Econ 701: Answers to Midterm Exam
Bart Lipman Fall 2009
1. (a) The independence axiom (as we stated it) says that if p q , then for every r and every [0, 1], we have p + (1 )r q + (1 )r. To show that this holds, suppose p q . Using the representation, we
Econ 701: Midterm Exam
Bart Lipman Fall 2009
Part 1: The following question is worth 30 points. 1. Prove any two of the following statements. Be sure to state clearly any denitions or other properties you are using in your proof. Each proof is worth 15 po
Theorem 3.1.2. For all non-negative measurable functions f, g and all constants
, 0,
(a) (f + g ) = (f ) + (g ),
(b) f g implies (f ) (g ),
(c) f = 0 a.e. if and only if (f ) = 0.
Proof. Dene simple functions fn , gn by
fn = (2n 2n f ) n,
gn = (2n 2n g )
Konstantin Milbradt
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MIT, Sloan School of Management, Assistant Professor of Finance
Microeconomic Theory
April 1, 2005
page 551
10. Market Power
Market power is the ability of a rm to increase prots by setting
a price above marginal cost.
Most real-world rms acquire some degree of market power by
producing goods that have no perfect su
Microeconomic Theory
December 10, 2004
page 451
9. Competitive Equilibria and Welfare
In this section, we dene the idea of equilibrium in competitive
markets.
We will also dene concepts of welfare.
We will ask in what ways competitive markets aect the
MicroeconomicTheory
November 29, 2004
page 321
7. Noncooperative Games
7.1 Basic Concepts
Game theory = theory of strategic interaction
Each agent chooses a strategy in order to achieve his goals with
the knowledge that other agents may react to his str
Microeconomic Theory
December 1, 2004
page 401
8. Uncertainty
8.1 Lotteries
An object is deterministic, if it has only one possible outcome (set
of characteristics is given).
A object is a lottery if it has a number of dierent possible
outcomes (sets of
MicroeconomicTheory
November 5, 2004
page 241
6. Production
Denition 6.1 Production is the transformation of a vector
of commodities into a dierent vector of commodities.
Production can be organized in either of two environments:
In hierarchical environm
Topic
October 13, 2004
page 161
4. Duality in Consumer Theory
Denition 4.1 For any utility function U (x ), the corresponding
indirect utility function is given by:
V (p , w ) maxcfw_U (x ) | x 0 , px w
x
maxcfw_U (x ) | x Bp ,w ,
x
so that if x is the
Topic
October 4, 2004
page 71
3. (Neo)Classical Demand Theory
3.1 Preferences
Not all preferences can be described by utility functions.
This is inconvenient.
We make the assumptions about preferences that utility functions
require.
Not very realistic
Microeconomic Theory
September 29, 2004
page 1
Manoves Microeconomic Theory Slides
[A substantial portion of these notes are based on materials from the
textbook for this course: Mas-Colell, Winston and Green, Microeconomic Theory, Oxford University Press
STOCHASTIC METHODS OF MATHEMATICAL FINANCE
CONSTANTINOS KARDARAS
1st step
Due date: Tuesday, 2nd of November
Exercise 1
If W is a standard Brownian motion, show that the process X dened via Xt = x + t + Wt for
t R+ is a Brownian motion starting at x with
MATHEMATICS FOR
ECONOMISTS
Carl P Simon
and
Lawrence Blume
W
l
W
l
NORTON & COMPANY
l
NEW YORK
l
LONDON
Copyright 0 1994 by W. W. Norton & Company, Inc.
ALL RIGHTS RESERVED
PRINTED IN THE UNITED STATES OF AMERICA
FIRST EDITION
The text of this book is com
LIMITS (FUNCTIONS OF TWO VARIABLES)
One of the main differences between limits of functions of one variable and limits
of functions of two variables is that limits of functions of one variable at a point
x = a are considered in an interval on the number l
Answer to Kreps Problem 18.1
(a) First calculate Drakes expected utility if he has no insurance. This is
.7
90, 000 + .3
40, 000 = 270.
Now calculate his utility if he buys the insurance policy. This is
.7
80, 000 + .3
60, 000 = 271.46
He would buy it
Microeconomic Theory Qualifying Exam
Department of Economics
Boston University
June 2010
Instructions. You have four hours to complete this exam, plus a 15 minute grace
period to wrap up if needed. Answer all four questions. The questions are equally
weig
The University of Auckland
Department of Economics
First Semester, 1999
616.301 FC Advanced
Microeconomics
Abstract
Contents
John Hillas
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Chapter 1. General Equilibrium Theory
1. The basic model of a competitive econom
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Lecture Notes in
Microeconomic Theory
The Economic Agent
Ariel Rubinstein
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
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