Econ 6100

Mathematical Methods for Economics

Dr. J. Zietz

Office: BAS N312

Tel.: 898-5619, E-mail: jzietz@mtsu.edu

 


Course Objectives and Requirements

This is a work-intensive applications-oriented course on basic mathematical methods for economics. The objective is to bring all new incoming students up to a minimum level of math competency before the core economics courses start in late August. This will enable incoming graduate students to concentrate on the content rather than on the mathematics in the first-semester core courses of the MA and Ph.D. programs in economics and to begin to make intelligent use of computer algebra software (Maple or some other software) in economic modeling.

The final grade will be based on the results of two exams. Practice quizzes will be given on a regular basis throughout the course. They are intended as feedback for students and are not graded.

Every student is responsible for checking his/her email and the course webpage regularly before and after class, as course information is transmitted via email and the course webpage (see below).

Computer Use: Every student needs a computer account on the frank computer system and learn how to use it. The course will require students to become familiar with mathematics software packages. The Getting Started web page will help you to understand how to accomplish this learning objective.

Prerequisites: Familiarity with the topics of Precalculus Algebra as outlined in the Course Outline is mandatory. A convenient way to review this material is provided here. In addition, students should have had a course in basic calculus or equivalent knowledge. Check the material in chapter 3 of the textbook below and go online and test your knowledge with the True/False Quiz and the Review Exercises. Also check this material and the associated True/False Quiz and Review Exercises. Very little time will be spent on the material outlined in section 2 of the course outline.

Class Meetings: This class is listed in the MTSU schedule book under the Summer Session that starts at the beginning of July and ends the beginning of August. All incoming Ph.D. students need to register for this Summer class.

Textbook: The course will not strictly follow a textbook. Students are expected to carefully study the lecture notes that are available on line. In addition to the lecture notes, students are expected to practice the relevant material with the help of a textbook. One of the following two inexpensive paperback books may be of some help in this regard: Edward T. Dowling, Introduction to Mathematical Economics. 3rd edition, Schaum's Outlines Series. McGraw-Hill, 2001. ISBN 0-07-135896-X; or Darrell A. Turkington, Mathematical Tools for Economics. Blackwell Publishing, 2007, ISBN 1-4051-3381-3. Since no textbook is offically required for this course, the university book store does not carry any of these books.

Course webpage To view the lecture notes, problem sets, and other material on the course webpage, you will need both a userid and a password. Both are available from the instructor at the beginning of the course.

Office hours: before and after class, by appointment, and via e-mail. Check all questions and problems first via e-mail.

Special Note: Students with a disability that may require assistance or accommodation, or with questions related to any accommodations for testing, note takers, readers, etc., should contact the instructor as soon as possible. Students may also contact the Office of Disabled Students Services (898-2783) with questions about such services.


Tentative Outline of Course

1. Review of Basic Algebra

  • rules of algebra, factoring, fractions, exponents
  • solving individual, quadratic, and simultaneous equations

2. Basics of Matrix Algebra

  • sums and products of matrices
  • matrix product, transpose
  • determinants, Cramer's rule
  • matrix inversion, rank of a matrix
  • eigenvalues, quadratic forms
  • simple rules for transforming matrix equations

3. Useful Tools

  • percentage change formulas for large changes
  • summation sign and applications
  • lag/forward/difference operator
  • algebraic and geometric series

4. Basics of Differentiation

  • difference quotient and limits
  • common rules of differentiation
  • partial differentiation, chain rule
  • inverse function rule, implicit differentiation

5. Exponential and Logarithmic Functions

  • rules applying to logarithms
  • differenting logarithmic and exonential functions
  • growth rates with and without logarithms
  • elasticities with and without logarithms

6. Total Differentials and Their Use in Economics

  • total differentials and total derivatives
  • identifying slopes of multi-variable functions in two-dimensional space
  • checking movements of multi-variable functions in two-dimensional space
  • total differentials of implicit functions, such as first-order conditions
  • converting equations of total differentials into matrix format, solving by Cramer's rule

7. More Useful Tools

  • test for homogeneity/homotheticity
  • Euler's theorem
  • elasticity of substitution
  • tests for (quasi-)concavity and (quasi-)convexity
  • Taylor series expansion
  • Newton-Raphson method

8. Basics of Integration

  • fundamental rules of integration
  • integration by substitution and by parts
  • differentiation under the integral sign (Leibniz' rule)
  • economic applications: Lorenz curve/Gini coefficient, consumer/producer surplus

9. Unconstrained Optimization

  • basics, second-order conditions
  • comparative static analysis
  • envelope theorem

10. Optimization Subject to Equality Constraints

  • Lagrangian approach, different formats, interpretation
  • second-order conditions
  • comparative static analysis using Cramer's rule
  • value functions and envelope theorem
  • intertemporal optimization, with applicaitons in macroeconomics 

11. Optimization Subject to Inequality Constraints

  • inequality constraints with non-linear objective or constraint functions
  • Kuhn-Tucker conditions, solution methods
  • linear programming: basic set-up of primal and dual
  • economic interpretation of primal/dual/shadow prices

12. More Advanced Matrix Algebra

  • dealing with more complex matrix equations
  • differentiating inner products, quadratic forms, linear equation systems
  • backward chain rule
  • applications to linear regression


Other Textbooks and Reference Works


Baldani, Jeffrey; Bradfield, James, and Robert Turner, Mathematical Economics. 2nd ed., Thompson-South Western, 2005.

Carter, Michael, Foundations of Mathematical Economics. MIT Press 2001.

Chiang, Alpha C. and Kevin Wainwright, Fundamental Methods of Mathematical Economics, 4th ed., Mc-Graw Hill-Irwin, 2005.

De la Fuente, Angel, Mathematical Methods and Models for Economists. Cambridge University Press, 2000.

Hands, D. Wade, Introductory Mathematical Economics. 2nd edition, Oxford University Press, 2004.

Hess, Peter, Using Mathematics in Economic Analysis. Prentice Hall, 2002.

Hoy, Michael; Livernois, John; McKenna, Chris; Rees, Ray, and Thanasis Stengos, Mathematics for Economics. 2nd edition, MIT Press, 2001.

Kendrick, David A., Mercado, Reuben P., and Hans M. Amman, Computational Economics. Princeton University Press, 2006.

Klein, Michael W., Mathematical Methods for Economics. 2nd edition, Addison-Wesley, 2002.

Novshek, William, Mathematics for Economists. Academic Press, 1993.

Parlar, Mahmut, Interactive Operations Research with Maple. Birkhäuser, Boston, 2000.

Searle, Shayle R. Matrix Algebra Useful for Statistics. John Wiley, New York, 1982.

Simon, Carl, P., and Lawrence Blume, Mathematics for Economists. Norton, 1994.

Sydsaeter, Knut, and Peter J. Hammond, Mathematics for Economic Analysis. Prentice Hall, 1995.

Toumanoff, Peter, and Farrokh Nourzad, A Mathematical Approach to Economic Analysis. West Publishing 1994.


last revised: August 6, 2009