Solutions
ECON 6090
December 05, 2015
Question 1
a. The expected utility associated with the bet is V (t) = pu(W +t)+(1p)u(W t). The marginal
expected utility with respect to changes in t is thus given by:
V 0 (t) = pu0 (W + t) (1 p)u(W t)
N
ECON 6090: Section VI
TA: Nahim Bin Zahur
October 09, 2015
NOTE: Since we did not have time to complete Part 2 in Section last week, I have included solutions for those questions.
1. EV and CV (Adapted from Aug 2011 Qualifying Exams, Part I)
Consider an a
Professor Easley
November 4, 2015
Econ 6090
Second Exam
Part I (40 points) Provide a brief answer for each of the following questions.
1. The price at which a firm sells its output varies from year to year. The
average of these prices is known to be p . E
Professor Easley
October 30, 2015
Econ 6090
Practice Second Exam with Brief Answers
Part I (30 points) Provide a brief answer for each of the following questions.
1. A firm produces output y 0 from inputs x1 0 and x2 0 using
the production function y = mi
Economics 6090
Professor David Easley
Fall 2015
Cornell University
Problem Set #3
Due September 25 in TA section
1.
A consumer has preferences on
2
represented by the utility function u(x,y) = x y where
0 1. The consumers budget set is cfw_( x, y )
2
: p
ECON 6090: Section III
TA: Nahim Bin Zahur
September 18, 2015
NOTE: As we did not fully finish Question 3, I have included solutions for them.
1. Local and global optima
Recall Result 2 from class:
Result 2: Suppose that
(i) can be represented by a C 2 ut
ECON 6090: Section VII
TA: Nahim Bin Zahur
October 16, 2015
NOTE: I have included solutions for the final part of Question 2 and Question 3. We will also
revisit the Cobb-Douglas problem during this Fridays section.
1. Cost minimization
a. You have estima
Professor Easley
December, 2015
Econ 6090
Practice Final Exam
Part I (40 points) Provide a brief answer for each of the following questions.
1. A consumers preferences over consumption in <n+ can be represented
by a utility function which is homogeneous o
ECON 6090 Fall 2015
Professor David Easley
Problem Set #3
Yuting Ji
[email protected]
Problem 1. The consumers problem (utility maximization problem) is given by
max u(x, y) = x + y
x,y
s.t. px + y = w.
Let be the Lagrangian multiplier associated with the
Problem Set Three, ECON 6090
Due: October 23rd, 2012
1. Some propositions on returns to scale
(a) Prove constant returns to scale implies decreasing and increasing returns to scale definitions hold.
(b) Prove fixed costs imply Y is not decreasing returns
Professor Easley
December, 2015
Econ 6090
Practice Final Exam
with Answers
Part I (40 points) Provide a brief answer for each of the following questions.
1. A consumers preferences over consumption in <n+ can be represented
by a utility function which is
ECON 6090: Section XI
TA: Nahim Bin Zahur
November 13, 2015
1. Horserace (Final 2013)
An individual who begins with wealth w > 1 can choose whether or not to bet at a horserace
and what bet to make if he chooses to bet. Two horses A and B will run a race
Problem Set 1 Solutions
ECON 6090
September 11, 2015
Question 1
a. Consider any x, y, z X such that x y and y z.
By the definition of ,
x y x y and y x
y z y z and z y
Then by transitivity, x y and y z imply that x z. Similarly, y x and z y imply that
z x
First Exam Solutions
ECON 6090
October 13, 2015
Part I
Question 1 (10 points)
We have the following utility maximization problem:
max ln(x) + (1 ) ln(y)
s.t. px x + py y = w
The utility function is strongly monotone, so Walras Law holds and the budget con
Department of Economics - Fall 2013 Course Schedule
R OO M S
COU RSE
INSTRUCTOR
TITLE
D AY AN D TIM E
KND 116 AUD
111 0-1
BURKHAUSER
INTRODUCTO RY MICROECONO MICS
MW 9:05 - 9:55
URH G 01
111 0-2
WISSINK
INTRODUCTO RY MICROECONO MICS
TR 10:10 - 11:00
URH G
ECON 6090: Section IX
TA: Nahim Bin Zahur
October 30, 2015
1. Comparative Statics (Continued from Last Week)
A profit maximizing firm uses 2 inputs, x <2+ , to produce one output, y <1+ , using the production
function f (x). The production function is str
Problem Set 6 Solutions
ECON 6090
December 05, 2015
Question 1
Note that actuarially fair insurance means that the price of one unit of insurance is equal to the
expected cost of insurance.
If Max buys the insurance, then he surely gets the expected value
Economics 6090
Fall 2015
Professor David Easley
Cornell University
IMPLICIT FUNCTIONS
Suppose that F: n+m 6 n has continuous partial derivatives and is specified by component
functions
Let
such that
Then there exists a neighborhood N of
Suppose the follow
ECON 6090: Section X
TA: Nahim Bin Zahur
November 06, 2015
NOTE: Solutions for Part I are included.
1. Investment Uncertainty (June 2010 Q)
Consider an investor with initial wealth w > 0 who must invest his wealth in a portfolio consisting
of two assets:
ECON 6090 - Midterm Two 75 Minutes. THREE PAGES TO EXAM Comments before you start: If you believe a question is unclear, please state how you interpret the question. In proofs use formal mathematical language. You must show all work for partial credit to
ECON 6090 - Midterm Two 75 Minutes. TWO SIDES TO EXAM SHEET If you believe a question is unclear, please state how you interpret the question and we will take this into account during grading. In proofs, please use formal mathematical language wherever po
ECON 6090, PS 3 Solution
1
a Easy to check by denition
b Fixed cost implies that there is some (F; 0) 2 Y such that
( F; ") 2
= Y for any " > 0. As soon as ( F 0 ; ") 2 Y
for some F 0 > F and some " > 0 we have that DRS is
violated.
c Draw the graph for t
ECON 6090: Section I
TA: Nahim Bin Zahur
September 4, 2015
NOTE: As we did not have time to finish Questions 3 and 4 last week, I have included solutions
for them. Let me know if you have any questions.
1. Rational preference relations
Are the following p
Problem Set 3 Solutions
ECON 6090
September 28, 2015
Question 1
The utility function is strongly monotone, so Walras Law holds and the budget constraint holds
= x1 , which goes to + as x tends to zero. So in any
with strict equality. Notice that u
x
optim
Economics 6090
Fall 2015
Professor David Easley
Cornell University
Problem Set 6
Due Friday, December 4 in TA Section
1. Evaluate the following argument: Max, who is a risk averse expected utility maximizer,
is offered an opportunity to buy fair insurance
Problem Set 4 Solutions
ECON 6090
October 28, 2015
Question 1
The Walrasian demand function has inherent restrictions placed on it due to the utility maximization assumption, namely, that the Slutsky matrix S(px , py , w) must be negative semi definite. W