A p p e n d i x
GRAPHS IN ECONOMICS
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 illustrated in Figure A1.1. The relationship is upward-sloping. ♦ Negative relationship or inverse relationship — the variables move in opposite directions, as shown in Figure A1.2. The relationship is downwardsloping.
♦ Maximum or minimum — the relationship reaches a maximum or a minimum point, then changes direction. 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 Δy/Δx, with Δ 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 tangent 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 calculating 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 variables 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.
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 analysis. All the key concepts you need to master are presented 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 constructing 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
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 illustrated in Figure A1.5,...
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