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QUANTITATIVE METHODS I

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. 63-86)

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

Section B: Systems of Linear Equations (Chapter 5, pp. 109- 126)

a) Basic notions
b) Operations on linear systems
c) Simultaneous equations
d) Applications: production problems , simultaneous equilibrium in related
markets, 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 properties of Linear Programming as a mathematical model
(c) Constrained maximization
(d) Constrained minimization

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

a) The general form of the quadratic function
c) Polynomials
d) Economic applications

3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS

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
e) Doubling time
f) Applied problems in business and economics

PART III: APPLIED DIFFERENTIAL AND INTEGRAL CALCULUS

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
f) 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 AND CONTRAINED OPTIMIZATION (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
g) the method of the Lagrange multiplier
h) 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) Anti-derivatives: the indefinite integral
b) Rules of integration
c) The definite integral
d) The fundamental theorem of calculus
i) Area and the definite integral
h) Applications: consumers' and producers' surplus; the Lorenz coefficient ,
and depreciation

Two mid- term exams  60%
Final exams  30%
Homework Assignments 10%

IMPORTANT REMINDER:

Exams must be taken at the times designed except in the case of illness with a physician's excuse.
No late assignment will be accepted. The final exam will be comprehensive. Violation of an
academic regulation could have a very serious consequence ranging from a reduction of grade on
a specific project to failure in a course. In this class, in no time and under no circumstance is