CHAPTER 2 Making and Using Graphs Michael Parkin ECONOMICS 5e CHAPTER 2 Making and Using Graphs 1 1

Learning Objectives Make and interpret a time-series graph, a scatter diagram, and a cross-section graph Distinguish between linear and nonlinear relationships and between relationships that have a maximum and a minimum 2 2

Learning Objectives (cont.) Define and calculate the slope of a line Graph relationships among more than two variables 3 3

Learning Objectives Make and interpret a time-series graph, a scatter diagram, and a cross-section graph Distinguish between linear and nonlinear relationships and between relationships that have a maximum and a minimum 2 4

Graphing Data Graphs represent a quantity as a distance on a line. The X-axis runs horizontally. The Y-axis runs vertically. The origin is their intersection. Instructor Notes: 1) All graphs have axes that measure quantities as distances. 2) Here, the horizontal axis (x-axis) measures temperature. 3) A rightward movement shows an increase in temperature. 4) The vertical axis (y-axis) measures height. 5) An upward movement shows an increase in height. 6) Point a represents a fishing boat at sea level (0 on the y-axis) on a day when the temperature is 32o (32o on the x-axis. 7) Point b represents a climber at the top of Mt. McKinley (20,320 feet above sea level on the y-axis) on a day when the temperature on Mt. McKinley is 0o (0o on the x-axis). 8) Point c represents a climber at the tope of Mt. McKinley, 20,320 feet above sea level (on the y-axis) when the temperature on Mt. McKinley is 32o (on the x-axis) 5 4

Graphing Data Point c can be identified by a pair of coordinates The points show relationships between 2 quantitative variables 5 6

Graphing Data Scatter Diagram A scatter diagram plots the value of one economic variable against the value of another variable. It can be used to reveal whether a relationship exists and the type of relationship that exists. 6 7

Scatter Diagrams 8 7 Instructor Notes: 1) The breaks in the axes is to avoid empty space. 2) A scatter diagram reveals the relationship between two variables. 3) The first graph shows the relationship between consumption and income between 1986 and 1996. 4) Each point shows the values of the two variables in a specific year. 5) For example, in 1992, average income was $18,000 and average consumption was $16,500. 6) The pattern formed by the points shows that as income increases, so does consumption. 7) The second graph shows the relationship between the price of an international call and the number of phone calls made per year between 1970 and 1993. 8) This graph shows that as the price of a phone call has fallen, the number of calls made has increased. 9) The third graph shows the inflation rate and unemployment rate in the United States between 1986 and 1996. 10) This graph shows that inflation and unemployment are not closely related. 8 7

Correlation and Causation Correlation describes the strength of the relationship that exists between two variables. Correlation does not imply causation. 8 9

Time-Series Graphs A time-series graph measures time on the x-axis and the variable or variables in which we are interested on the y-axis. They also reveal trends. A trend is a general tendency for a variable to rise or fall. 9 10

Time-Series Graphs 11 10 Instructor Notes: 1) A time-series graph plots the level of a variable on the y-axis against time (day, week, month, or year) on the x-axis. 2) This graph shows the price of coffee (in 1996 cents per pound) each year from 1966 to 1996. 3) It shows us when the price of coffee was high and when it was low, when the price increased, and when it decreased, and when it changed quickly, and when it changed slowly. 11 10

Comparing Two Time-Series Instructor Notes: 1) These two graphs show the unemployment rate and the balance of the government’s budget. 2) The unemployment line is identical in the two graphs. 3) The top graph shows the budget surplus--taxes minus spending--on the right scale. 4) It is hard to see a relationship between the budget surplus and unemployment. 5) The bottom graph shows the budget as a deficit--spending minus taxes. 6) It inverts the scale of the top graph. 7) With the scale for the budget balance inverted, the graph reveals a tendency for unemployment and the budged deficit to move together. 12 11

Cross-Section Graphs Cross-section graphs show the values of an economic variable for different groups in a population at a point in time. The values can be shown with the use of bars, lines, or bars. 12 13

Cross-Section Graphs 14 13 Instructor Notes: 1) A cross-section graph shows the level of a variable across the members of a population. 2) This graph shows the average income per person in each of the ten largest metropolitan areas in the United States in 1995. 14 13

Graphs Used in Economic Models Economic models are used to show relationships among variables. They are simplified descriptions of an economy or a component of the economy. 14 15

Graphs Used in Economic Models Four Patterns to Watch For: Variables that move in the same direction. Variables that move in opposite directions. Variables that have a maximum or a minimum. Variables that are unrelated. 14 16

Variables Moving in the Same Direction Instructor Notes: 1) Each graph of this figure shows a positive (direct) relationship between two variables. 2) That is, as the value of the variable measured on the x-axis increases, so does the value of the variable measured on the y-axis. 3) The first graph shows a linear relationship--as the two variables increase together, we move along a straight line. 4) The second graph shows a positive relationship such that as the two variables increase together, we move along a curve that becomes steeper. 5) The third graph shows a positive relationship such that as the two variables increase together, we move along a curve that becomes flatter. 17 15

Variables Moving in Opposite Directions Instructor Notes: 1) Each part of this figure shows a negative (inverse) relationship between two variables. 2) The first graph shows a linear relationship--as one variable increases and the other variable decreases, we move along a straight line. 3) The second graph shows a negative relationship such that as the journey length increases, the curve becomes less steep. 4) The third graph shows a negative relationship such that as leisure time increases, the curve becomes steeper. 18 15

Learning Objectives Make and interpret a time-series graph, a scatter diagram, and a cross-section graph Distinguish between linear and nonlinear relationships and between relationships that have a maximum and a minimum 2 19

Variables That Have a Maximum or a Minimum Instructor Notes: 1) The first graph shows a relationship that has a maximum point, a. 2) The curve slopes upward as it rises to its maximum point, is flat at its maximum, and then slopes downward. 3) The second graph shows a relationship with a minimum point, b. 4) The curve slopes downward as it falls to its minimum, is flat at its minimum, and then slopes upward. 20 15

Variables That Are Unrelated Instructor Notes: 1) This figure shows how we can graph two variables that are unrelated to each other. 2) In the first graph, a student’s grade in economics is plotted at 75 percent regardless of the price of bananas on the x-axis. 3) The curve is horizontal. 4) In the second graph the output of vineyards of France does not vary with the rainfall in California. 5) The curve is vertical. 21 15

Learning Objectives Define and calculate the slope of a line Graph relationships among more than two variables 3 22

The Slope of a Relationship The influence one variable has on another can be measured by the slope of the relationship. Slope = 15 23

The Slope of a Straight Line Instructor Notes: 1) To calculate the slope of a straight line, we divide the change in the value of the variable measured on the y-axis (y) by the change in the value of the variable measured on the x-axis (x) as we move along the curve. 2) The first graph shows the calculation of a positive slope. 3)When x increases from 2 to 6, x equals 4. 4) That change in x brings about an increase in y from 3 to 6, so y equal 3. 5) The slope (y / x) equals 3/4. 6) The second graph shows the calculation of a negative slope. 7) When x increases from 2 to 6, x equals 4. 8) That increase in x brings about a decrease in y from 6 to 3, so y equals -3. 9) The slope (y / x) equal -3/4. 24 15

Slope at a Point 25 15 Instructor Notes: 1) To calculate the slope of the curve at point a, draw the red line that just touches the curve at a--the tangent. 2) The slope of this straight line is calculated by dividing the change in y by the change in x along the line. 3) When x increases from 0 to 4, x equals 4. 4) That change in x is associated with an increase in y from 2 to 5, so y equals 3. 5) The slope of the red line is 3/4. 6) So the slope of the curve at point a is 3/4. 25 15

Slope Across an Arc 26 15 Instructor Notes: 1) To calculate the average slope of a curve along an arc bc, first draw a straight line from b to c. 2) The slope of the line bc is calculated by dividing the change in y by the change in x. 3) In moving from b to c, 26 15

Learning Objectives (cont.) Define and calculate the slope of a line Graph relationships among more than two variables 3 27

Graphing Relationships Among More Than Two Variables In order to isolate the relationships that exist between two variables, other things must remain the same. Ceteris Paribus 15 28

Graphing Relationships Among More Than Two Variables Price Ice cream consumption (cents per scoop) (gallons per day) 30ºF 50ºF 70ºF 90ºF 15 12 18 25 50 30 10 12 18 37 45 7 10 13 27 60 5 7 10 20 75 3 5 7 14 90 2 3 5 10 105 1 2 3 6 15 29

Graphing Relationships Among More Than Two Variables Instructor Notes: 1) The quantity of ice cream consumed depends on its price and the temperature. 2) The table gives some hypothetical numbers that tell us how many gallons of ice cream are consumed each day at different prices and different temperatures. 3) For example, if the price is 60 cents a scoop and the temperature is 70oF, 10 gallons of ice cream are consumed. 4) This set of values is highlighted in the table and each part of the figure. 5) To graph a relationship among three variables, the value of one variable is held constant. 6) The first graph shows the relationship between price and consumption when temperature is held constant. 7) Once curve holds temperature at 90oF and the other at 70oF. 8) The second graph shows the relationship between temperature and consumption when the price is held constant. 9) Once curve holds the price at 60 cents a scoop and the other at 15 cents a scoop. 10) The third graph shows the relationship between temperature and price when consumption is held constant. 11) One curve holds consumption at 10 gallons and the other at 7 gallons. 30 15

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