1) 2) Finally, suppose that the two firms behave as a cartel and have the following cost functions: C,(g,) = 100q, + 0.5g7 C:(g2) = 243 The cartel faces an inverse demand function of' P(Q)=300-@ a) What is the profit maximizing level of output of each firm (cartel)? b) Calculate firm profits behaving as a cartel (if profits are shared proportional to output). ) What would be the profit maximizing level of output if the firms were a non-colluding duopoly (Cournot model)? d) What are firm profits? Consider a differentiated products market with two Bertrand competitors. The firms have identical cost functions: Cy(qy) = cqy C:(g2) = cq2 The demand function for each firm 1s a function of own price and other firm's price: g, =a bp, +dp; Gz = a+dp, bp; a. What 1s the Bertrand Nash equilibrium price and quantity (your answer will have a, b, and d). b. Suppose one of the firms operated in a monopoly market (d=0). What 1s the monopoly equilibrium price and quantity? . What does the constant \"d\" represent in the demand functions? d. How does price change with d