ECON 5113 Advanced Microeconomics
Winter 2011
Answers to Selected Exercises
Instructor: Kam Yu
The following questions are taken from Georey A. Jehle Ex. 1.45 Since di is homogeneous of degree zero in p
and Philip J. Reny (2001) Advanced Microeconomic The
2
1 The Expenditure Function
If preferences satisfy LN, the function v (p; w) is strictly increasing in w: We can invert that function to
solve for w as a function of the level of utility. That is, given some level of utility u; we can nd the
minimal amou
Lecture 9 Consumer Theory I
AAE 635 Fall 2010
9.1 Introduction
So far we have explored the production behavior of cost minimizing firms and profit maximizing
firms. We have also investigated the short run production equilibrium and the long run production
141
5.2 Indirect Utility Function and Expenditure Functions
Each households optimization problem can be written in two forms: (i) as a utility maximization problem for a given budget constraint, or (ii) as an expenditure minimizing problem for a given ut
Economics 603: Microeconomics
Larry Ausubel
Matthew Chesnes
Updated: Januray 1, 2005
1
Lecture 1: August 31, 2004
1.1
Preferences
Dene the set of possible consumption bundles (an nx1 vector) as X . X is the set of
alternatives.
Usually all elements of X
1
Hicksian Demand Functions, Expenditure Functions & Shephard's Lemma
Consider a world with 2 goods (x and y), where Wilbur has well-defined preferences over bundles of those two goods, and those preferences can be represented by the utility function . Wi
CALIFORNIA INSTITUTE OF TECHNOLOGY
Division of the Humanities and Social Sciences
Eulers Theorem for Homogeneous Functions
KC Border
Let f : Rn R. We say that f is homogeneous of degree k if for all
+
x Rn and all > 0,
+
f (x) = k f (x).
1 Eulers theorem
Consumer theory: Demand functions
Maria Saez Marti
Oce 210, IEW
tel. 044 634 37 13 e-mail: saez@iew.uzh.ch
Summary
x B such that x % x for all x B
(1)
max u (x) s.t. p x y.
n
(2)
xR+
Continuous preferences can be represented by utility functions
For suc
Economics 210B
Due: Tues., Sept. 5, 2006
Problem Set 5.
Problem 1. Consumption versus leisure, part 3. Consider again the optimization problem we started studying in PS3: max U (c, h) ln(c) + ln(T - h) c, h subject to: c = wh
This time we will use MATLAB
Notes on optimization
Francesc M. Torralba
January 12, 2005
1
Unconstrained optimization
An unconstrained optimization problem is a problem of the form
max f ( x)
x
subject to x 2 X
or
min f (x)
x
subject to x 2 X
where f : <n ! < is at least once dierent
DB 802 Advanced Economics
Lecture 2: Consumer Theory
Concepts:Preferences, Utility,
UMP, Indirect and Expenditure
function, Demand function and its
properties
Chaiyuth Punyasavatsut 2011
1
applications
If you introduce a new product, how
much should it ch
Advanced Microeconomics
Topic 3: Consumer Demand
Primary Readings: DL Chapter 5; JR - Chapter 3; Varian, Chapters 7-9.
3.1 Marshallian Demand Functions
Let X be the consumer's consumption set and assume that the X = Rm+. For a given price vector p
of comm
Lecture 3: Consumer Theory (contd)
Topics 1.5
Properties of Demand
Keywords: Relative prices, real income
Substitution and income effects,
Slutsky equation, Law of Demand
Chaiyuth DB802 2011
1
1.5.1 Relative Prices and real
income
Relative prices of good
Partial Equilibrium: Positive Analysis
Simon Board
This Version: November 28, 2009
First Version: December 1, 2008.
In this Chapter we consider consider the interaction between dierent agents and rms, and
solve for equilibrium prices and quantities.
Secti
Firms Problem
Simon Board
This Version: September 20, 2009
First Version: December, 2009.
In these notes we address the rms problem. We can break the rms problem into three
questions.
1. Which combinations of inputs produce a given level of output?
2. Giv
Expenditure Minimisation Problem
Simon Board
This Version: September 20, 2009
First Version: October, 2008.
The expenditure minimisation problem (EMP) looks at the reverse side of the utility maximisation problem (UMP). The UMP considers an agent who wish
Utility Maximisation Problem
Simon Board
This Version: September 20, 2009
First Version: October, 2008.
The utility maximisation problem (UMP) considers an agent with income m who wishes to
maximise her utility. Among others, we are interested in the foll
Preferences and Utility
Simon Board
This Version: October 6, 2009
First Version: October, 2008.
These lectures examine the preferences of a single agent. In Section 1 we analyse how the
agent chooses among a number of competing alternatives, investigating
New York University Department of Economics V31.0006 Mathematics for Economists C. Wilson May 7, 2008
Homogeneous Functions
For any R, a function f : Rn R is homogeneous of degree if f (x) = f (x) for all > 0 + n . A function is homogeneous if it is homog
E CON 711 A NSWER K EY TO HW4
Chang-Koo(CK) Chi
October 8, 2009
Problem 6
Each person i cfw_1, 2, 3 faces two problems; choosing xiA how much he has for dinner
when plan A is selected and xiB . In case of plan A, his(say, person 1) budget constraint is
de
316611 Microeconomics
Semester 1, 2007
Seminar 3
Yuelan Chen
yuelanc@unimelb.edu.au
March 22, 2007
Please prepare the following questions before the class on 21 March, 2007.
Q 1. Derive the Marshallian demand functions from the following utility functions
ECON 403 Lecture Notes
Consumer Theory.
DISCLAIMER: If you do not attend lectures, you are duly warned that these notes
do not contain all of the material presented in class. You do not attend lectures at
your own peril! Also note that not all material in
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Thammasat Economic Journal
Vol.26, No.4, December 2008
The Effects of Immigration on Capital Inflow
Kiriya Kulkolkarn*
Abstract
In this theoretical paper, we study the relationship between immigration and capital inflow.
We apply the idea of H