Paul Krugman - Essentials of Economics

Whether youre reading about economics in the Wall Street Journal or in your economics textbook, you will see many graphs. Visual images can make it much easier to understand verbal descriptions, numerical information, or ideas. In economics, graphs are the type of visual image used to facilitate understanding. To fully understand the ideas and information being discussed, you need to be familiar with how to interpret and construct these visual aids. This appendix explains how to do this.

One reason to attend college is that a bachelors degree provides access to higher-paying jobs. Additional degrees, such as MBAs or law degrees, increase earnings even more. If you were to read an article about the relationship between educational attainment and income, you would probably see a graph showing the income levels for workers with different amounts of education. And this graph would depict the idea that, in general, more education increases income.

This graph, like most of those in economics, would depict the relationship between two economic variables. A is a quantity that can take on more than one value, such as the number of years of education a person has, the price of a can of soda, or a households income.

variableA quantity that can take on more than one value is called a variable.

As you learned in this chapter, economic analysis relies heavily on models, simplified descriptions of real situations. Most economic models describe the relationship between two variables, simplified by holding constant other variables that may affect the relationship.

For example, an economic model might describe the relationship between the price of a can of soda and the number of cans of soda that consumers will buy, assuming that everything else affecting consumers purchases of soda stays constant. This type of model can be described mathematically or verbally, but illustrating the relationship in a graph makes it easier to understand, as youll see next.

Most graphs in economics are based on a grid built around two perpendicular lines that show the values of two variables, helping you visualize the relationship between them. So a first step in understanding the use of such graphs is to see how this system works.

shows a typical two-variable graph. It illustrates the data in the accompanying table on outside temperature and the number of sodas a typical vendor can expect to sell at a baseball stadium during one game. The first column shows the values of outside temperature (the first variable) and the second column shows the values of the number of sodas sold (the second variable). Five combinations or pairs of the two variables are shown, each denoted by A through E in the third column.

FIGURE 2A-1 Plotting Points on a Two-Variable Graph

The data from the table are plotted where outside temperature (the independent variable) is measured along the horizontal axis and number of sodas sold (the dependent variable) is measured along the vertical axis. Each of the five combinations of temperature and sodas sold is represented by a point: A, B, C, D, and E. Each point in the graph is identified by a pair of values. For example, point C corresponds to the pair (40, 30)an outside temperature of 40F (the value of the x-variable) and 30 sodas sold (the value of the y-variable).

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Now lets turn to graphing the data in this table. In any two-variable graph, one variable is called the x-variable and the other is called the y-variable. Here we have made outside temperature the x-variable and number of sodas sold the y-variable. The solid horizontal line in the graph is called the , and values of the y-variablenumber of sodas soldare measured along it.

horizontal axisThe line along which values of the x-variable are measured is called the horizontal axis or x-axis. The line along which values of the y-variable are measured is called the vertical axis or y-axis. The point where the axes of a two-variable graph meet is the origin.

At the , the point where the two axes meet, each variable is equal to zero. As you move rightward from the origin along the x-axis, values of the x-variable are positive and increasing. As you move up from the origin along the y-axis, values of the y-variable are positive and increasing.

You can plot each of the five points A through E on this graph by using a pair of numbersthe values that the x-variable and the y-variable take on for a given point. In , at point C, the x-variable takes on the value 40 and the y-variable takes on the value 30. You plot point C by drawing a line straight up from 40 on the x-axis and a horizontal line across from 30 on the y-axis. We write point C as (40, 30). We write the origin as (0, 0).

Looking at point A and point B in , you can see that when one of the variables for a point has a value of zero, it will lie on one of the axes. If the value of the x-variable is zero, the point will lie on the vertical axis, like point A. If the value of the y-variable is zero, the point will lie on the horizontal axis, like point B.

Most graphs that depict relationships between two economic variables represent a . In our example of soda sales, the outside temperature is the independent variable. It directly influences the number of sodas that are sold, the dependent variable in this case.

causal relationshipA causal relationship exists between two variables when the value taken by one variable directly influences or determines the value taken by the other variable. In a causal relationship, the determining variable is called the independent variable; the variable it determines is called the dependent variable.

By convention, we put the independent variable on the horizontal axis and the dependent variable on the vertical axis. is constructed consistent with this convention; the independent variable (outside temperature) is on the horizontal axis and the dependent variable (number of sodas sold) is on the vertical axis.

An important exception to this convention is in graphs showing the economic relationship between the price of a product and quantity of the product: although price is generally the independent variable that determines quantity, it is always measured on the vertical axis.

Panel (a) of .

FIGURE 2A-2 Drawing Curves

The curve in panel (a) illustrates the relationship between the two variables, outside temperature and number of sodas sold. The two variables have a positive linear relationship: positive because the curve has an upward tilt, and linear because it is a straight line. It implies that an increase in the