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1 Appendix Using Graphs: A Review Graphs Used in Economic Analysis ● Display large quantity of data quickly ● Facilitate data interpretation and analysis ● Important statistical relationships more apparent than from written descriptions or long lists of numbers Copyright© 2006 South-Western/Thomson Learning. All rights reserved. Two-Variable Diagrams ● Variable = something measured by a number ♦ Examples: price and quantity ● View two variables together to see if they exhibit a relationship. Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 1: Quantities of Natural Gas Demanded at Various Prices TABLE Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 1: Hypothetical Demand Curve for Gas FIGURE 6 6 5 5 Price Price D 4 a P 3 b 2 1 4 P 3 a b 2 D 1 0 20 40 60 Q 80 100 120 140 Quantity (a) 0 20 40 60 Q 80 100 120 140 Quantity (b) Copyright© 2006 South-Western/Thomson Learning. All rights reserved. The Definition and Measurement of Slope ● Slope = ratio of vertical change to horizontal change ♦ Rise/run ♦ Measure of steepness of the line Copyright© 2006 South-Western/Thomson Learning. All rights reserved. The Definition and Measurement of Slope ● The slope of a straight line ♦ Negative slope = one variable rises while the other variable falls ■ The two variables move in opposite directions. ♦ Positive slope = two variables rise and fall together ■ The two variables move in the same direction. Copyright© 2006 South-Western/Thomson Learning. All rights reserved. FIGURE 2a: Negative Slope Y Negative slope 0 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. FIGURE 2b: Positive Slope Y Positive slope 0 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. The Definition and Measurement of Slope ♦ Zero slope = the variable on the horizontal axis can be any value while the variable on the vertical axis is fixed ■ Horizontal line ♦ Infinite slope = the variable on the vertical axis can be any value while the variable on the horizontal axis is fixed ■ Vertical line Copyright© 2006 South-Western/Thomson Learning. All rights reserved. FIGURE 2c: Zero Slope Y Zero slope 0 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. FIGURE 2d: Infinite Slope Y Infinite slope 0 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. The Definition and Measurement of Slope ● The slope of a straight line ♦ Slope is constant along a straight line. ♦ Slope can be measured between any two points on one axis and the corresponding two points on the other axis. Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 3: How to Measure Slope FIGURE Y Y 3 Slope = — 10 C 11 C 9 8 0 1 Slope = — 10 B A 3 13 (a) X 8 0 B A 3 13 X (b) Copyright© 2006 South-Western/Thomson Learning. All rights reserved. The Definition and Measurement of Slope ● The slope of a curved line ♦ Slope changes from point to point on a curved line. ■Curved line bowed toward the origin has a negative slope. ● Variables change in opposite directions. ■Curved line bowed away from the origin has a positive slope. ● Variables change in the same direction. Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 4a: Negative Slope in Curved Lines FIGURE Y Negative slope 0 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 4b: Positive Slope in Curved Lines FIGURE Y Positive slope 0 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. The Definition and Measurement of Slope ● The slope of a curved line ♦ A curved can have both a positive and negative slope depending on where on the curve is measured. ♦ The slope at a point on a curved-line is measured by a line tangent to that point. Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 4c,d: Behavior of Slope in Curved Lines FIGURE Y Y Negative slope Positive slope Negative slope Positive slope 0 X 0 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 5: How to Measure Slope at a Point on a Curve FIGURE Y r 8 D 7 6 5 R t F C E 4 G T 3 r M 2 1 0 A t B 1 2 3 4 5 6 7 8 9 10 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. Rays Through the Origin and 45-degree Lines ● Y-intercept = point at which a line touches the y axis ● Ray through the origin = straight line graph with a y-intercept of zero Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 6: Rays through the Origin FIGURE Y Slope = + 2 5 Slope = + 1 4 B 3 C A 2 K 1 E 0 1 2 Slope = + 1 – 2 D 3 4 5 X Copyright© 2006 South-Western/Thomson Learning. All rights reserved. Squeezing 3 Dimensions into 2: Contour Maps ● Some problems involve more than two variables ● Economic “contour map” called a production indifference map ♦ Shows how variable Z changes as we change either X or Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 8: An Economic Contour Map FIGURE Y Yards of Cloth per Day 80 70 60 50 A 40 Z = 40 B 30 Z = 30 20 Z = 20 10 Z = 10 0 10 20 30 40 50 60 70 80 X Labor Hours per Day Copyright© 2006 South-Western/Thomson Learning. All rights reserved.