Choice Under Uncertainty
Sam Hwang
January 22, 2016
1 / 137
Welcome to Econ 303-002
I
Instructor: Sam Hwang (hwangii@mail.ubc.ca, IONA 205)
I
TA: Anujit Chakraborty (anujit2006@gmail.com)
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
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
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
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
Econ. 303: Intermediate microeconomics II
Professor Wei Li
2014-2015, Term 2
Problem set 4
OBJECTIVES:
1. Adverse selection, signaling and screening
2. Moral hazard and incentive contracts
DIRECTIONS:
1. Problem set 4 is posted on March 27 and due back on
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 (hwangii@mail.ubc.ca)
TA: Anujit Chakraborty (anujit2006@gmail.com)
Welcome to Econ 303-002. The objective of this course is to help you understand important
concepts in Microeconomics. In d
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
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
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
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
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
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,
QUESTION TRHEE
a. Answer: if the type is known, the bank offers an different interest rate for each type. The bank
earns zero profit because the financial market is perfectly competitive. To break even, the
expected repayment must equal to her investment.
Econ 303 (001)
Winter Session, Term II, January 2015
M. Vaney
Quiz #1
NAME:_
STUDENT NUMBER:_
Answer all questions. Total marks: 20
1. Find a Nash equilibrium to the following game between players 1 and 2: (ignore the third payo
( 1; 2; C )
Player 2
L
R
f
NAME:_
Econ 303 (001)
Winter Session, Term II, February 2012
M. Vaney
Quiz #1
STUDENT NUMBER:_
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
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
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 303 (001)
Winter Session, Term II, January 2013
M. Vaney
Quiz #1 - Solutions
1. Consider the following 2 player simultaneous game where both players have 4 strategies:
a
Player 1 b
c
d
Player 2
x
y
z
(1; 1)
(4; 3) (3; 5)
(3; 0)
(2; 4) (4; 2)
(0; 1)
(
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
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
Choice Under Uncertainty
Sam Hwang
January 14, 2016
1 / 76
Welcome to Econ 303-002
I
Instructor: Sam Hwang (hwangii@mail.ubc.ca, IONA 205)
I
TA: Anujit Chakraborty (anujit2006@gmail.com)
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
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
Mathematics 220 Workshop 1 - Set Theory
Note: Your goal is to practice working with notation and definitions. Some problems will
require knowledge of definitions - as you encounter a definition that you have to look up, then
do so and immediately learn it
The symbols and .
I received several questions whether the symbols and mean the
same thing. The answer is, NO please read this handout carefully
and do not confuse them!
The symbol is used to express that something is an element of a
set: a A means that a
Notes on indexed collections of sets, and quantifiers.
Please read Section 1.4 about Indexed Collections of Sets. In this
handout (as in lecture), we give a precise definition for the union and
intersection of an indexed collection of sets.
Suppose we hav
Mathematics 220 Workshop 2 - Logic
Note: to be able to solve logic problems easier, you should know by heart all definitions what is
a converse? what is a contrapositive? conjunction? tautology? You may wish to write for yourself
a dictionary of logic ter
Mathematics 220
A note about such that and review problems
A note about the use of such that and other issues with quantifiers.
This note is about correct use of the expression such that (and more generally, about
understanding statements that involve qua