The inverse market demand curve for bean sprouts is given by P(Y) = 100−2Y , and the total cost function for any firm in the industry is given by TC(y) = 4y.
(a) The marginal cost for any firm in the industry is equal to ______. The change in price for a one-unit increase in output is equal to ______.
(b) If the bean-sprout industry were perfectly competitive, the industry output would be 48 , and the industry price would be ______.
(c) Suppose that two Cournot firms operated in the market. The reaction function for Firm 1 would be y1 = ______. (Reminder: Unlike the example in your textbook, the marginal cost is not zero here.) The reaction function of Firm 2 would be ______. If the firms were operating at the Cournot equilibrium point, industry output would be ______, each firm would produce ______, and the market price would be ______.
(d) For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graph below.
(e) If the two firms decided to collude, industry output would be ______ and the market price would equal ______.
(f) Suppose both of the colluding firms are producing equal amounts of output. If one of the colluding firms assumes that the other firm would not react to a change in industry output, what would happen to a firm’s own profits if it increased its output by one unit? ______.
(g) Suppose one firm acts as a Stackleberg leader and the other firm behaves as a follower. The maximization problem for the leader can be written as ______. Solving this problem results in the leader producing an output of 24 and the follower producing ______. This implies an industry output of ______ and price of ______.