1. 1 1 Appendix Using Graphs: A Review Appendix Using Graphs: A Review

2. Copyright© 2006 South-Western/Thomson Learning. All rights reserved. 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 ●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

3. 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. ●Variable = something measured by a number ♦ Examples: price and quantity ●View two variables together to see if they exhibit a relationship.

4. TABLE 1: Quantities of Natural Gas Demanded at Various Prices Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

5. Q b a P Price Quantity (a) 140120100806040200 1 2 3 4 5 6 D D b a Q P Price Quantity (b) 140120100806040200 1 2 3 4 5 6 FIGURE 1: Hypothetical Demand Curve for Gas Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

6. The Definition and Measurement of Slope ●Slope = ratio of vertical change to horizontal change ♦Rise/run ♦Measure of steepness of the line ●Slope = ratio of vertical change to horizontal change ♦Rise/run ♦Measure of steepness of the line

7. 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. ●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.

8. FIGURE 2a: Negative Slope Negative slope 0 X Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

9. FIGURE 2b: Positive Slope Positive slope 0 X Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

10. 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 ♦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

11. FIGURE 2c: Zero Slope Zero slope 0 X Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

12. FIGURE 2d: Infinite Slope Infinite slope 0 X Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

13. 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. ●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.

14. FIGURE 3: How to Measure Slope 3 — 10 Slope = 1 — 10 Slope = (b)(a) A X B C 1330 Y 8 11 X A B C 1330 Y 8 9 Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

15. 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. ●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.

16. FIGURE 4a: Negative Slope in Curved Lines Negative slope 0 X Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

17. FIGURE 4b: Positive Slope in Curved Lines Positive slope 0 X Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

18. 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. ●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.

19. FIGURE 4c,d: Behavior of Slope in Curved Lines Negative slope Positive slope 0 X Y Negative slope Positive slope 0 X Y Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

20. FIGURE 5: How to Measure Slope at a Point on a Curve r r t t A B R M G T E F D C Y X 109876543210 8 7 6 5 4 3 2 1 Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

21. 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 ●Y-intercept = point at which a line touches the y axis ●Ray through the origin = straight line graph with a y-intercept of zero

22. FIGURE 6: Rays through the Origin 1 – 2 Slope = + Slope = + 1 Slope = + 2 B E K A C D 0 5 4 3 2 54321 1 Y X Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

23. 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 ●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

24. FIGURE 8: An Economic Contour Map Z= 40 Z= 30 Z = 20 Z= 10 Yards of Cloth per Day Labor Hours per Day Y X 80706050403020100 20 30 40 50 60 70 80 B A Copyright© 2006 South-Western/Thomson Learning. All rights reserved.