Choice Under Uncertainty
Sam Hwang
January 22, 2016
1 / 137
Welcome to Econ 303-002
I
Instructor: Sam Hwang ([email protected], IONA 205)
I
TA: Anujit Chakraborty ([email protected])
I
Lecture: Tuesdays and Thursdays 12:30 to 14:00
I
Instructor offic
University of British Columbia
Vancouver School of Economics
ECON 465
Problem Set 1
Due February 11 in class or Feb 12 until 2:30pm in my office IONA 119
Groups up to 5 students
Justify your reasoning for full credit
ANSWERS MUST BE TYPED EXCEPT FOR GRAPH
Problem Set I
Intermediate Microeconomics 2
January 16th, 2016
Sam Hwang1
Submit your solution individually. The deadline is January 22nd, Friday. Throughout
this problem set, We are always going to assume that all decision makers Bernoulli utility
functi
Econ. 303: Intermediate Microeconomics
Midterm 2 Solution
QUESTION ONE
1-5: b b c d a
6-10: a b b a c
QUESTION TWO
a) Answer: Firm 2 is the follower. Given q1, it maximizes:
2= q2(40-q1-q2), and we get the best response function q2(q1)=0.5*(40-q1);
Firm 1
University of British Columbia
Vancouver School of Economics
Economics 303 (001)
April 2013
M. Vaney
Final Examination
NAME
Part Points Available
A
20
B.1
20
B.2
20
B.3
20
C
20
Total
100
Points Earned
Instructions
1. Check that your name and student numbe
Problem Set 2
Intermediate Microeconomics 2
January 29th, 2016
Sam Hwang1
Submit your solution individually. You can either type or handwrite. The deadline is
February 5th, Friday.
1
Denitions
Problem 1.1. Let cfw_$x1 , $x2 , . . . , $xn denote a set of
Econ 303 (001)
Winter Session, Term II, January 2016
M. Vaney
Problem Set 1 - Solutions
1. denitions
(a) s^i is a Best Response for player i if
^
i (si ; s i )
for all s0i
and for some s
i
0
i (si ; s i )
2 Si
2 S
i
(b) s#
i is a strictly dominant strateg
Econ 303 (001)
Winter Session, Term II, January 2016
M. Vaney
Problem Set 1
Due: January 21 at the start of lecture. At least one question will be graded.
1. Consider the basic normal form of a game. There are I players, i = 1; 2; : : : ; I: Each
player i
Economics 303 (001)
Winter Session, Term II, March 2016
M. Vaney
Problem Set 3 - Solutions
1. Bernouilli utility functions
(i) u0 (w) = 13 w
(ii) u0 (w) = w
(iii) u0 (w) =
1
;
w
(iv) u0 (w) = ae
1
3
; u00 (w) < 0 when
u00 (w) < 0 =) risk averse,
aw
(vi) u
Econ 303 (001)
Winter Session, Term II, 2016
M. Vaney
Problem Set 4
Due: Tuesday April 5, 2016 by the end of lecture.
1. Suppose the market portfolio, M; has E frM g = 23%; : M = 32%: The risk-free rate
is rf = 7%: The minimum variance portfolio (MVP) is
NAME:_
Econ 303 (001)
Winter Session, Term II, January 2013
M. Vaney
Quiz #1
STUDENT NUMBER:_
Answer all questions. Total marks: 20
1. Consider the following 2 player simultaneous game where both players have 4 strategies:
a
Player 1 b
c
d
w
(3; 2)
(4; 3)
Econ 406: Discussion Assignment 1
Jonathan L. Graves
This assignment is to help you practice relevant topics in probability and
start using the tools we have learned.
This assignment will be scored out of 4, as explained in the syllabus.
The assignment
University of British Columbia
Vancouver School of Economics
ECON 465
Problem Set 2
Due April 7
Groups up to 5 students
Justify your reasoning for full credit
ANSWERS MUST BE TYPED EXCEPT FOR GRAPHS
Chapter 9-#3, # 8
Chapter 10- #2, #4
Chapter 11 - # 2,#
NAME:_
Econ 303 (001)
Winter Session, Term II, February 2012
M. Vaney
STUDENT NUMBER:_
Quiz #1
Answer all questions. Total marks: 20
1. Consider the following 3 player game. Player 1 chooses the row of the game, Player 2
chooses the column and Player 3 ch
Econ 303 (001)
Winter Session Term II, 2016
M. Vaney
Note on Approximating the Certainty Equivalent
Taylors Formula
Given:
- random wealth, w with mean or expected value, E fwg = w and variance,
2
w
- an individual with preferences characterized as VNM ex
PROBABILITY MODELS FOR ECONOMIC DECISIONS by Roger Myerson
excerpts from Chapter 3: Utility Theory with Constant Risk Tolerance
3.1. Taking account of risk aversion: utility analysis with probabilities
In the decision analysis literature, a decision-maker
Economics 303 (001)
Winter Session, Term II, 2016
M. Vaney
Problem Set 3
This problem set is due Thursday March 17 at the start of lecture.
1. Consider the following Bernoulli utility functions:
(i) u(w) =
(ii) u(w) =
(iii) u(w) =
(iv) u(w) =
(v) u(w) =
1
Economics 303 (001)
Winter Session, Term II, 2016
M. Vaney
Extra Problems - A
Solutions
1. Bertrand with capacity constraints
(a) Under the usual Bertrand equilibrium p1 = p2 = c = 0; which will hold when
minfK1 ; K2 g 10. Both rms can singly satisfy mark
Simultaneous Games
Sam Hwang
February 2, 2016
1 / 303
Simultaneous games?
I
Simultaneous games are the ones in which players move only
once and at the same time, therefore do not observe other
players choices
I
Example 1: Matching Pennies
I
Example 2: Roc
Econ 303 (001)
Winter Session, Term II, January 2015
M. Vaney
Quiz #1 - Solutions
1.
( 1;
2;
C)
Player 1
Player 2
L
R
U (5; 8 ; 18)
(7; 4; 6)
D (8; 2; 24) (1; 6 ; 12)
No pure strategy Nash equilibrium. For the mixed strategy Nash equilibrium: let player 1
Choice Under Uncertainty
Sam Hwang
January 14, 2016
1 / 76
Welcome to Econ 303-002
I
Instructor: Sam Hwang ([email protected], IONA 205)
I
TA: Anujit Chakraborty ([email protected])
I
Lecture: Tuesdays and Thursdays 12:30 to 14:00
I
Instructor o ce h
Game Theory
Sam Hwang
January 27, 2016
1 / 91
Introduction to Game Theory
I
I
So far we have been only concerned with situations in which
individuals well-being depends only on the choices she makes
Now we want to study situations in which
1. Multiple ind
Chapter 3
Preferences
If this is coffee, please bring me some tea; but if this is tea, please
bring me some coffee. Abraham Lincoln
Consumer Preferences
Matter!
Jul. 2011
Its not just that the loyalty
program cards or key chain fobs
are a hassle. Savvy cu
Marginal & Average Cost
Functions
cv ( y)
AVC( y )
,
Since
y
AVC( y ) y MC( y ) 1 c v ( y )
.
2
y
y
Therefore,
AVC( y )
0 as y MC( y ) c v ( y ).
y
c ( y)
AVC( y )
0 as MC( y ) v
AVC( y ).
y
y
Chapter 21
Cost Curves
An economist is a person who,
Chapter 25
Monopoly Behavior
How Should a Monopoly
Price?
How firms can enhance and exploit their
market power?
So far a monopoly has been thought of as a
firm which has to sell its product at the
same price to every customer. This is
uniform pricing.
C
Chapter 23
Industry Supply
Supply From A Competitive
Industry
How are the supply decisions of the many
individual firms in a competitive industry to
be combined to discover the market supply
curve for the entire industry?
Since every firm in the industry
Chapter 24
Monopoly
I think that its wrong that only one company makes the game Monopoly
Steven Wright.
Antitrust
The Archer, Daniels, Midland (ADM) case
One of the largest price-fixing conspiracies seen in modern
times. The overcharges imposed on U.S.
Chapter 19
Profit-Maximization
Economic Profit
A firm uses inputs j = 1,m to make
products i = 1,n.
Output levels are y ,y .
1
n
Input levels are x1,xm.
Product prices are p1,pn.
Input prices are w1,wm.
The Competitive Firm
The competitive firm takes all
Econ 303-002
Intermediate Microeconomics 2
Instructor: Sam Hwang ([email protected])
TA: Anujit Chakraborty ([email protected])
Welcome to Econ 303-002. The objective of this course is to help you understand important
concepts in Microeconomics. In d