ECON 205:  QUANTITATIVE METHODS I
    (Winter 2004)

Instructor:  Ahmed M. Hussen
Office Phone:  337-7025; email (hussen@kzoo.edu)
Office Hours:


COURSE DESCRIPTION:

    This is the first of a two-course sequence designed to give economics majors the quantitative skills necessary for upper-level courses in the department.  The principal topics covered are:  i) linear equations, systems of linear equations, and exponential and logarithmic functions as they applied to economics and business problems, ii) basic mathematics of finance, and iii) applied calculus--differentiation, optimization and simple integration.  In this course, mathematics is viewed as a means rather than an end in itself.  Thus, applications of the relevant mathematical concepts and theories to economics and business related problems are strongly emphasized.  Prerequisite: at least two years of high school algebra.


TEXTBOOK: 

Rosser, Mike, Basic Mathematics for Economists, Routledge Publishing, 2nd edition, 2003.


PART I:  BASIC CONCEPTS OF FUNCTIONS AND ALGEBRAIC RELATIONSHIPS 

1.   LINEAR RELATIONSHIPS

Section A:  Functions and Linear Equations  (Chapter 4, pp. 61-86)

a)   The basic concept functions
b)   Linear functions
c)   Equation of a line:  the slope-intercept form
d) Applications: linear demand and supply functions, break-even analysis and a straight-line
      depreciation of a capital asset.

Section B:  Systems of Linear Equations (Chapter 5, pp. 109- 147)
    
a)   Basic notions
b)   Operations on linear systems
c) Simultaneous equations
d) Applications:  budget equation, production problems, simultaneous equilibrium in related
       markets, price discrimination, and aggregate consumption function

Section C:  Fitting a Linear Function – an overview
   
(a) Scattered diagram
(b) The least square estimators

Section D:  Linear Programming   (Chapter 5, pp. 148-167)

a)  The general model of Linear Programming
b)  Constrained maximization
c) Constrained minimization


2. QUADRATIC  FUNCTIONS AND THEIR APPLICATIONS IN ECONOMICS
(Chapter 6, pp. 168-184)

a) The general form of the quadratic function
b) Quadratic equations
c) Economic applications
 
3.   EXPONENTIAL AND LOGARITHMIC FUNCTIONS  (Chapter 14, pp. 440-446)
     
a)   Exponential functions and their properties
b)   Graphs of exponential functions
c)   The function e
d)   Logarithms and logarithm rules
e)   Common and natural logarithms
f)   Economic applications:  growth functions, log-linear demand and production  
           functions

PART II:  MATHEMATICS OF FINANCE  (Chapter 7, pp. 189-218)
    
a)   Compound interest and the future value
b)   Compound discount: present value 
c)   Continuous compounding
d)    Doubling time
e) Applied problems in business and economics


PART III:  APPLIED DIFFERENTIAL AND INTEGRAL CALCULUS (Six Weeks)

1.   INTRODUCTION TO DIFFERENTIAL CALCULUS: Single Variable Functions
      (Chapter 8, pp. 247-271; Chapter 12, pp. 372-379)

a)   The concept of limits and basic limit theorems
b)   The concept of continuity and the basic notion of continuous functions
c)   The average rate of change: the difference quotient
d)   The derivative
e)   Basic differentiation rules
f)   Derivatives of exponential and logarithmic functions
e) Economic applications:  marginal concepts and analysis, relationships among total,
average and marginal concepts, tax yield, point elasticity of demand, the Keynesian multiplier, etc..


2. UNCONSTRAINED OPTIMIZATION:  Functions of Single Variable
(Chapter 9, pp. 272-290)

a)   The basic notion of optimization
b)   Maxima and minima of functions:  the first derivative test
c)   The second derivative test
d)   Economic applications: maximization of revenue and profit functions and 
      minimization of cost functions, inventory control, comparative static effects of taxes

3.   MULTIVARIATE CALCULUS (Chapter 10, pp. 291-328; Chapter 11, pp. 334-363)

a)   The partial derivative
b) Maxima and minima:  two independent variables
c) Total differentials and total derivatives
d)   Constrained optimization
e)   the method of the Lagrange multiplier
f)   Applications:  production, revenue, cost and profit functions.

4.   MORE ON DIFFERENTIAL CALCULUS (Chapter 12, pp. 364-377)

a)   The chain rule
b)   Implicit differentiation
c)   Economic applications:  elasticity of demand and total revenue and
       the multiplier

5.   SIMPLE INTEGRATION (Chapter 12, pp. 384-394)

a)   Antiderivatives:  the indefinite integral
b)   Rules of integration
c)   The definite integral
d)   The fundamental theorem of calculus
e)   Area and the definite integral
f)   Applications:  consumers' and producers' surplus; the Lorenz coefficient,
     and depreciation