In an economy, the supply curve of labor, \(S\), is given by

\[ S=-100+200 w_{n} \]

where \(w_{n}\) is the after-tax wage rate. Assume that the before-tax wage rate is fixed at 10.

a. Write a formula for tax revenues as a funccion of the tax rate, and sketch the function in a diagram with the tax rate on the horizontal axis and tax revenues on the vertical axis. (Hint: Note that \(w_{n}=(1-t) 10\), where \(t\) is the tax rate, and that tax revenues are the product of hours worked, the gross wage, and the tax rate.) Suppose that the government currently imposes a tax rate of 70 percent. What advice would you give it?

b. Try this problem if you know some calculus: At what tax rate are tax revenues maximized in this economy?