Economics 4113, Fall 2011.
Instructor: David Rahman, University of Minnesota.
Homework 5Due Thursday, December 8, 2011, in class
Question 1 (Incremental Investment ). Consider a rm facing the demand function
P = X Q
at every instant in time, where 0 and X
Economics 4113, Spring 2010. Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 1Due February 2, 2010
1. Given a matrix A Rmn , dene
span A = cfw_y Rm : x Rn s.t. Ax = y .
Intuitively, span A is the set
Economics 4113, Spring 2010. Instructor: David Rahman, University of Minnesota.
Homework 2Due February 18, 2009
1. Consider the following Markov chains.
(a) Let A be the following matrix:
A=
p 1p
q 1q
.
Describe the set of all invariant distributions of A
Economics 4113, Spring 2010. Instructor: David Rahman, University of Minnesota.
Homework 2Due March 11, 2010
1. Derive the dual of the following primal problem:
V = max x1 + 2x2
x1 ,x2
s.t.
8
x1 + 3 x2 4,
x1 + x2 = 2,
2x1 3,
x1 0.
2. Write down the duals
Economics 4113, Spring 2010. Instructor: David Rahman, University of Minnesota.
Problem Set 4Due April 13, 2010
1. Consider the following optimization problem, called the budget problem.
maxcfw_U (x, y ) : px + qy I ,
x,y 0
where , , p, q, I > 0. Intuitiv
SELECTION, GROWTH, AND THE SIZE
DISTRIBUTION OF FIRMS
Erzo G.J. Luttmer
University of Minnesota and
Federal Reserve Bank of Minneapolis
August 25, 2006
Abstract
This paper describes an analytically tractable model of balanced growth that
is consistent wit
Economics 4113, Spring 2011. Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 4Due May 5, 2011
Question 1 (Incremental Investment ). Consider a rm facing the demand function
P = X Q
at every instant in
An Option Value Problem from Seinfeld
Avinash Dixit
Forthcoming, Economic Inquiry
January 26, 2011
Abstract
This is a paper about nothing.
1
Introduction
In an episode of the sitcom Seinfeld (season 7, episode 9, original air date December 7,
1995), Elain
Economics 4113, Spring 2011. Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 3Due March 3, 2011
Question 1 (Envelope Theorem ). (a) Let g (x, u) be continuously dierentiable in
both arguments, and ass
Economics 4113, Spring 2011. Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 2Due February 15, 2011
Question 1 (Random walk ). Recall the random walk representation of Brownian
motion from class. Give
Economics 4113, Spring 2011. Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 1Due January 28, 2011
Question 1 (Bad news principle ). In the context of the two-period example we
studied in class, let t
Economics 4113, Fall 2011.
Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 1Due Tuesday, September 20, in class
Question 1 (Bad news principle ). In the two-period example we studied in class,
let the
Economics 4113, Fall 2011.
Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 2Due October 11, in Class
Question 1 (Random walk ). Recall the random walk representation of Brownian
motion from class. Giv
Economics 4113, Fall 2011.
Instructor: David Rahman, University of Minnesota.
Request: Please substantiate your answers.
Homework 3Due October 20, 2011, in class
Question 1 (Envelope Theorem ). (a) Let g (x, u) be continuously dierentiable in
both argumen
Economics 4113, Fall 2011.
Instructor: David Rahman, University of Minnesota.
Please substantiate your answers.
Homework 4Due Tuesday, November 15, 2011, in class
Question 1 (American Put ). Consider a stock price S that follows a geometric
Brownian motio
Econ 4113 Lecture Notes 1
Course Objectives
To develop an appreciation of mathematical modelling in economics.
To learn the theory of functions of several real variables, with special emphasis
on issues related to maximization.
To solidify skills and u