If the price of movies increases, fewer consumers go to see movies.
More experienced workers typically have higher incomes than less experienced workers.
Whatever the temperature outside, Americans consume the same number of hot dogs per day.
Consumers buy more frozen yogurt when the price of ice cream goes up.
Research finds no relationship between the number of diet books purchased and the number of pounds lost by the average dieter.
Regardless of its price, Americans buy the same quantity of salt.
Which is the independent variable? Which is the dependent variable? On which axis do you therefore measure the income tax rate? On which axis do you measure income tax revenue?
What would tax revenue be at a 0% income tax rate?
The maximum possible income tax rate is 100%. What would tax revenue be at a 100% income tax rate?
Estimates now show that the maximum point on the Laffer curve is (approximately) at a tax rate of 80%. For tax rates less than 80%, how would you describe the relationship between the tax rate and tax revenue, and how is this relationship reflected in the slope? For tax rates higher than 80%, how would you describe the relationship between the tax rate and tax revenue, and how is this relationship reflected in the slope?
In panel (a), what is the slope of the line? Show that the slope is constant along the line.
In panel (b), what is the slope of the line? Show that the slope is constant along the line.
Taking measurements of the slope of a curve at three points farther and farther to the right along the horizontal axis, the slope of the curve changes from −0.3, to −0.8, to −2.5, measured by the point method. Draw a schematic diagram of this curve. How would you describe the relationship illustrated in your diagram?
Taking measurements of the slope of a curve at five points farther and farther to the right along the horizontal axis, the slope of the curve changes from 1.5, to 0.5, to 0, to −0.5, to −1.5, measured by the point method. Draw a schematic diagram of this curve. Does it have a maximum or a minimum?
For each of the accompanying diagrams, calculate the area of the shaded right triangle.
The base of a right triangle is 10, and its area is 20. What is the height of this right triangle?
Name | Quantity of labor (hours per week) | Wage rate (per hour) |
---|---|---|
Athena | 30 | $15 |
Boris | 35 | 30 |
Curt | 37 | 45 |
Diego | 36 | 60 |
Emily | 32 | 75 |
Which variable is the independent variable? Which is the dependent variable?
Draw a scatter diagram illustrating this relationship. Draw a (non-linear) curve that connects the points. Put the hourly wage rate on the vertical axis.
As the wage rate increases from $15 to $30, how does the number of hours worked respond according to the relationship depicted here? What is the average slope of the curve between Athena’s and Boris’s data points using the arc method?
As the wage rate increases from $60 to $75, how does the number of hours worked respond according to the relationship depicted here? What is the average slope of the curve between Diego’s and Emily’s data points using the arc method?
Which variable is the independent variable? Which is the dependent variable?
Suppose that in the country of Sudland, when the yearly rate of economic growth fell from 3.0% to 1.5%, the yearly rate of increase in air-borne pollutants fell from 6% to 5%. What is the average slope of a non-linear curve between these points using the arc method?
Now suppose that when the yearly rate of economic growth rose from 3.5% to 4.5%, the yearly rate of increase in air-borne pollutants rose from 5.5% to 7.5%. What is the average slope of a nonlinear curve between these two points using the arc method?
How would you describe the relationship between the two variables here?
Draw a diagram that depicts this finding with number of firefighters on the horizontal axis and amount of property damage on the vertical axis. What is the argument made by this diagram? Suppose you reverse what is measured on the two axes. What is the argument made then?
In order to reduce its payouts to policyholders, should the insurance company therefore ask the city to send fewer firefighters to any fire?
Name | Annual salary | Annual income tax owed |
---|---|---|
Susan | $22,000 | $3,304 |
Eduardo | 63,000 | 14,317 |
John | 3,000 | 454 |
Camila | 94,000 | 23,927 |
Peter | 37,000 | 7,020 |
If you were to plot these points on a graph, what would be the average slope of the curve between the points for Eduardo’s and Camila’s salaries and taxes using the arc method? How would you interpret this value for slope?
What is the average slope of the curve between the points for John’s and Susan’s salaries and taxes using the arc method? How would you interpret that value for slope?
What happens to the slope as salary increases? What does this relationship imply about how the level of income taxes affects a person’s incentive to earn a higher salary?