Let the inverse demand curve be p(q) = a − bq. Suppose there are two firms, with constant marginal cost equal to C.
Now suppose that the two firm engage in price competition (set p) instead of quantity competition (set q).
1. (Bertrand) If both firms move simultaneously, what are their equilibrium strategies and what is the equilibrium outcome?
2. Compare the efficiency of this outcome to that of Cournot and Stackelberg.
3. If the firms have different marginal costs, how does your answer to part 1 change?
4. Explain the corner solution of one firm pricing at the monopoly’s price.