7 During the Reagan administration, economist Arthur Laffer became famous for his Laffer curve, which implied that an increase in the tax rate might decrease tax revenues, while a decrease in the tax rate might increase tax revenues.

This problem illustrates the idea behind the Laffer curve.

Suppose that if an individual puts in a degree of effort

e, he or she earns a revenue of 10e1/2. Also suppose that an individual associates a cost of e with an effort level of e.

Suppose further that the tax rate is T. This means that each individual gets to keep a fraction 1 T of before-tax revenue.

Show that T  .5 maximizes the government’s tax revenues.

Thus, if the tax rate were 60%, then a cut in the tax rate would increase revenues.