1
Answers for Problems
1.D.2: Need to show that for any B X there is at least one alternative x B
such that x
y for all y B . Choose any x1 B . By completeness, x1 can
be compared with every y B . If x1
y for all y B , we are nished. So
suppose this is no
1
Choi e Theory with Un ertainty
Last Revised:
2008-09-20 14:42:04 -0700 (Sat, 20 Sep 2008)(Revision:
X
let
96)
be a nite set of possible out omes, or onsequen es
for example,
onsumption bundles,
payos to a sto k portfolio,
out omes of a resear h proje t
1
General Equilibrium
Last Revised: 2007-01-13 16:47:46 -0800 (Sat, 13 Jan 2007)(Revision: 72)
n individuals
unknown types i for individual i characterize things about i that
are unknown to traders other than i
0 is a set of things unknown to all trade
Assignment 3 2016
Econ 600
1. Prove that in a stable many to many matching with (strict) responsive
preferences that the matching achieved by the DAA is both stable and
pareto optimal.
2. Use the student proposing DAA, then the college proposing DA to fin
Econ 600
Second Assignment
1. There are 3 schools, UBC, SFU and UT each of which wants to interview
3 applicants, 1, 2 and 3. There are 3 interview slots s1 , s2 and s3 . Currently
the following interviews have been arranged
s1
s2
s3
s1
s2
s3
s1
s2
s3
whe
1
General Equilibrium
n individuals
unknown types Ti for individual i characterize things about i that
are unknown to traders other than i
types are never observed and individuals types only indirectly by
observing that people do
T=
n
i=1
Ti is the se
1
Abstract Choice Theory
Last Revised: 2007-01-13 17:06:40 -0800 (Sat, 13 Jan 2007)(Revision: 74)
Let X be a set of alternatives, X X is the Cartesian product of
X with itself. A binary relation on X is a subset P X X
orderings of alternatives can be th
Uncertainty
Michael Peters
December 27, 2013
1
Lotteries
In many problems in economics, people are forced to make decisions without
knowing exactly what the consequences will be. For example, when you buy a
lottery ticket, you dont know whether or not you
X
N
X x X
(X p) p RN p = cfw_p1 , . . . pN
+
N
pi = 1
i=1
pi
i
X
X = cfw_(Y1 , p1 ) , . . . (YN , pN )
(X q )
Yi = Y
i Y
M
X = cfw_(Y , p1 ) , . . . (Y , pN )
Y,
( X q )
Hedonic Equilibrium
December 1, 2011
Goods have characteristics Z RK
sellers characteristics X Rm
buyers characteristics Y Rn
each seller produces one unit with some quality, each buyer
wants to buy 1 unit of some quality
p (z ) is the price of a good of
LARGE GAMES - DIRECTED SEARCH
MICHAEL PETERS
One of the interesting properties of directed search is that with nite numbers,
when a rm changes the wage it oers, it changes the outside option available to
all the other workers. The reason is that when a rm
How to Characterize Solutions to Constrained
Optimization Problems
Michael Peters
September 25, 2005
1
Introduction
A common technique for characterizing maximum and minimum points in math
is to use rst order conditions. When a function reaches its maximu
Cumulative Prospect Theory
October 23, 2013
based on Advances in Prospect Theory, by Tversky and
Kahneman, Journal of Risk and Uncertainty 5:297-323
(1992)
S is the set of states, subsets A S are called events
X is a set of outcomes,
a prospect is a funct
n colleges in a set C , m applicants in a set A, where m is much
larger than n.
each college ci C has a capacity qi - the maximum number of
students it will admit
each college ci has a strict order i over applicants, j i j means
college i would strictl
EXTRA PROBLEMS
(1) In the following matching problem, each college has the capacity for only a single student (each college will admit only one
student). The colleges are denoted by A, B , C , D, while the
students are a, b, c, d. The preferences of colle