There are two firms in the market for a homogenous good with (inverse) demand given by P = 255 5Q. Both firms have a constant unit (marginal) cost of production c1 = c2 = 25. Firms compete by setting prices and consumers in this market will always purchase from the firm with the lower price. If the two firms are charging the same price then they split the demand. In addition, suppose that firms can only set integer prices. This means that firms can choose a price of $20 or $25 but not $20.50 or $24.99.

a)Suppose that firm 1 charges a price p1 = 25 and firm 2 charges a price p2 = 30. What are the profits of each firm? Are these prices a Nash Equilibrium? If your answer is yes, you should show that no firm has an incentive to deviate. If your answer is no, you need to show a profitable deviation for at least one firm.

b)Suppose that firm 1 charges a price p1 = 26 and firm 2 charges a price p2 = 26. What are the profits of each firm? Are these prices a Nash Equilibrium? If your answer is yes, you should show that no firm has an incentive to deviate. If your answer is no, you need to show a profitable deviation for at least one firm

c)Now suppose that firm 1 invested in a new technology that lowered its marginal cost to c1 = 15. Firm 2's marginal cost is still c2 = 25. Find a Nash Equilibrium of this game (Hint: You need to show that no firm has an incentive to change their price from what you suggest.). Is this equilibrium unique?