The market for aircraft is operated as a duopoly by Boeing (firm 1) and Airbus (firm 2). The inverse demand in the market is given by P = 12 Q, where Q is the aggregate quantity. Both firms have a total cost function given by C(qi) = 4qi , i {1, 2}. (a) Find the Nash equilibrium (q 1 , q 2 ) when firms do not collude, and compute the price and profits of each firm in this equilibrium. (b) Suppose that Boeing and Airbus collude to act as a monopolist that split profits evenly. Compute the new equilibrium quantity, price and profits. (c) Now, suppose the total cost functions are C(q1) = 4q1 and C(q2) = 8q2. Find the new Nash equilibrium and compute the price and profits of each firm in this new equilibrium.