Assume for simplicity that a monopolist has no costs of production (MC=0) and faces a demand curve given by Q = 150 - P.

a) Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist's profit.

b) Suppose instead that there are two firms in the market facing the demand and cost conditions just described for their identical products. Firms choose quantities simultaneously as in the Cournot model. Compute the outputs in the Nash equilibrium. Also compute market output, price and firm profits.

c) Suppose the two firms choose prices simultaneously as in the Bertrand model. Compute the prices in the Bertrand equilibrium. Also compute firm output and profit as well as market output.

d) Graph the demand curve and indicate where the market price-quantity combination from parts (a)-(c) appear on the curve.

e) Stackelberg competition. Assume as in the previous sections that firms have no production costs (MC=0), facing demand Q = 150 - P, and choose quantities q1 and q2. Compute the equilibrium of the Stackelberg version of the game in which firm 1 chooses q1 first and then firm 2 chooses q2.

f) Now add an entry stage after firm 1 chooses q1. In this stage, firm 2 decides whether or not to enter. If it enters then it must sink cost K2, after which it is allowed to choose q2. Compute the threshold value of K2 above which firm 1 prefers to deter firm 2's entry.