Suppose two natural gas producers are competing in quality over the market demand given by the inverse demand function P(Q) = 120 - Q/2, where Q = Q_1 + Q_2. The producers' cost function are TC(Q_1) = 6 + 3/2 Q^2 _1 and TC(Q_2) = 4 + 2Q_2. (a) What output levels, Q_1 and Q_2, will the two firms produce? (b) What will be the market price per unit of natural gas? (c) What is the marginal cost of the last unit produced by producer 1? By producer 2? (d) How much profit does each producer make? (e) How much deadweight loss does the Cournot duopoly generate?