Appendix: A Note on Mathematics and
Graphs
As you proceed through this book, you will encounter many
graphs and some mathematical equations. Economists use
graphs and equations because they are quick and clear ways
to express ideas. Very often a couple of graphs are worth a
thousand words.
There are three sorts of ideas for which graphs and
equations are especially well suited. The first is
relationships. Examples or relationships from outside of
economics are: the higher the altitude, the lower the
boiling point of water; the further from the sun a planet
lies, the slower its speed in its orbit; the saltier the
water, the heavier it is. All of these relationships can be
expressed more precisely in the form of graphs and equations
than they can be in words. The same will be true of the
economic relationships that you will meet in later
chapters.
There are two kinds of relationships. If larger values of
variable A cause larger values of variable B, the
relationship is direct. For example, as income rises, people
spend more. On the other hand, when larger values of
variable A cause smaller values of variable B, the
relationship is inverse or indirect. For example, when the
price of apples rises, people buy fewer.
A second use of graphs and equations is to specify
limits. As you now know, economic activity is grounded in
the need of choice caused by scarcity. As a result, many
economic relations can also be interpreted as limits. You
will also see examples of this use of graphs as you read
further.
A third use of graphs is to show how a series moves over
time. If you look at the back of The Wall Street
Journal or in the financial section of most large
newspapers, you will see examples of this sort of graph.
If you have a good understanding of high school algebra,
you will have no trouble at all with the level of
mathematics used in these pages. You will, for example,
realize that algebraic equations can be illustrated
graphically and that graphs can be represented
algebraically. (Because they are visual and easier for the
beginner to grasp, this book relies more heavily on graphs
than equations.) If you do not have a good mathematical
background, take heart. First, most ideas that yield graphs
are first explained verbally and then in tables. And second,
the course will give you an opportunity to practice and
learn some of the basic mathematics that you should have
learned in high school.
(Can you illustrate what each of the three relationships
mentioned (altitudeboiling point, etc.) above look like.
Which are direct and which are inverse relationships?)
Copyright
Robert Schenk
