Professor:                 Yang-Ming Chang

Office and Phone:     Waters Hall 319, Tel. 532?4573
E-mail:                      ymchang@ksu.edu

Class Hours:             11:05 a.m. - 12:20 p.m., Monday and Wednesday
Office Hours:            1:30 - 2:30 p.m., Tuesday and Thursday, or by appointment

Objectives:
 
            This course is intended to help students to set up a kit of mathematical tools employed in
solving economic problems.  Emphasis will be placed on the development of techniques of
classical mathematical programming and the theories of comparative statics and dynamic
optimization. A systematic application of mathematical methodology to the microeconomic
theories of the consumer, the producer and firm, market equilibrium and structure, and aggregate
growth will be examined. Applications of both comparative statics method and dynamic
optimization theory to macroeconomic models of linear and non?linear economy will also be
analyzed.

Prerequisites:

            Mathematics: General Calculus and Linear Algebra (MATH 205), or Analytic Geometry
                                 and Introductory Calculus (MATH 220).

            Economics: Intermediate Microeconomics (ECON 520).

Required Textbooks:
 
            The required textbooks for the course are:

Chiang, A. C., Fundamental Methods of Mathematical Economics, McGraw?Hill, 1984.

Silberberg, E., The Structure of Economics: A Mathematical Analysis, McGraw?Hill, 2nd
Edition, 1990.  (Third edition will be available in July 2000.)
 
(Optional) Supplementary Readings:

             Tadiboyina Venkateswarlu, "Mathematical Economics: Survey of Reading Materials in
             Universities in Canada and the United States," The American Economist (Journal of the
             International Honor Society in Economics), Fall 1988, Vol. XXXII, No.2, pp.79-83.

             Herbert G. Grubel and Lawrence A. Boland, "On the Efficient Use of Mathematics in
             Economics: Some Theory, Facts and Results of an Opinion Survey," Kyklos, Vol. 39,  1986,  pp. 419-442.

Tentative Course Outline:

            (1) Introduction

            Economic Models
            Static Analysis
            Comparative Static Analysis
            Economic Dynamics and Dynamic Optimization
            Applications: Demand, Supply, and Market Equilibrium
            *Chapters  1, 2, 3 (Chiang)
            *Chapter    1 (Silberberg)

            In taking this graduate course, you are supposed to have a working knowledge of
            calculus (Math 205 or 220).  You should have already known some fundamentals of set
            theory, linear algebra, integral, and differential calculus (such as limits, continuity,
            differentiability, derivatives, partial derivatives, and chain rule etc.).  To review these
            fundamentals, read chapters 2 through 8 in Chiang and chapters 2, 3, and 5 in Silberberg.
            We will have a quick review on some of those chapters.

            Linear Models and Matrix Algebra

            Matrices, Matrix Operations
            Determinants and Basic Properties of Determinants
            The Inverse of a Matrix
            Cramer's Rule
            *Chapters  4, 5 (Chiang)
            *Chapter   5 (5.1 and 5.2) (Silberberg)

            Differential Calculus

            Limits, Continuity, Differentiability, and Derivatives
            Rules of Differentiation
            Chain Rules
            Partial Differentiation
            Rules of Differentials
            Total Derivatives
            Jacobian Determinants
            The Implicit Function Theorem
            Applications: The Comparative Statics of Macroeconomic Models
            *Chapters  5 (5.3), 6, 7, 8 (Chiang)
            *Chapters  2, 3 (Silberberg)
 __________________
       Midterm Exam 1
 __________________
 

(2) Optimization Methods and Comparative Statics

Unconstrained Optimization Theory
Necessary and Sufficient Conditions
Theory of Profit Maximization
            Output Supply Function
            Input Demand Function
            Indirect Profit Function
            The Long Run vs. The Short Run
            The Le Chatelier Principle

Constrained Optimization Theory
Necessary and Sufficient Conditions
Positive and Negative Definiteness
Hessian Matrix and Bordered Hessian Matrix
Concavity and Convexity
Quasi-Concavity and Quasi?Convexity
         *Chapters   9, 10, 11, 12  (Chiang)
         *Chapters   4, 6 (Silberberg)
 

(3) The Comparative Statics of Optimization Models  (Applications)

Profit?Maximization Model of Firm
Theory of Cost Minimization of Firm:
          Traditional Methodology vs. Duality Approach
The Duality of Cost and Production Functions
Theory of Firms in Long?Run Competitive Equilibrium
*Chapters  7 (Section 7.5 may be skipped), 8 (Silberberg)
__________________
      Midterm Exam 2
__________________
 
(4) Optimization with Inequality and Nonnegativity Constraints

Nonnegativity
Inequality Constraints
Kuhn-Tucker Conditions
The Saddle Point Theorem
Nonlinear Programming
*Chapter 14 (Silberberg)

(5) Dynamic Analysis

Economic Dynamics and Integral Calculus
Some Applications of Integrals
Continuous Time
First-order Differential Equations
Second-order Differential Equations
Simultaneous Differential equations
Phase Diagrams
Linearization of a Nonlinear Differential-Equation Systems
Stability Analysis
Optimal Control Theory (If time permitting)
*Chapters  13, 14, 15, 18 (Chiang)
*Chapter   18 (Silberberg)
_______________________
              Final Exam
_______________________
 

Homework, Exams, and Grading:

            An important part of this course is the problems assigned for homework. Complete them
systematically and rigorously.  It might be easy to be lulled into a false sense of confidence when
reading texts and listening lectures.  Attempting problems forces one to grips with the material.
Problem sets will be distributed regularly.

            Your course grade will depend upon your performance on homework assignments, two
midterm exams, and a comprehensive final exam. Exams will be held in the evening. The weights
for grading are as follows:

                                                    Homework               15%
                                                    Midterm Exam 1       20%
                                                    Midterm Exam 2       30%
                                                    Final Exam                35%

 
             There will be no make?up exams and no extra credit work available.  Grades will be based
on relative performance in the class.

Plagiarism and Cheating

              The administration requires that each syllabus include the following statement regarding
KSU's policy on plagiarism and cheating:

"Plagiarism and cheating are serious offenses and may be punished by failure on the exam, paper
or project; failure in the course; and/or expulsion from the university. For more information refer
to the 'Academic Dishonesty' policy in Inside KSU or Appendix F in the Faculty Handbook."

Academic Accommodations for Disable Students

             If you have any condition, such as a physical or learning disability, which will make it
difficult for you to carry out the work as I have outlined it or which will require academic
accommodations, please notify me in the first two weeks of the course. Updated: 9/12/23