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Q2. (Cournot Duopoly) Firms 1 and 2 produce a homogeneous product. Firm i chooses to produce quantity qi E R+ at a unit cost ci, i.e., the total cost to produce quantity qi is ci( qi) = Ciqi. The market clearing price is P(Q) = a - bQ where Q = q1 + 92 is the aggregated quantity. (5) (a) Write down firm 's profit maximization problem and find best response function. (5) (b) Find a Nash equilibrium. For (c-d), assume a = 200, b = 1, c1 = C2 = 20. (5) (c) Calculate the social surplus (i.e., sum of payoffs of two firms) in equilibrium. (5) (d) Now, a social planner wants to maximize social surplus. Find the aggregated quantity and social surplus for the socially efficient outcome