A market has two quantity-setting duopolistic firms, 1 and 2, that produce a homogenous product at the same constant marginal cost of . (1) Given an arbitrary inverse demand p(Q), where Q = q1 + q2, firm i's revenue (where i = 1 or 2) is denoted by Ri(Q) = p(Q)qi . Write down each firm's profit function as a function of revenue and cost. (2) In the Cournot-Nash equilibrium, each firm maximizes its profit. Write down the corresponding first-order condition of a firm's profit maximization (Hint: marginal revenue must equal marginal cost). (3) Express marginal revenue as a function of the price-elasticity of demand (Hint: In the current notation, e = p/Q *Q /p and since firms are identical, each firm chooses the same quantity qi = q so that Q = 2q in equilibrium). (4) Assume that elasticity is constant at e (because firms face a constant-elasticity market demand curve as in (0.1) in the previous exercise). Do the firms transfer more than the tax to consumers in equilibrium?