6. Consider a market with two firms in Cournot (quantity) competition. Market demand is given by q(p) =ap. Each firm faces a constant marginal cost of c.

a. Suppose that the government imposes a unit tax of , so that if a firm sells q units of the good, that firm owes q to the government. Find the equilibrium quantity, price paid by consumers, consumer surplus, and tax revenue. Your answers should be functions of a,, and c. Make sure you box your answers. Hint: you can think of as an increase in the firms' marginal cost.

b. Now suppose the government imposes a excise tax of, so that if pR is the price charged by firms, the price that consumers pay is p=pR(1 +). Find the equilibrium quantity, price paid by consumers, consumer surplus, producer surplus, and tax revenue. Your answers should be functions ofa,, and c. Make sure you box your answers. Note: This is the most math-intensive question on the exam. Feel free to skip this on first glance and come back to it. Hint: Start by solving for pR as a function of a, q1, q2 and .