ECON 431

Mathematical Economics

Kevin Wainwright
Office:3689 West Mall
Summer 2007


The course will develop some of the tools of mathematical analysis, which have been fruitfully used in modern economic analysis. Applications of the tools will be stressed. Topics that will be covered are noted below:

1. Review and Extension of Static Optimization Techniques

unconstrained optimization and concave functions, optimization under equality constraints and quasiconcave functions, comparative statics, maximum value functions and duality, nonlinear programming and the Kuhn-Tucker conditions.

2. Integration, Ordinary Difference and Differential Equations

integration, first order difference equations with an introduction to cycles and chaos, first and second order ordinary differential equations, applications to growth theory, systems of linear and nonlinear ordinary differential equations, phase diagrams, economic applications.

3. Optimal Control Theory

examples of dynamic optimization problems in economics, discounting, the maximum principle, its application and its economic interpretation..



Assignments 10 percent
 Mid-Terms 30 percent
Paper 20 percent
Final Examination 40 percent

ECON 331 Materials:

Lecture/Study Notes:
Matrix Algebra (ch 4 & 5)
Partial Derivatives and Implicit differentiation 1 (ch 7& 8)
Two Variable Optimization With Economic Applications (ch 11)
  • Matrix Algebra Practice problems 1: click here
  • Matrix Algebra Practice problems 2: Click here
  • single and multivariable calculus Problems 1: Click here
  • Implicit differentiation and multivariable chain rule: Click here
  • Single Variable optimization (Chapter 9) Click here
  • Multivariable optimization (Chapter 11) Click here
  • Lagrange Multiplier Method (Chapter 12) Click here

ECON 431 Materials:

Notes and Handouts
Envelope Theorem (ch 13)
First Order Differential Equations (ch 15)
Optimal Control: Bang-Bang Example
Homework 1
Homework 2
Homework 5
Homework 6: Sec 20.2 Q2, Q3, Q4
Answers to Assignments
Homework 5
Homework 6

Maple Files:

    Tutorial 0 Review of Matrix Algebra
    Tutorial 1 the Basics
    Tutorial 2 Functions and Plots
    Tutorial 3 Inverse Functions and NPV
    Tutorial 4 Introduction to the derivative

    Maple Class #2

    Assigments 1 to 4 (based on Econ 331 Homework #7 to #10)
    Assignment 1 Maple Code  PDF
    Assignment 2 Maple Code  PDF
    Assignment 3 Maple Code  PDF
    Assignment 4 Maple Code  PDF