13. (10 points) Suppose P = 1602Q is the inverse demand for fuel and P = 40+2Q is the inverse supply of fuel. Calculations are preferred, but you may use a graph for partial credit.

(a) Without a tax, what is P and Q?

(b) What is the consumer surplus and producer surplus, without a tax?

(c) If the tax on fuel is set at $20, how much fuel will be purchased? You might assume that the buyers pay the tax (but it doesn't matter).

(d) What is the deadweight loss of the tax?