the market for aircraft is operated as a duopoly by

Question 1 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 E {1, 2}. (a) Find the Nash equilibrium (qi, q2) 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) = 892. Find the new Nash equilibrium and compute the price and profits of each firm in this new equilibrium