University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Problem Set 5: Due Thursday, October 10th1
Exercise 1
(a) Exercise 4 from PS4.
Exercise 2
Question marked as HW in lecture notes on uncertainty. Assume the following preferences on
lot
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Problem Set 2: Due Thursday, September 191
Exercise 1
Consider a world with only two commodities, such that the following preference relation holds
x
y
x1 + x2 > y1 + y2 or x1 + x2 = y
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Additional Problems
Exercise 1
Consider that the set of alternatives is the set of real numbers, that is, X = R. There is an individual
whose attitude is the more the better ; however,
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Problem Set 4: Due Thursday, October 3rd1
Exercise 1
Choi, Fisman, Gale and Kariv (2007). Consider the following experiment. Participants are told
that either state x or state y will o
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Problem Set 3: Due Thursday, September 261
Exercise 1
The budget of a given consumer is entirely spent on the following two goods, during the months of
September and October,
Table 1:
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Problem Set 1: Due Thursday, September 121
Exercise 1
Envelope Theorem without Constraints. A monopolist produces a good using the linear cost
function C (q ) = c q , with c > 0. Facin
BAMS 517
Decision Analysis II
1
Complex decision trees
2
1
Complex decisions
So far, the decisions we have
studied have been quite simple,
usually consisting of a single
decision and a single uncertain
event
Well now show how to solve
more complex decisio
Producer theory
Vitor Farinha Luz
Readings:
JR chapter 3
1
Basic Notions
We consider the problem of a firm that uses n inputs x = (x1 , . . . , xn ) in order to produce
output y 2 R+ . The production process is modeled via a production function f : Rn+ 7
Answer Key of PS1
Q1
For a, b, c parts to show A1: For any points x and y, either u(x) u(y) or u(y) u(x)
Therefore, either x < y or y < x.
For d part to show A1: For any points x and y, either x y 1 or y x + 1 x 1
Therefore, either x < y or y < x.
For a,
Problem 1:
We already solved the rst 3 parts of this problem in class. So we will focus
on the last part of the question which asks for nding the unique mixed strategy
equilibrium.
First note that the police ran
When woud the bad guy be ready to randomize
Review Session 4
LAM, Wing Tung
October 7, 2016
1
Ranking Of Monetary Lotteries
Let u(:) denote the Bernoulli utility over monetary amounts. u is increasing, concave and
twice continuously dierentiable, unless specied otherwise. A monetary lottery is deno
Review Session 3
LAM, Wing Tung
September 30, 2016
1
Expected Utilities Representation
If the preference ordering
resenting
satises (A1)-(A6) then there exists a utility function u rep-
such that for any lottery g
u(g) =
Xn
i=1
pi u(ai )
where p = (p1 a1
Review Session 2
LAM, Wing Tung
September 26, 2016
1
Slutsky Equation and Compensated Demand
Assume x o 0 throughout. The Slutsky equation is given by
@xi (p; y)
@xhi (p; V (p; y)
=
@pj
@pj
@xi (p; y)
xj (p; y):
@y
Apart from Hicksian demand, one can dene
Review Session 1
LAM, Wing Tung
September 26, 2016
1
Marginal Utility of Income
Suppose that (x; ) satises (FOC-C). How shall we interpret
? Assume x o 0 and
p o 0 throughout. From (FOC-C),
@u(x (p; y)
= pi ;
@xi
P
pi xi (p; y) = y:
i
Dierentiating the bu
ECON 500
Problem set 1
Question 1) Show whether the preferences represented by these utility functions satisfy
the axioms (A1-A4) discussed in class.
(a) u (x1 , x2 ) = x1 ,
(b) u (x1 , x2 ) = x1 (x2 3),
(c) u (x1 , x2 ) = (x1 2)2 + (x2 2)2 ,
(d) No utili
Econ 500
Fall, 2012
Li, Hao
UBC
Lecture 3. Producer Theory
1. Production function
Production possibility set. A rm produces outputs by using inputs according to a production
possibility set Y RL . If y Y , then the netput vector y is feasible. Negative co
University of British Columbia
Econ 500 L1A
Fall 2014
TA Evan Calford
Problem Set 1: Due Thursday, September 111
Exercise 1
Envelope Theorem without Constraints. A monopolist produces a good using the linear cost
function C (q) = c q, with c > 0. Facing a
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Solutions to Problem Set 1
Exercise 1
(a) The monopolist solves the following problem
max (c, p) = (p c) D (p)
The prot maximizing price p satises
D (p )
= D (p ) + (p c)
=0
p
p
p 1 +
Question 1.
The question was fairly straight forward.
Every individual maximizes ui (xi ) subject to a budget constraint. Write
down the Lagrangean, take rst order conditions, then re-use the budget constraint to get xk =
i
k
i
pk
k
k
pk i
.
k
k i
For goo
General Equilibrium as a Fixed Point
September 2, 2014
Preliminaries
the rst variant of the basic model we study restricts to
private values and complete information
all preferences are known - there are m rms and n
consumers and k physical goods
X = Rmnk
Arrow Debreu Equilibrium
October 31, 2015
0 = cfw_s1 , . . . sS - the set of (unknown) states of the
world assuming there are S unknown states.
information is complete but imperfect
n - number of consumers
K - number of physical commodities
m number of r
Chapter 1
The Lovely but Lonely Vickrey Auction
Lawrence M. Ausubel and Paul Milgrom
1. Introduction
William Vickreys (1961) inquiry into auctions and counterspeculation marked the
first serious attempt by an economist to analyze the details of market rul
Reading on Directed Search
Michael Peters
November 17, 2015
This reading will describe a model that is used extensively in macroeconomics to understand labor markets. The model is a part of a larger
literature on search and matching. Ill explain the model
1
Theory of Auctions
1.1
Independent Private Value Auctions
for the moment consider an environment in which there is a single
seller who wants to sell one indivisible unit of output to one of n
buyers whose valuations are private, a buyer whose valuation
Econ 500
Second Assignment
Problem 1: Do problem 7.19 in Jeheil and Reny
Problem 2: Consider the following game in which the payos are dollar
values (it comes from an experiment)
A
B
C
X
25,20
14,20
18,12
Y
14,12
25,12
18,22
Solve the game using iterated
Econ 500
Third Assignment - Auctions
1. Question 9.2 in the text Jeheil Reny. After that show that the equilibrium bidding strategy in an iid (independent and identically distributed) rst price auction has each bidder bidding what he expects
the second hi
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Solutions to Problem Set 5
Exercise 1
A risk neutral decision-maker evaluates gambles by their expected values.
The expected utility of the gamble is given by the following expression:
University of British Columbia
Econ 500 L1A
Fall 2014
TA Evan Calford
Solutions to Problem Set 4
Exercise 1
1. The rst preference relation over lotteries is not continuous. Assume a case with three possible
outcomes c1 , c2 and c3 such that v (c1 ) > v (c
University of British Columbia
Econ 500 L1A
Fall 2013
TA Maria D. Tito
Solutions to Problem Set 2
Exercise 1
(a) Convexity. First, observe that x y implies that x = y. Then, in order to prove convexity, we
need to analyse some cases
Case 1. x
y and z = y
University of British Columbia
Econ 500 L1A
Fall 2013
Evan Calford
Solutions to Problem Set 3
Exercise 1
(a) The consumption bundle in September, under September prices, costs
p0 x0 = 24
and if the consumer were to buy his October consumption bundle x1 un