Suppose that firm 1 and firm 2 each produce the same product and face a market demand curve given byQ= 40010P. Firm 1 has a unit (marginal) cost of productionc1= 20 while firm 2 has a unit cost ofc2= 30. Firms compete by setting prices and consumers in this market will always purchase from the firm with the lower price. In addition, suppose thatfirms must choose an integer price. This means that firms can choose a price of$7 or$11 but not$14.99 or$9.50.

a) 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?

b)Given your answer in (a), what are the profits of each firm?

c)Suppose that firm 2 could invest in a technology that lowers its unit cost toc2= 20. How much would firm 2 be willing to pay for this technology