A person's annual labor supply, measured in hours worked per year, is given by

400 * sqrt(Wn)

where is the after-tax wage rate. Assume that the before-tax wage rate is fixed at $36 (i.e., that before-tax wages do not change in response to income taxes and that labor supply bears the entirety of both statutory and economic burden).

a. Write it out for a person's annual income tax payment as a function of the tax rate, , where can range from 0 to 1 (i.e., from 0% to 100%). It may help to break this into steps:

i. Write the values for the after-tax wage rate as a function of the tax rate. Reminder: the before-tax wage rate is $36 per hour.

ii. Now that you have a value for the after-tax wage rate, write a formula for the person's annual labor supply as a function of the tax rate (i.e., plug your formula for the after-tax wage rate in for in the labor supply equation given at the beginning of the problem).

iii. Now that you have a values for the person's annual labor supply, write a formula for the person's annual income (i.e., the product of labor supply and the pre-tax wage rate) as a function of the tax rate.

iv. Now that you have a values for the person's annual income, write a formula for the person's annual tax payment (i.e., the product of the tax rate and annual income) as a function of the tax rate.

b.Calculate the amount of tax revenue at = 0, 0.2, 0.4, 0.6, 0.8, and 1.0. (You'll need to use a calculator or computational software like Excel. Round each answer to the nearest dollar.)

c. Sketch the general shape of the Laffer curve based on your calculations from part b. (The tax rate goes on the horizontal axis and tax revenue goes on the vertical axis.)

d. Suppose that the government currently imposes a tax rate of =0.80. What advice would you give? Explain your answer.