4. Suppose that firm 1 and firm 2 each produce the same product and face a market demand curve given by Q = 1000 -20P. Firm 1 has a unit (marginal) cost of production c1 = 10 while firm 2 has a unit cost of c2 = 20. Firms compete by setting prices and consumers in this market will always purchase from the firm with the lower price. In addition, suppose that firms must choose an integer price. This means that firms can choose a price of $17 or $21 but not $14.99 or $19.50. a. Suppose that p1 = p2 = 30. What are the profits of each firm? Is this set of prices a Nash Equilibrium? Explain why or why not. (5 pts) b. Find a Bertrand-Nash Equilibrium of this game. Explain clearly why the prices you chose is a Nash Equilibrium. Is this the only equilibrium of this game? (10 pts) c. Given your answer in (b), what are the profits of each firm? (5 pts) d. Suppose that firm 2 could invest in a technology that lowers its unit cost to c2 = 10. How much would firm 2 be willing to pay for this technology? (5 pts)