Consider the Bertrand duopoly discussed in class. Assume each firm has constant marginal cost c = 10 and zero fixed cost. Each firm chooses a price Pi 0. The market demand is given by Q = 130 P, where P = min{P1, P2} is the market price. Refer to the notes for more details on how payoffs are computed.

a) (2pts) If firm 1 is the only firm on the market, what price would this monopolist charge?

b) (2pts) In the Bertrand model with both firms on the market, if firm 2 chooses a price higher than the monopoly price, what is firm 1's best response?

c) (3pts) Use payoffs to explain why (P1 = 10, P2 = 10) is Nash equilibrium.

d) (3pts) Suppose both firms choose the monopoly price. How much profit would each firm make? Explain why it is not Nash equilibrium.