Assume a market with two firms 1 and 2 supplying slightly differentiated products competing against each other in what is known as Bertrand oligopoly model. If firms 1 and 2 choose prices P1 and P2, respectively, the quantity that consumers demand from firm 1 is (11 = 12'!) - 8P1 + 5F; and for rm 2 is Q3= IUD lull; + 4P1. The fixed costs of production of each rm are zero and the marginal costs are for Firm 1 c1: 1!} and for Firm 2 C2: 3. Assume further that the two rms choose prices simultaneously. {a}: Identify and graph the reaction functions of the two rms and explain intuitively their shapes. Find the equilibrium prices, quantities and profits in the Nash equilibrium of the game {b} Assume that firm 1 is a Stackelberg leader and rm 2 is a Stackelberg follower. What are the equilibrium prices, quantities and profits in this case? All sub-questions carry equal weights