### Econ 210B - Mathematical Methods in Economics

"Maths Concentration Camp"
This course is intended to refresh and extend entering graduate students’ understanding of the major Mathematical tools used in economic analysis. The main topics to be covered are linear algebra, differential and integral calculus, static and dynamic optimization, and difference and differential equations.

Lecture Schedule

Textbook readings are assigned below. (chapters referenced with parenthesis are just basic background chapters, not required)

Lecture 1: View Lecture Notes (2009)
(1A) Linear equations and vector spaces. SB (10), 11
(1B) Matrix algebra. SB 8

Lecture 2: View Lecture Notes (2009)
(2A) Determinants and matrix inverses. SB 9, 26
(2B) Differentiation. SB (2), (4), 14

Problem Set for Lecture 2

Lecture 3:
(3A) Differentiation and approximation. SB 14, 30
(3B) The implicit function theorem and comparative statics. SB 15
(3C) Introduction to MATLAB.

Lecture 4:  View Lecture Notes (2009)
(4A) Introduction to optimization.     SB (3), 17
(4B) Constrained optimization: Lagrangians. SB 18, (16), (19); D 2

Problem Set 4 Questions (2009)
Problem Set 4 MATLAB

Lecture 5:  View Lecture Notes (2009)
(5A) Optimization with inequality constraints. SB 18, (19); D 3
(5B) Integral calculus. SB App. A

Lecture 6:  View Lecture Notes (2009)
(6A) Integral calculus, continued. SB App. A
(6B) Introducing dynamics: first-order difference equations. SB 23

Lecture 7: View Lecture Notes (2009)
(7A) The eigenvalue problem. SB 23
(7B) Systems of difference equations.  SB 23

Lecture 8: View Lecture Notes (2009)
(8A) First-order ordinary differential equations. SB 24
(8B) Higher-order differential equations: characteristic equation. SB 24

Lecture 9: View Lecture Notes (2009)
(9A) Systems of ordinary differential equations. SB 25
(9B) Introduction to dynamic optimization: Lagrangian approach.  AC 2.3.1; D 10

Lecture 10: View Lecture Notes (2009)
(10A) Dynamic programming: Bellman’s equation. AC 2, see also: D11, Stokey & Lucas Ch. 2
(10B) Solving Bellman’s equation: guess and verify, backwards induction.                                                                     AC 2.3.2

Lecture 11: View Lecture Notes (2009)
(11A) Solving Bellman’s equation: Euler equation approaches.
(11B) States, costates, and saddle path stability.

Lecture 12: View Lecture Notes (2009)
(12) Numerical dynamic programming.          AC 3

Main Textbooks

: Mathematics for Economists
Key Text

by Carl Simon and Lawrence Blume, 1994 (SB)

Digital Version:  all files .PDF

Solution Manual: all files .PDF

Optimization in Economic Theory
by Avinash Dixit, 2nd ed., 1990 (D)

Dynamic Economics: Quantitative Methods and Applications
by Jerome Adda and Russell Cooper, 2004 (AC)

Matrix Calc - matrix inverses, determinants, multiplication, combos etc
Wolfram Alpha - mathamatica online: double check your work
This Website - problem sets, past exams, notes and other digital resources.
Texas A&M Intro to MATLAB - Fall 2009 - video lessons on using MATLAB. Might expire after Fall '09. You can always search google for tools too.
MATLAB Videos on Mathworks - click around in categories and check out other people's video blogs

Fundamental Methods of Mathematical Economics
by Alpha Chiang, 1984

A First Course in Optimization Theory
by Rangarajan Sundaram, 1996

Dynamic Optimization
by Morton Kamien and Nancy Schwartz, 1991

Recursive Methods in Economic Dynamics
by Nancy Stokey and Robert Lucas, 1989

Investment under Uncertainty
by Avinash Dixit and Robert Pindyck, 1994

Recursive Macroeconomic Theory
by Lars Ljungqvist and Thomas Sargent, 2nd ed., 2004

Final Exam Resources

Final Exam
: Friday, three hours
The final will be rough. Know your basics, solving differential equations, matrix operations. Discrete time phase diagram vs continuous time phase diagrams. You should be comfortable at least setting up Lagrangians and Bellmans correctly. And given first order equations, be prepared to discuss some economic intuition for the models given.

ECON 210B Final Exam 'Cheat' Sheet [.PDF] - In previous finals, we were permitted one sheet of notes. (2,300 words, 560 lines. A few typos likely, be vigilant)

Previous Finals -  [FINAL 2009 .PDF] - [FINAL 2008 .PDF] - [FINAL 2007 .PDF] - [FINAL 2005 .PDF] - [FINAL 2004 .PDF] - [FINAL 2003 .PDF] - [FINAL 2002 .PDF] - [FINAL 2001 .PDF] - [FINAL 2000 .PDF] - [FINAL 1999 .PDF] - [FINAL 1998 .PDF] - [FINAL 1997 .PDF]

Errors & Suggestions? - Just Let Me Know