Q5 (4 marks). 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 the price. Calculate the Bertrand-Nash equilibrium price, quantity and profits of 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?