Final Exam
Economics 501b
Microeconomic Theory
Dirk Bergemann
May 2006
Suggested Solutions
for
Final Exam Microeconomic Theory 501b
2005/06
1. Consider the following model of Cournot competition with dierentiated products and I
rms. The price for the prod
ECON501b, Spring 2010
Problem Set 10 Solution
Yijia Lu
Apr 5-7, 2010
Question 10.1 Local and Global Constraints with Spence Mirrlees
Preferences
10.1(a) [Salani 2.1] and (b)
(Comments: we covered something similar in section 09 with a slightly dierent app
ECON501b, Spring 2010
Problem Set 11 Solution
Yijia Lu
Apr 13-15, 2010
Question 11.1 Optimal Taxation [Salani 3.1]
Note: the question actually refers to an old model in the rst edition of the text. When Salanie updated his
book to the second edition in 20
Dirk Bergemann
Department of Economics
Yale University
Microeconomic Theory (501b)
Problem Set 12. Moral Hazard
4/24/08
This problem set is not due on Thursday, 5/1/08, or at any other time for
that matter. Enjoy your summer!
1. Consider the regular moral
Econ 501b Lecture Notes
Dirk Bergemann
Yale University
Spring 2008
1
Games of Incomplete Information
The second section of the course deals with games of incomplete information. The focus will be on situations where the information is
asymmetric so that o
Dirk Bergemann
Department of Economics
Yale University
Microeconomic Theory (501b)
Problem Set 11. Adverse Selection and Mechanism Design
4/17/08
This problem set is due on Thursday, 4/24/08.
1. Consider the following problem with I agents and a social pl
Dirk Bergemann
Department of Economics
Yale University
Microeconomic Theory (501b)
Problem Set 10. Signalling and Insurance Markets
4/10/08
This problem set is due on Thursday, 4/17/08.
1. Informed Principal. Consider the problem we discussed at the end o
Dirk Bergemann
Department of Economics
Yale University
Microeconomic Theory (501b)
Problem Set 7. Bayesian Games
3/6/08
This problem set is due on Thursday, 3/27/08.
1. A Simple Bayesian Game. Consider the following Bayesian game.
Nature determines whethe
Dirk Bergemann
Department of Economics
Yale University
Microeconomic Theory (501b)
Problem Set 8. Bayesian Games
3/27/08
This problem set is due on Thursday, 4/3/08.
1. First Price Auction with Private Values. Consider a rst-price
sealed-bid auction of an
Dirk Bergemann
Department of Economics
Yale University
Microeconomic Theory (501b)
Problem Set 9. Bilateral Trade and Signalling
4/3/08
This problem set is due on Thursday, 4/10/08.
1. Bilateral Trading. Consider the following trading game between a buyer
Economics 501, Microeconmics, Spring 2009
Homework 7, March 5, 2009,
Due March 26, 2009
Jorge Balat & Eduardo Souza Rodrigues
7.1 (Akerlof s Lemon in a General Equilibrium Model) Suppose there is a continuum of
buyers with a characteristic [0, 1] distribu
Economics 501, Microeconmics, Spring 2009
Homework 9, April 2, 2009,
Due April 9, 2009
Jorge Balat & Eduardo Souza Rodrigues
9.1 Semi-Separating Equilibria In the job market signalling model in classed, we only discussed pure strategy equilibria. Now cons
ECON501b, Spring 2010
Problem Set 9 Solution
Yijia Lu
Mar 29-Apr 3, 2010
Question 9.1 [Gibbons 4.3 and 4.5]
9.1 [Gibbons 4.3]
(a)
In a pooling equilibrium there is no updating of beliefs on the equilibrium path. Therefore, if the receiver
observes R she w
ECON501b, Spring 2010
Problem Set 8 Solution
Yijia Lu
Mar 22-25, 2010
1
Question 8.1: First Price Auction w/ Private Values
8.1(a)
First, notice that given bj (tj ), bidding bi gives player i of type ti an expected payo of
1
bi ) Pr(bi > bj (tj ) + (ti +
Microeconomic Theory (501b)
Suggested Solutions
Problem Set 12
05/01/08
1. (Moral Hazard and Renegotiation) Consider the regular moral hazard model with a risk-neutral
principal and a risk averse agent. The agent can choose between two eort levels, ai 2 f
Final Exam
Economics 501b
Microeconomic Theory
Dirk Bergemann
May 2006
This is a closed-book exam. The exam lasts for 180 minutes. Please write clearly and legibly.
Be especially careful in the denition of the game, the payo function and the equilibrium
n
Dirk Bergemann and George Mailath
Department of Economics
Yale University
Final Exam Solutions
Economics 501b
Microeconomic Theory
May 2007
1. (30 minutes) Suppose the government (through its agency, the Internal Revenue Service IRS) wants to ensure compl
Dirk Bergemann and George Mailath
Department of Economics
Yale University
Final Exam
Economics 501b
Microeconomic Theory
May 2007
This is a closed-book exam. The exam lasts for 180 minutes. Please
write clearly and legibly. Be especially careful in the de
Dirk Bergemann and Larry Samuelson
Department of Economics
Yale University
Final Exam
Economics 501b
Microeconomic Theory
May 2008
This is a closed-book exam. The exam lasts for 180 minutes. Please
write clearly and legibly. Be especially careful in the d
Dirk Bergemann and Larry Samuelson
Department of Economics
Yale University
Final Exam
Economics 501b
Microeconomic Theory
May 2008
This is a closed-book exam. The exam lasts for 180 minutes. Please write clearly
and legibly. Be especially careful in the d
Econ 501b Lecture Notes
Dirk Bergemann
Yale University
Spring 2008
1
Games of Incomplete Information
The second section of the course deals with games of incomplete information. The focus will be on situations where the information is
asymmetric so that o
Econ 501b. Problem Set 7: Suggested Solutions.
March 27, 2008
1
A Simple Bayesian Game
(a) Draw the extensive-form tree of the above game.
hmmm. not too easy to do in latex. You could think of drawing two trees, in either
case the information sets should
Economics 501, Microeconmics, Spring 2008
Homework 8
Due April 3, 2008
8.1 First Price Auction
(a) Given the result in class where the valuation is ti , a reasonable
guess is that bi (ti ) = 1 + 1 ti : We now show that this is in fact an
2
2
equilibrium.
Microeconomic Theory 501b
Problem Set 9: Suggested Solutions
April 11, 2008
1
Bilateral Trading
(a) Trade is ex post ecient if v c. The surplus is given by the expression
E [v c|v > c]
which can be calculated from
1
v
E [v c|v > c] =
(v c)dcdv
0
0
1
=
0
=
Economics 501, Microeconmics, Spring 2008
Homework 10
Due April 17, 2008
10.1 Informed Principal
We found in class that there are pooling and separating equilibria of
the game when the rm oers contracts to the worker after observing
education. We look to
Economics 501b: Problem Set 11
Suggested Solution
April 28, 2008
1
Social Welfare Functions
(a) The egalitarian Social Welfare function is
I
max
cfw_xi I=0
i
ui (xi )
i=0
(b) The Utilitarian Social Welfare function is
I
max
cfw_xi I=0
i
i ui (xi )
i=0
for
Economics 501, Microeconmics, Spring 2009
Suggested Solutions to Problem Set 8: Bayesian Games and Auctions
Jorge Balat & Eduardo Souza Rodrigues
1. First Price Auction. Consider the rst price auction in a symmetric
environment with binary valuations, i.e