Consider a Cournot competition model with market demand P(Q) = 1 Q. Two firms have different cost functions: TC1(q1) = c1q1 and TC2(q2) = c2q2, where...

Consider a Cournot competition model with market demand P(Q) = 1 − Q. Two firms have different cost functions: TC1(q1) = c1q1 and TC2(q2) = c2q2, where c1 < c2. Explain why total welfare in Cournot equilibrium is WC = 1/2Q^2+(q1)^2 1+(q2)^2 (a) , where qi is equilibrium output of firm i and Q = q1 + q2. (b) Imagine that the total output produced in the Cournot equilibrium could be allocated across firms in a different way. Which allocation would be socially optimal? (c) Suppose that the firms form a cartel. What would the ideal output of that cartel be? How is production allocated across firms? (d) Explain why the ideal cartel allocation would be hard to implement in the presence of antitrust scrutiny.(e) Explain why total welfare under cartel is Wm = 3/2(Qm)^2 , where Qm is the cartel output. (f) Are there values of c1 and c2 such that consumer welfare goes up as a result of cartelisation? Interpret. (g) Suppose that c1 = 0. Are there values of c2 such that social welfare goes up as a result of cartelisation? Interpret.