Course Description
This course introduces some basic mathematical methods and solution techniques in economic analyses.  The mathematical methods and tools you will learn in this course are indispensable for good understanding and  application of economic theory.  It forms such a good prerequisite in courses as microeconomic and macroeconomic theory, economic growth and  development, production economics and etc.

Instructor:  E. M. Makaudze

Lectures:   Monday 11 - 12
                Wednesday 8 - 9 and 2 -4
                Thursday 10 - l 1
Course Grades:    Your  final grade  will  be  evaluated  on the  basis of  a series  of homework problems,
                             quizzes,  a  mid  term  test  a  final  examination.  Your grade will be determined using the method
                             outlined  below:

                                                    Homework       8%
                                                    Quiz               10%
                                                    Mid-term       12%
                                                    Final              70%

Recommended:

Chiang, A. A Fundamental Methods of Mathematical
    Economics, third edition.
 

Meter, J., Wasserman W., Kutner M; Applied Linear
    Regression Models. Second edition.

Part I Introduction

      1. Mathematical Economics
            1.1 Mathematical versus non mathematical economics
            1.2 Mathematical economics versus econometrics
            1.3 Concept of sets
            1.4 Relations and Functions

Economic Models
      2. Equilibrium Analysis
            2.1 Equilibrium Analysis in Economics
            2.2 Partial unit equilibrium (A Linear Model)
            2.3 Partial market equilibrium (non linear model)
            2.4 General Market Equilibrium
            2.5 Equilibrium in National income Analysis

     3.    Linear Models and Matrix Algebra
            3.1 Matrices and vector
            3.2 Matrix operations
            3.3 Commutative, Associative and Distributive Laws
            3.4 Identify Matrices and Null Matrices
            3.5 Transposes and inverses

      4.    Linear Models and Matrix Algebra
            4.1 Conditions for non-singularity of a matrix
            4.2 Test of non singularity by use of determinant
            4.3 Basic properties of determinants
            4.4 Finding the inverse matrix
            4.5 Cramer's rule
            4.6 Applications

   Part II Comparative Static Analysis
     5.    5.1     The nature of comparative statistics
            5.2     Rate of change and the derivative
            S.3     The derivative and the slope of a curve
            5 4     Rules of differentiation
            5.5     Partial differentiation
            5.6     Differentials, total differentials
            5.7     Total derivatives
            5.8     Applications

    6.0   Optimization problems
            6.1 Optimum values and extreme values
            6.2 Relative Maximum and minimum; First-derivative test
            6.3 Second and higher derivatives
            6.4 Second derivative test
            6.5 Digression on Macluarin and Taylor Series

    7.0   Logarithmic function
            7.1 Exponential and Logarithmic Functions
            7.2 The nature of Exponential functions
            7.3 Logarithmic functions
            7.4 Derivatives of exponential functions and the problem of
                  growth

   8.0   Application of Matrix Approach in Regression Analysis
            8.1 Matrix Approach to Simple Linear Regression Analysis
            8.2 Revision of some basic theorems for matrices
            8.3 Random vectors and matrices
            8.4 Simple linear regression model in matrix terms
            8.5 General linear regression model in matrix form.