11 GRAPHS IN ECONOMICS Key Concepts  Graphing Data Graphs represent quantity as a distance on a line. On a graph, the horizontal scale line is the x-axis, the vertical scale line is the y-axis, and the intersection of the two scale lines is the origin. The three main types of economic graphs are: ♦ Time-series graphs demonstrate the relationship between time, measured on the x-axis, and other variable(s), measured on the y-axis. Time-series graphs show the variable’s level, direction of change, speed of change, and trend, which is its general tendency to rise or fall. ♦ Cross-section graphs show the values of a variable for different groups in a population at a point in time. ♦ Scatter diagrams plot the value of one variable against the value of another to show the relationship between two variables. Such a relationship indicates how the variables are correlated, not whether one variable causes the other.  Graphs Used in Economic Models The four important relationships between variables are: ♦ Positive relationship or direct relationship — the variables move together in the same direction, as il-lustrated in Figure A1.1. The relationship is up-ward-sloping. ♦ Negative relationship or inverse relationship — the variables move in opposite directions, as shown in Figure A1.2. The relationship is downward-sloping. Appendix12 CHAPTER 1 ♦ Maximum or minimum — the relationship reaches a maximum or a minimum point, then changes di-rection. Figure A1.3 shows a minimum. ♦ Unrelated — the variables are not related so that, when one variable changes, the other is unaffected. The graph is either a vertical or horizontal straight line, as illustrated in Figure A1.4. A relationship illustrated by a straight line is called a linear relationship.  The Slope of a Relationship The slope of a relationship is the change in the value of the variable on the y-axis divided by the change in the value of the variable on the x-axis. The formula for slope is ∆y/∆x, with ∆ meaning “change in.” A straight line (or linear relationship) has a constant slope. A curved line has a varying slope, which can be calculated two ways: ♦ Slope at a point — by drawing the straight line tan-gent to the curve at that point and then calculating the slope of the line. ♦ Slope across an arc — by drawing a straight line across the two points on the curve and then calcu-lating the slope of the line.  Graphing Relationships Among More Than Two Variables Relationships between more than two variables can be graphed by holding constant the values of all the vari-ables except two (the ceteris paribus assumption, that is, “other things remaining the same”) and then graphing the relationship between the two with, ceteris paribus, only the variables being studied changing. When one of the variables not illustrated in the figure changes, the entire relationship between the two that have been graphed shifts. Helpful Hints 1. IMPORTANCE OF GRAPHS AND GRAPHICAL ANALYSIS : Economists almost always use graphs to present relationships between variables. This fact should not “scare” you nor give you pause. Economists do so because graphs simplify the analy-sis. All the key concepts you need to master are pre-sented in this appendix. If your experience with graphical analysis is limited, this appendix is crucial to your ability to readily understand economic analysis. However, if you are experienced in con-structing and using graphs, this appendix may be “old hat.” Even so, you should skim the appendix and work through the questions in this Study Guide.APPENDIX: GRAPHS IN ECONOMICS 13 2. CALCULATING THE SLOPE : Often the slopes of various relationships are important. Usually what is key is the sign of the slope — whether the slope is positive or negative — rather than the actual value of the slope. An easy way to remember the formula for slope is to think of it as the “rise over the run,” a saying used by carpenters and others. As illus-trated in Figure A1.5, the rise is the change in the variable measured on the vertical axis, or in terms of symbols, ∆y. The run is the change in the vari-able measured on the horizontal axis, or ∆x. This “rise over the run” formula also makes it easy to remember whether the slope is positive or negative. If the rise is actually a drop, as shown in Figure A1.5, then the slope is negative because when the variable measured on the horizontal axis increases, the variable measured on the vertical axis decreases. However, if the rise actually is an increase, then the slope is positive. In this case, an increase in the variable measured on the x-axis is associated with an increase in the variable measured on the y-axis. Questions  True/False and Explain Graphing Data 11. The origin is the point where a graph starts. 12. A graph showing a positive relationship between stock prices and the nation’s production means that an increase in stock prices causes an increase in production. 13. In Figure A1.6 the value of y decreased between 1998 and 1999. 14. In Figure A1.6 the value of y increased most rapidly between 2001 and 2002. 15. Figure A1.6 shows a trend with y increasing, gener-ally speaking. 16. A cross-section graph compares the values of differ-ent groups of a variable at a single point in time. Graphs Used in Economic Models 17. If the graph of the relationship between two vari-ables slopes upward to the right, the relationship between the variables is positive. 18. If the relationship between y (measured on the ver-tical axis) and x (measured on the horizontal axis) is one in which y reaches a maximum, the slope of the relationship must be negative before and positive after the maximum. 19. To the left of a minimum point, the slope is nega-tive; to the right, the slope is positive. 10. Graphing things that are unrelated on one diagram is NOT possible.14 CHAPTER 1 The Slope of a Relationship 11. It is possible for the graph of a positive relationship to have a slope that becomes smaller when moving rightward along the graph. 12. The slope of a straight line is calculated by dividing the change in the value of the variable measured on the horizontal axis by the change in the value of the variable measured on the vertical axis. 13. For a straight line, if a large change in y is associ-ated with a small change in x, the line is steep. 14. The slope of a curved line is NOT constant. 15. The slope of a