Consider the two firm Bertrand duopoly studied in class. Firms 1 and 2 set prices p1,p2 0 simultaneously (assume that the firms can set prices that are any positive, real number). Whoever sets the lowest price supplies the whole market while if the two firms set the same price the firms split the market equally. Suppose that the marginal cost of production of both firms is 20 and the demand is given by:

Q = 60 21P.

Part a: [5 pts] What is the best response of firm 1 if firm 2 sets a price of 80? Justify your answer.

Part b: [5 pts] What is the best response of firm 1 if firm 2 sets a price of 25? Justify your answer.

Part c: [5 pts] What is the best response of firm 1 if firm 2 sets a price of 15?

Part d: [5 pts] What is the Nash equilibria of this game? What are the profits of each firm in the Nash equilibrium?

Part e: [Extra Credit +10] Now suppose that the game is modified so that each firm faces a fixed cost of production of 10. In other words, each firm faces a per-unit cost of 20, but on top of this cost, must pay an additional cost of 10 if the firm produces. For example, if firm 1 chooses a price of p1 < p2, then firm 1's profits are:

1 60 2p1 (p1 20)10.

If the firm doesn't produce (for example if firm sets price p1 > p2), then the firm does not need to pay the fixed cost nor the marginal cost. What are the Nash equilibria of this game? Justify your answer.