Two firms compete in a market by selling imperfect substitutes (i.e. differentiated products). The demand equations for each firm are given by the following equations:

q1 = 50-p1+p2

q2 = 50-p2+p1

a.) Suppose the marginal cost of each firm is $10 and both firms compete by simultaneously choosing price. Calculate the Bertrand Nash equilibrium price, quantity and profits for each firm.

b.) Suppose Firm 1's marginal cost has increased to $20, but Firm 2's marginal cost stays at $10. Calculate the Bertrand- Nash equilibrium price, quantity and profits of each firm. If both firms sell perfect substitutes, what would be the Bertrand Nash equilibrium?