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 (altitude-boiling point, etc.) above look like. Which are direct and which are inverse relationships?)

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Copyright Robert Schenk