Problem Set 3
November 1, 2016
Due: 9 November 2016
1. Imagine a second grade class with 20 students in which each student has a
best friend. For any pair of students x and y, if x is y's best friend, then y
is x's best friend. Suppose that the teacher re
1. (49.2) Consider a voter i who prefers A to B. Fix a profile of votes a i for the other
voters. The provisional outcome given a i is what would happen if i did not participate
in the election and all other voters voted as in a i . There are two votes wh
1. In what follows let (x) be xs best friend.
(a) A strategy for player i specifies:
i. which student x would make an offer to if the teacher selects y.
ii. for each student x 6= y, whether x would accept ys offer if y made x an offer.
(b) Theorem 1 A str
Strategic Games
D EFINITION
A strategic game (with ordinal preferences) consists of:
a set of players
for each player, a set of actions
for each player, preferences over the set of action proles.
What Is an Action Prole?
We may assume that the set of play
1. .
(a) cfw_A, B
(b) cfw_(A, A), (A, B), (B, A), (B, B)
(c) (A, B) 1 (B, B) 1 (B, A) 1 (A, A).
(d) (A, A) and (B, B)
(e) It would be reasonable to say: I would pick A, because (A, A) is a Nash equilibrium, and
also the strategy profile which gives both p
Entry Game
An incumbent faces the possibility faces the possibility of
entry by a challenger.
The challenger may be a firm considering entry into an
industry currently occupied by a monopolist.
The challenger may be a politician competing for the
leadersh
Problem Set 1
September 26, 2015
Due date: 10/5/2015
Rules of the Game: students may form a group of at most 3 students. Each
group should hand in a single assignment, and must put the names of all people
in the group on the assignment. If there is disagr
Nash Equilibrium and Best Responses
D EFINITION
The action profile a is a Nash equilibrium if, for every player i,
ui (a ) > ui (ai , ai
) for every action ai of player i.
Bi (ai ) = cfw_ai Ai : ui (ai , ai ) > ui (ai0 , ai ), for all ai0 Ai
T HEOREM
The
Guess 2/3 of the Average
Each student submits a real number between 0 and 100.
All students whose numbers are closest to 2/3 of the average
evenly split $1. All other students get $0.
Assume that there are at least 2 students.
Guess 2/3 of the Average
T H
Problem Set 3
November 5, 2015
Due: 16 November 2015
Rules of the Game: students may form a group of at most 3 students. Each
group should hand in a single assignment, and must put the names of all people
in the group on the assignment. If there is disagr
ECON 4109H
LECTURE 9
M IXED S TRATEGY E QUILIBRIUM
October 16, 2014
Matching Pennies
H
T
H
1, -1
-1, 1
T
-1, 1
1, -1
players match ) player 2 prefers to switch choice.
players dont match ) player 1 prefers to switch choice.
So there is no Nash equilibrium
Coalitional Games
A Coalitional game is a model of interacting decision-makers
that focuses on behavior of groups of players.
For every group of players, there is a set of actions
. not only for individuals.
A group of players is a coalition.
The group of
Incomplete Information
Until now, we have assumed that all aspects of the game are
common knowledge.
In many situations, there is uncertainty about certain aspects
of the game or other players preferences.
In an auction, a bidder may be uncertain about th
Auctions: Ascending Auctions
Common Auction Form: People sequentially submit higher
bids for an object.
When no one wishes to submit a bid higher than the current
bid, the person making the current bid wins the object at the
price she bid.
Imagine each pe
University of Minnesota
Economics 3101: Intermediate Microeconomics
Spring 2016
8:15-9:30 am Tuesday and Thursday, Anderson Hall 210
Instructor: Joaquin Garcia-Cabo Herrero
Email: garci584@umn.edu
Office: Hanson Hall 3-101 (Office Phone: 612.625.8310)
Off
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
gt = y t y t y t
(yt )
I
yt
yt
= ytyt
(yt ) ' gt
yt
I
I
I
I
I
I
I
Y
N
f :R!R
x
f (x) ' f (x ) + f 0 (x )(x
f (x) = ( + x)
x )
x =
f (x ) = ( + ) = ( ) =
f 0 (x) =
) f 0 (x ) =
=
+x
+
) f (x) ' + (x
)=x
x = gt
gt
( + gt
Business Cycle Measurement
Econ 3102
Ignacio Campomanes
University of Minnesota
Fall 2015
Ignacio Campomanes (UofM)
Business Cycle Measurement
Fall 2015
1 / 20
Chapter 3 - Topics
Regularities in GDP Fluctuations
Comovement
Behavior of Key Macroeconomic Va
ECON 3102: Problem Set
4
Due by Dec 10, 2015 on class
Instructor: Canhui Hong
Dec 1, 2015
1
Firm's Problem (60pts)
Consider a rm whose objective is to maximize its two period present-value prots
+
1+r
Suppose the rm produces output Y and Y using a technol
ECON 3102: Problem Set 3
Due by Nov 19, 2015 on class
Instructor: Canhui Hong
Nov 4, 2015
1 A Two-Periods Consumer's Problem (40pts)
Consider a two-periods (current and future period) model such that the consumer's preference is
U (c, c ) = u (c) + u (c )
Problem 1:
a. Set up the equation as below:
Max (Nd) = F(k,Nd) Nd and Nd 0
Nd
b.
=
=
= 0 , so
As F(k,Nd) = K0.5Nd0.5, so
= 0.5
=
, and
, so Nd =
/
c. Nd would decrease since represents the cost of hiring.
d.
Max (Nd) = F(k,Nd) (1+t)Nd and Nd 0
Nd
e.
=
so
ECON 3102: Problem Set 1
Due by Oct 1, 2015 on class
Instructor: Canhui Hong
Sep 22, 2015
1
Utility functions (60 pts)
Consider the following utility functions which are widespreadly used in macroeconomic models
(a) :
u (c, l)
= log c + (1 ) log l
(b) :
u
ECON 3102: Intermediate Macroeconomics
Lecture 12: Midterm Review
Canhui Hong
Oct 15, 2015
1/11
Topics
Midterm Reviews
2/11
Closed-Economy One-Period Macro Model
Consumer problem
max U (C, l)
C,l
s.t. C = w (h l) + T
Optimization
M RSl,C =
Ul
=w
UC
Income
ECON 3102: Intermediate Macroeconomics
Lecture 11: Income Disparity Among Countries and Endogenous
Growth
Canhui Hong
Oct 13, 2015
1/16
Topics
Convergence
Is there a tendency for poor countries to catch up with rich countries
with respect to standards of
ECON 3102: Intermediate Macroeconomics
Lecture 9: Economic Growth: Solow and Malthus (III)
Canhui Hong
Oct 6, 2015
1/12
Topics
Solow growth model
2/12
An Increase in the Savings Rate s
Pure level eects
In the steady state, this increases capital per worke
ECON 3102: Intermediate Macroeconomics
Lecture 10: Economic Growth: Solow and Malthus (IV)
Canhui Hong
Oct 8, 2015
1/13
Topics
Summary on the growth models
Growth accounting
2/13
Two Models on Economic Growth
Malthusian Model
Production function:
Y = zF (
ECON 3102: Intermediate Macroeconomics
Lecture 7: Economic Growth: Solow and Malthus (I)
Canhui Hong
Sep 29, 2015
1/18
Topics
Economic growth facts
Malthusian model of economic growth
2/18
U.S. Per Capita Real Income Growth
Except for the Great Depression
ECON 3102: Intermediate Macroeconomics
Lecture 8: Economic Growth: Solow and Malthus (II)
Canhui Hong
Oct 1, 2015
1/13
Topics
Solow growth model
2/13
Historical Facts of Economic Growth
Historical facts
Robert E. Lucas The Industrial
Revolution: Past and
ECON 3102: Intermediate Macroeconomics
Lecture 6: A Closed Economy One-Period Macroeconoic Model (III)
Canhui Hong
Sep 24, 2015
1/17
Topics
Experiments: Increases in government spending and total factor
productivity
Consider a distorting tax on wage incom
ECON 3102: Intermediate Macroeconomics
Lecture 5: A Closed Economy One-Period Macroeconoic Model (II)
Canhui Hong
Sep 22, 2015
1/22
Topics
Economic eciency and Pareto optimality
Experiments: Increases in government spending and total factor
productivity
2
ECON 3102: Intermediate Macroeconomics
Lecture 3: Consumer and Firm Bahavior
Canhui Hong
Sep 15, 2015
1/26
Topic
Behavior of the representative consumer
Static v.s. Dynamic
Intratemporal v.s. Intertemporal
Tradeo between consumption and leisure
Behavior o