McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Appendix to Chapter 1: Graphs in Economics

A1 -2 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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

A1 -3 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Graphing Data  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. Figure A1.1

A1 -4 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Graphing Data  Economists use three types of graphs to reveal relationships between variables. They are:  Time-series graphs  Cross-section graphs  Scatter diagrams

A1 -5 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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  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.

A1 -6 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.2

A1 -7 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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

A1 -8 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.3

A1 -9 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -10 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.4

A1 -11 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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

A1 -12 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -13 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.5

A1 -14 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -15 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.6

A1 -16 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -17 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.7

A1 -18 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -19 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.8

A1 -20 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -21 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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

A1 -22 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.9

A1 -23 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -24 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -25 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.10

A1 -26 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -27 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.11

A1 -28 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -29 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure A1.12

A1 -30 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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

A1 -31 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure 1, page 30

A1 -32 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Mathematical Note  The slope of a relationship is the change in x, (  x), divided by the change in y, (  y), or:  x/  y In Figure 2: y 1 = a + bx 1 and: y 1 +  y = a + b(x 1 +  x)

A1 -33 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Mathematical Note  To calculate the slope of the line, subtract the first equation: y 1 = a + bx 1 from the second equation: y 1 +  y = a + b(x 1 +  x) to obtain:  y = b  x

A1 -34 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Mathematical Note  Now divide both sides by  x to obtain:  y/  x = b  The slope of the line is b.

A1 -35 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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

A1 -36 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure 3, page 31

A1 -37 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia 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.

A1 -38 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia Figure 4, page 31

A1 -39 McTaggart, Findlay, Parkin: Microeconomics © 2007 Pearson Education Australia END CHAPTER 1 Appendix