# 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, 2^{nd} 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)

(Chapter 6, pp. 168-184)

a) The general form of the quadratic function

b) Quadratic equations

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)

(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

GRADING:

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

academic dishonesty tolerated.

Prev | Next |