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Appendix to Chapter 1:

Appendix to Chapter 1:. Graphs in Economics. Objectives. After studying this appendix, you will be able to: Make and interpret a time-series graph, a cross-section graph, and a scatter diagram

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Appendix to Chapter 1:

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  1. Appendix to Chapter 1: Graphs in Economics

  2. Objectives After studying this appendix, you will be able to: • Make and interpret a time-series graph, a cross-section graph, and a scatter diagram • Distinguish between linear and nonlinear relationships and between relationships that have a maximum and a minimum • Define and calculate the slope of a line • Graph relationships between more than two variables

  3. A graph represents “quantity” as a distance. A two-variable graph uses two perpendicular scale lines. The vertical line is the y-axis. The horizontal line is the x-axis. The zero point in common to both axes is the origin. Graphing Data Figure A1.1

  4. Graphing Data • Economists use three types of graphs to reveal relationships between variables. They are: • Time-series graphs • Cross-section graphs • Scatter diagrams

  5. Graphing Data • Time-Series Graphs • A time-series graph measures time (for example, months or years) along the x-axis and the variable or variables in which we are interested along the y-axis. • The time-series graph on the next slide shows the price of coffee between 1972 and 2002. • The graph shows the level of the price, how it has changed over time, when change was rapid or slow, and whether there was any trend.

  6. Figure A1.2

  7. Graphing Data • Cross-Section Graphs • A cross-section graph shows the values of a variable for different groups in a population at a point in time. • The cross-section graph on the next slides shows the number of Australians over 15 years of age who participate in various sporting activities

  8. Figure A1.3

  9. Graphing Data • Scatter Diagrams • A scatter diagram plots the value of one variable on the x-axis and the value of another variable on the y-axis. • A scatter diagram can make clear the relationship between two variables. • The three scatter diagrams on the next slide show examples of variables that move in the same direction, in opposite directions, and in no particular relationship to each other.

  10. Figure A1.4

  11. Graphs Used in Economic Models • Graphs are used in economic models to show the relationship between variables. • The patterns to look for in graphs are the four cases in which: • Variables move in the same direction • Variables move in opposite directions • Variables have a maximum or a minimum • Variables are unrelated

  12. Graphs Used in Economic Models • Variables that move in the same direction • A relationship between two variables that move in the same direction is called a positive relationship or a direct relationship. • A line that slopes upward shows a positive relationship. • A relationship shown by a straight line is called a linear relationship. • The three graphs on the next slide show positive relationships.

  13. Figure A1.5

  14. Graphs Used in Economic Models • Variables that move in opposite directions • A relationship between two variables that move in opposite directions is called a negative relationship or an inverse relationship. • A line that slopes downward shows a negative relationship. • The three graphs on the next slide show negative (inverse) relationships.

  15. Figure A1.6

  16. Graphs Used in Economic Models • Variables that have a maximum or a minimum • The two graphs on the next slide show relationships that have a maximum and a minimum. • These relationships are positive over part of their range and negative over the other part.

  17. Figure A1.7

  18. Graphs Used in Economic Models • Variables that are unrelated • Sometimes, we want to emphasise that two variables are unrelated. • The two graphs on the next slide show examples of variables that are unrelated.

  19. Figure A1.8

  20. The Slope of a Relationship • The slope of a relationship is the change in the value of the variable measured on the y-axis divided by the change in the value of the variable measured on the x-axis. • We use the Greek letter  (capital delta) to represent “change in.” • So y means the change in the value of the variable measured on the y-axis and x means the change in the value of the variable measured on the x-axis. • Therefore, the slope of a relationship is y/x.

  21. The Slope of a Relationship • The slope of a straight line • The slope of a straight line is constant. • Graphically, the slope is calculated as the “rise” over the “run.” • The slope is positive if the line is upward sloping. • The slope is negative if the line is downward sloping

  22. The Slope of a Relationship • The slope of a curved line • The slope of a curved line at a point varies depending on where along the curve it is calculated. • We can calculate the slope of a curved line either at a point or across an arc.

  23. The Slope of a Relationship • Slope at a point • The slope of a curved line at a point is equal to the slope of a straight line that is the tangent to that point. • Here, we calculate the slope of the curve at point A.

  24. The Slope of a Relationship • Slope across an arc • The average slope of a curved line across an arc is equal to the slope of a straight line that joins the endpoints of the arc. • Here, we calculate the average slope of the curve along the arc BC.

  25. Graphing Relationships Among More Than Two Variables • When a relationship involves more than two variables, we can plot the relationship between two of the variables by holding other variables constant—by using ceteris paribus. • The graphs on the next slide show an example.

  26. Figure A1.12

  27. Mathematical Note: • Equations to straight lines • Figure 1 shows a linear relationship—a relationship between two variables that graphs as a straight line. • A linear equation describes a linear relationship between x and y as: y = a + bx

  28. Mathematical Note • The slope of a relationship is the change in x, (Dx), divided by the change in y, (Dy),or: Dx/Dy In Figure 2: y1 = a + bx1 and: y1 + Dy =a + b(x1 + Dx)

  29. Mathematical Note • To calculate the slope of the line, subtract the first equation: y1 = a + bx1 from the second equation: y1 + Dy =a + b(x1 + Dx) to obtain: Dy =bDx

  30. Mathematical Note • Now divide both sides by Dx to obtain: Dy/Dx =b • The slope of the line is b.

  31. Mathematical Note • Position of line • The y-axis intercept, a, determines the position of the line on the graph • If a changes, the relationship shifts, as you can see in Figure 3. • The value of the y-axis intercept does not influence the slope of the line

  32. Mathematical Note • Positive and negative relationships • If b is positive, the relationship is described by an upward-sloping line like those in Figures 1, 2, and 3. • If b is negative, the relationship is described by a downward-sloping line like that in Figure 4.

  33. END CHAPTER 1 Appendix

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