Exercises refer to the Laffer curve, originated by the economist Arthur Laffer. An idealized version of this curve is shown here. According to this curve, decreasing a tax rate, say from x₂ percent to x₁ percent on the graph, can actually lead to an increase in government revenue. The theory is that people will work harder and earn more money if they are taxed at a lower rate, so the government ends up with more revenue than it would at a higher tax rate. All economists agree on the endpoints—0 revenue at tax rates of both 0% and 100%—but there is much disagreement on the location of the tax rate x₁ that produces the maximum revenue.

An economist might argue that the models in the two previous exercises are unrealistic because they predict that a tax rate of 50% gives the maximum revenue, while the actual value is probably less than 50%. Consider the function

where y is government revenue in millions of dollars from a tax rate of x percent, where 0 ≤ x ≤ 100.
(a) Graph the function, and discuss whether the shape of the graph is appropriate.
(b) Use a graphing calculator to find the tax rate that produces the maximum revenue. What is the maximum revenue?

Transcribed Image Text:

0 Maximum revenue x1 X2 Tax rate (percent) 100x