Tables And Graphs

A brief glance at this text will tell you that graphs are important in economics. Graphs provide a convenient way to display data. Take the example of Len & Harry's, an up-and-coming manufacturer of high-end ice cream products, located in Texas. Suppose that you've just been hired to head Len & Harry's advertising department, and you want to learn as much as you can about how advertising can help the company's sales.

Table A.1 records the company's total advertising outlay per month in the left-hand column, and the company's ice cream sales during that same month are shown in the right-hand column. Notice that the data are organized so that advertising outlay increases as we move down the first column. Often, just looking at such a table can reveal useful patterns. In this case, it seems that higher advertising outlays are associated with higher monthly sales. This suggests that there may be some causal relationship between advertising and sales.

To explore this relationship further, we might decide to plot the data and draw a graph (see Figure A.1). First, we need to choose units for our two variables. We'll measure both advertising and sales in thousands of dollars. Different values of one variable are then measured along the horizontal axis, increasing as we move rightward from the origin. The corresponding values of the other variable are measured along the ver tical axis, increasing as we move upward, away from the origin.

Using the data in the table, let X stand for advertising outlay per month, and let Y stand for sales per month. Notice that each row of the table gives us a pair of numbers: The first is always the value of the variable we are calling X, and the second is the value of the variable we are calling Y. We often write such pairs in the form (X, Y). For example, we would write the first three rows of the table as (2, 46), (3, 49), and (6, 58), respectively.

To plot the pair (X, Y) on a graph, begin at the origin, where the axes meet. Count rightward X units along the horizontal axis, then count upward Y units parallel to the vertical axis, and then mark the spot. For example, to plot the pair (2, 46), we go rightward 2 units along the horizontal axis and then upward 46 units along the vertical axis, arriving at the point marked A in Figure A.1. To plot the next pair, (3, 49), we go rightward from the origin 3 units and then upward 49 units, arriving at the point marked B. Carrying on in just this way, we can plot all remaining pairs in Table A.1 as the points C, D, E, and F.

If we connect points A through F, we see that they all lie along the same straight line. Now we are getting somewhere. The relationship we've discovered appears from the graph to be very regular, indeed.

Study the graph closely. You will notice that each time advertising increases (moves rightward) by \$1,000,

 TABLE A.1 ADVERTISING AND SALES AT LEN & HARRY'S Advertising (\$1,000s per Month) Sales (\$1,000s per Month) 2 46 3 49 6 58 7 61 11 12 76 