Consider a market with two firms in Cournot (quantity) competition. Mar-
ket demand is given by q(p) = a −p. Each firm faces a constant marginal cost of c.
(a) Suppose that the government imposes a unit tax of δ, so that if a
firm sells q units of the good, that firm owes q ·δ to the government. Find the
equilibrium quantity, price paid by consumers, consumer surplus, and tax revenue.
Your answers should be functions of a,δ, and c. Make sure you box your answers.
Hint: you can think of δ as an increase in the firms’ marginal cost.
(b) Now suppose the government imposes a excise tax of τ, so that if pR
is the price charged by firms, the price that consumers pay is p = pR(1 + τ). Find
the equilibrium quantity, price paid by consumers, consumer surplus, producer
surplus, and tax revenue. Your answers should be functions of a,τ, 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 τ.