2September2009
APPENDIX A: MATHEMATICAL FOUNDATIONS
A.1 IS IT REALLY TRUE?
Methods of proof
1
A.2 MAPPINGS OF A SINGLE VARIABLE
Neighborhood and limit point
Continuous Function
6
A.3 DERIVATIVES AND
A Tutorial on Simple First Order Linear Difference Equations
(for Economics Part I Paper 3)
Corrections to Dr Ian Rudy (http:/people.pwf.cam.ac.uk/iar1/contact.html) please.
An example of a simple fir
The Envelope Theorem
The envelope theorem concerns how the
optimal value for a particular function
changes when a parameter of the function
changes
This is easiest to see by using an example
The Env
Extreme Walrasian Dynamics:
The Gale Example in the Lab
By Sean Crockett, Ryan Oprea, and Charles Plott*
Abstract
We study David Gales (1963) economy using laboratory markets. Tatonnement theory
predi
Journal of Convex Analysis
Volume 11 (2004), No. 1, 95110
On the Necessity of some Constraint Qualication
Conditions in Convex Programming
Dan Tiba
Weierstrass Institut, Mohrenstr. 39, D-10117 Berlin,
CONSTRAINT QUALIFICATIONS FOR NONLINEAR PROGRAMMING
RODRIGO G. EUSTAQUIO , ELIZABETH W. KARAS, AND ADEMIR A. RIBEIRO
Abstract. This paper deals with optimality conditions to solve nonlinear programmin
ECONOMIC APPLICATIONS OF LAGRANGE MULTIPLIERS
MATH 232
Maximization of a function with a constraint is common in economic situations. The rst section considers the problem in consumer theory of maximi
Fall Semester '05-'06 Akila Weerapana
LECTURE 15: DIFFERENTIAL EQUATIONS
I. INTRODUCTION
The last two lectures covered theory and applications in the area of difference equations. The next two lectur
Fall Semester '04-'05 Akila Weerapana
LECTURE 19: Phase Diagram Analysis
I. INTRODUCTION
Today's lecture discusses how to analyze the dynamics of a system of non-linear difference or differential equ
14.102, Math for Economists
Fall 2005
Lecture Notes, 9/15/2005
These notes are primarily based on those written by George Marios Angeletos
for the Harvard Math Camp in 1999 and 2000, and updated by St
Constrained Optimization: Examples
Consumers problem: Suppose that a consumer has a utility function
U (x, y ) = x0.5y 0.5, the price of x is $2, the price of y is $3 and the
consumer has $100 in inco
Lagrange Multiplier Problems in Economics
John V. Baxley and John C. Moorhouse, Wake Forest University, Winston-Salem, NC 27109
American Mathematical Monthly, AugustSeptember 1984, Volume 91, Number 7
Mathematical Appendix II
II.1 Theorem of the Maximum
There are two sets S I n and T I m . Further, there are a correspondence
R
R
mapping S into the sets of subsets of T and a function f : S T I
R.
T
Introduction to MATLAB for Economists
Seth Neumuller
September 12, 2011
Module III: An Application
This set of modules is designed to introduce the rst year graduate student in economics to programmin
Theorem of the Maximum
Economists are often interested in characterizing the effect of some environmental parameter on
the decision made by a maximizing agent. Consider the following problem, where we
JohnRiley
Fall2010(revised)
Econ 200 Diagnostic Quiz
Attempt all three questions. Time allowed: 10 minutes reading and 100 minutes writing. To test
out you need to show some progress on all three ques
John Riley
22 September 2006
Econ 200 Diagnostic Test
Summer 2006
Time allowed: ninety (90) minutes. Answer three questions only. You must answer
question 4 and any two of the first three questions.
1
John Riley
2 September 2009
APPENDIX B: MAPPINGS OF VECTORS
B.1 VECTORS AND SETS
1
Orthogonal vectors and hyper-planes
Convex sets
Open and Closed Sets
B.2 FUNCTIONS OF VECTORS
8
Functions of 2 varia
Econ 200 Homework Exercises
1. Elasticity
For any function y = f ( x) , the elasticity of this function is
(a) Show that
( y, x) =
( y, x) = x dy .
y dx
d
ln y ( x)
dx
.
d
ln x
dx
(Thus if you graph
JohnRiley
Econ 200 Diagnostic Quiz
Fall 20111
Attempt all three questions. Time allowed: 10 minutes reading and 100 minutes writing. To test
out you need to show some progress on all three questions s
John Riley
24 July 2011
ANSWERS TO EVEN NUMBERED EXERCISES IN APPENDIX B
Section B.2. FUNCTIONS OF VECTORS
Exercise B.2-2: Positive definite quadratic form
2
What are the necessary and sufficient con
John Riley
24 July 2011
ANSWERS TO ODD NUMBERED EXERCISES IN APPENDIX B
Section B.1 VECTORS ANS SETS
Exercise B.1-1: Convex sets
(a) Let x 0 , x1 X 1 , X 2 , hence x 0 , x1 X 1 and x 0 , x1 X 2 . Sin
John Riley
24 July 2008
ANSWERS TO EXERCISES IN APPENDIX B
Section B.1 VECTORS ANS SETS
Exercise B.1-1: Convex sets
(a) Let x 0 , x1 X 1 , X 2 , hence x 0 , x1 X 1 and x 0 , x1 X 2 . Since X 1 and X
John Riley
28 July 2011
ANSWERS TO EVEN NUMBERED EXERCISES IN APPENDIX C
SECTION C.1: TWO VARIABLES
Exercise C.1-2: Firm with interdependent demands
A firm sells two products. Demand prices for these
John Riley
28 July 2011
ANSWERS TO ODD NUMBERED EXERCISES IN APPENDIX C
SECTION C.1: TWO VARIABLES
Exercise C.1-1: Consumer Choice
(a) Since U is strictly increasing, for any x not on the boundary of
John Riley
15 August 2011
APPENDIX B: MAPPINGS OF VECTORS
B.1 VECTORS AND SETS
1
Orthogonal vectors and hyper-planes
Convex sets
Open and Closed Sets
B.2 FUNCTIONS OF VECTORS
9
Functions of 2 variabl
09/09/2011
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