The supply and demand curves in a particular market are given by the following equations:

Demand: Q = 100 - P Supply: Q = P, where P is the price of the good and Q is the quantity supplied or demanded.

a. Solve for the market-clearing price in the absence of a tax.

b. Suppose that the government taxes the good at a rate of t. Specifically, if P is the price that demanders pay for the good, then the government collects tP as tax, and the supplier receives (1–t)P. Calculate the equilibrium values of P and Q.

c. Solve for the tax rate that will maximize the government’s revenue.