Economics 3102 Midterm 2 Solutions
Gregory Veramendi
December 2, 2008
1
Short Questions
1. False. U is a strictly dominant strategy for player 1. Given that player 1 chooses U,
Table 1: Counter example to 1
L
R
U (3,2) (4,2)
D (1,5) (2,6)
player 2 is ind
Practice Problems for the Final Exam
Jerey Mensch
3/17/2013
Please note that these problems are not meant to be representative of what will be on the exam;
rather, they are meant to help students practice the concepts taught in the course. The problems on
Introduction and Pareto Efficiency
Scott Ogawa

Overview
Most of what we learn in this class will help us answer one of the following questions:
1. What should society prefer? (Normative)
2. How do people behave? (Positive)
3. What happens when people in
Problem Set 5  Solutions
Economics 3102
1
Sequential Game
Suppose player 1 must choose between A, B, and C. If player 1 chooses A, then both players 1 and 2 get (2,3)
ie player 1 gets 2 and player 2 gets 3. If player 1 plays B, then player 2 choose
Problem Set 1  Solution
Economics 3102
Pareto Eciency for Dan, Jorge, and Matteo (Problems 1, 2,
and 3)
Dan, Jorge, and Matteo share an oce. They face all sorts of social choice problems, such as how to
place a fridge, what poster to put on the door, an
Problem Set 4  Solution
Economics 3102
1
Hawks and Doves
Two types of birds compete for territory. Their
evolutionary tness
is determined by how much territory they oc
cupy, at least on average (or in expectation). Suppose there are genes that code som
Problem Set 9 Answer
1
Production Economy
Consider a singleconsumer, single rm economy in which the consumer has utility over leisure (l) and consumption
(c)
u(l, c) = c l
A protmaximizing rm uses the following technology to convert labor (L) into a con
Economics 3102
Spring 2016
Professor Jeff Ely
Problem Set 5
Due May 13
1. We have shown that the Vickrey auction satisfies the following three criteria:
(utilitarian) Allocate the good to the bidder with the highest value.
(incentive compatible) Ensure
Economics 3102
Spring 2016
Professor Je Ely
Problem Set 3
Due April 29
1. Miley Cyrus will give an exclusive concert in a theater that has 15 seats. Coincidentally there are 15 people in town potentially interested in attending. 5 of them are
true fans a
Microeconomics 3102: Midterm review session
May 1, 2016
May 2, 2016
May 3, 2016
1. There are three individuals, A, B, C, and three alternatives, x, y, z. Consider the following
SWF: A and B will attempt to choose the top alternative. If they agree, that
Problem Set 6  Solutions
Economics 3102
1
Three Situations for Flatmates
Anne, Bob, and Charlie are atmates that have several decisions to make.
They hire an arbitrator who will
implement the VCG mechanism. In each situation, determine the nal allocatio
Problem Set 2  Solution
Economics 3102
1 SWF Criteria
For each of the following social welfare functions, consider the four criteria that Arrow showed can
never be simultaneously satised:
Universal domain (UD), Pareto criterion (PC), independence of
irr
Choice Under Uncertainty

[For more on this topic please see the textbook.
Specically, 15.1, 15.2, and the rst part of 15.3 discusses
everything that we will cover today. The remainder of Chapter 15, however, has some other nice applications, as
well as
Game Theory (SimultaneousMove)

[There is one full chapter on Game Theory Chapter 14 of Besanko and Braeutigam. This chapter will be useful
if you want additional practice. In particular, if you need additional practice with mixedstrategy equilibria th
Utilitarianism

For the moment let us try to relearn what you were told to unlearn in the past: That the numerical values of
utility functions have meaning and thus we can compare dierent people's utilities. If we allow ourselves to make
such comparisons
The Edgeworth Box and Pareto Eciency

[Section 16.4 of Besanko/Braeutigam provides the technical coverage the topics discussed in this set of notes
and the next. The rest of chapter 16 provides nice context but are not essential. Our focus in this class
Social Choice and Arrows Impossibility Theorem

Previously we came up with an extremely weak criterion (Pareto efficiency) for judging alternatives. In some
sense, Pareto efficiency can be used as a crude method of aggregating preferences: Whatever socie
VCG Mechanism
Scott Ogawa

Problems with secondprice auction
We have seen that the secondprice sealedbid auction (also called a Vickrey auction) is really great:
Each player truthfully reveals his or her valuation as a (weakly) dominant strategy.
This
Game Theory (SequentialMove)

[Section 14.3 in Basenko/Breautigam.]
Denition.
A prole of strategies is a
subgame perfect (Nash) equilibrium (SPE) if the strategies of all players
form a Nash equilibrium not only in the game as a whole, but also in every
Game Theory: 2ndPrice Auction

[Section 15.5 of the textbook has a nice discussion of auctions that complements these notes quite nicely. It
discusses several auction formats, including the secondprice auction, which will be the focus in this class.]
A
VCG Mechanism: How to get people to tell the truth
Scott Ogawa
Northwestern University

Scott Ogawa (Northwestern University)
VCG Mechanism

1 / 12
Review: SecondPrice Auctions
Each player submits bid. Highest bidder gets the good and pays the
SECOND h
Economics 3102
Spring 2016
Professor Jeff Ely
Problem Set 7
Due Tuesday, May 31
1. Lets reconsider the public goods problem and now suppose that the cost of producing
the public good is no longer known. The two individuals 1 and 2 have values for the
pub
Problem Set 4: Solutions
May 3, 2016
1
Problem 1
If your value v > r, then yes, bidding below the reserve price r is a dominated strategy
in a first price auction. Consider the alternative of bidding bi (ri , vi ). Bidding below
the reserve price guarante
Lecture 10 General Equilibrium
Ron Siegel
Northwestern University
Winter 2013
Now that we understand the basics of the twoperson exchange economy, we are ready
to introduce prices and investigate consumers optimal choices given prices. We will then
ask u
Lecture 8 Game Theory: ExtensiveForm Games
Ron Siegel
Northwestern University
Winter 2013
1
Introduction
One shortcoming of normalform games is that they do not capture dynamic or sequential
aspects of interactions well. In some situations it may be tha
Lecture 7 Game Theory: NormalForm Games Mixed Strategies
Ron Siegel
Northwestern University
Winter 2013
1
Introduction
A mixed strategy for player i is a probability distribution over the players (pure) strategies.
It assigns to each pure strategy of pla
Lecture 6 Game Theory: NormalForm Games
Ron Siegel
Northwestern University
Winter 2013
1
Introduction
In this lecture we begin the study of game theory, a rich set of mathematical tools developed over the past decades, which has transformed economics. Ga
Lecture 5 Choice under Uncertainty: Applications
Ron Siegel
Northwestern University
Winter 2013
In this lecture, we use the expected utility framework introduced in the previous lecture
to analyze (1) individuals insurance purchasing decisions, and (2) th
Lecture 4 Choice under Uncertainty: Expected
Utility
Ron Siegel
Northwestern University
Winter 2013
1
Introduction
In this lecture, we expand the framework of individual choice introduced in 3101 to include
uncertainty. Recall that in 3101 the set of al
Lecture 3 Social Choice
Ron Siegel
Northwestern University
Winter 2013
To understand the diculties presented by choices that involve more than one economic
agent, we will consider the notion of Social Choice, i.e., how individual preferences are
aggregate