Download ECON 1078-001 Math Tools for Economists I

Math Tools for Economists-Econ 1078-100
Steve Thorpe
University of Colorado-Boulder
Spring 1996
Office: ECON 107
Phone: 492-7908
E-mail: [email protected]
Office hours: Mondays and Wednesdays , 2:00-3:50; Fridays, 9:00-10:50; by appointment.
Introduction Let me begin this course with a challenge: find an issue or topic that does
not in any way involve mathematics. I think that you will be surprised to find out just how
ubiquitous math is in our world. Note that this does not imply that all issues are equally
interesting to all people. I do believe, however, that each of us finds something interesting.
[n this course, we will strive to use our interests (yours and mine) to our advantage in order
to learn the mathematical tools necessary to live in our complex society.
Although math is everywhere, it is more prevalent in some areas-Bconomics, for
example-than in other areas. Most issues in economics are inherently quantitative. For
example, you care not only that you earn interest on your savings, but also about how
much interest you get. Some issues are qualitative: If interest rates rise, would you expect
the price of a share of Nintendo stock to rise or fall?
You could think about this question as follows: A Nintendo share is worth
something because it will pay dividends, and because you can sell it later. Imagine that the
money you use to buy the share would otherwise be put into a savings account. If the
interest rate on the savings account is higher, then savings is more attractive and,
correspondingly, the Nintendo stock is less attractive. Thus. the price of a Nintendo stock
falls when interest rates rise because fewer people will want to hold Nintendo stocks. We
are still left with the question of how much the stock price will fall. In this course, we will
answer questions like these , and many other types, using mathematical models.
Resources There is no single "textbook" for the course. Rather, we will spend time
reading and analyzing the mathematical aspects of everyday economic issues found in
newspapers and magazines, and on television. A student subscription to a good newspaper
such as The Wall Street Journal or The New York Times is strongly recommended. There
is, however, one required resource for the course: A Mathematical Skills Primer, by John
Martin. You should treat this volume as a reference book. Keep it next to your dictionary
and thesaurus. (Unless you have trouble sleeping at night, don't try to read through the
primer as a textbook or a novel.)
Grades Your final letter grade for the course will be based primarily on your performance
on three exams, two midterm exams and a final exam (30% each), and on your scores on
periodically assigned problem sets. The final exam is scheduled by the University for
Monday, May 13th, from 7:30 to 10:30 a.m. If you cannot make this exam do not
take this course.
General Course Outline*
Material Comprising Exam 1: The Basics
• Number systems
• Fractions, decimals, and percents
• Exponents and Logarithms
• Scientific notation and unit conversions
• Algebra
• Sets
• Graphing
Material Comprising Exam 2: Modeling
• Functions and equations
• Simultaneous equations
• Matrices
• Linear programming
Material Comprising Exam 3 (final exam): Information for Making Choices
• Simple and compound interest
• Present value/discounting
• Probability and statistics
*Since we are not using a traditional textbook for this course, the order of the topics is not
set in stone. In general, we will cover the topics in an order in which they are needed for
the issues we are discussing at the time.
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