Problem
A homogeneous-good duopoly faces an inverse market demand function of p = 50-Q.
I. Assume that both firms face the same constant marginal cost, MC1 = MC2 = 10. Calculate the output of each firm, the market output, and the market price in a Nash-Cournot equilibrium.
II. Re-solve part (I) assuming that the marginal cost of firm 2 rises to MC1 = 25.
III. Explain the equilibrium outcome that would arise if the firms engaged in Bertrand (price) competition, rather than Cournot (quantity) competition, assuming that their marginal costs were equalized as in part (I).