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
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