Production Quotas under Cartel Agreements: In exercise 25.8, we investigated the acquisition price that an incumbent firm might pay to acquire a competitor under different bargaining and economic settings. Instead of one firm acquiring or merging with another, two firms in an oligopoly might choose to enter a cartel agreement in which they commit to each producing a quota of output (and no more).
A: Suppose again that both firms face a linear downward sloping demand curve, the same constant marginal cost, and no recurring fixed costs.
(a) Under the different bargaining settings and economic environments described in exercise 25.8,3 what are the profits that the two firms in the cartel will make in terms of πM, πC , πSL and πSF (as these were defined in A(d) of exercise 25.8)?
(b) It turns out that πC = (4/9)πM, πSL = (1/2)πM and πSF = (1/4)πM for examples like this. Using this information, can you determine the relative share of profit that each firm in the cartel will get for each of the bargaining and economic settings from (a)?
(c) Assuming the cartel agreement sets xM — the monopoly output level — as the combined output quota across both firms, what fraction of xM will be produced by firm 1 and what fraction by firm 2 under the different bargaining and economic settings we are analyzing? 3 There is a total of 9 such cases: 3 market settings (Bertrand, Cournot, Stackelberg) and three bargaining settings (ultimatum game with firm 1 proposing, ultimatum game with firm 2 proposing, and the alternating offer game).
(d) Assume that any cartel agreement results in xM being produced, with each firm producing a share depending on what was negotiated. True or False: For any such cartel agreement, the payoffs for firms could also have been achieved by one firm acquiring the other at some price.
(e) Explain why the firms might seek government regulation to force them to produce the prescribed quantities in the cartel agreement.
(f) In the early years of the Reagan administration, there was a strong push by the US auto industry to have Congress impose protective tariffs on Japanese car imports. Instead, the administration negotiated with Japanese car companies directly — and got them to agree to “voluntary export quotas” to the US, with the US government insuring that companies omplied. How can you explain why Japanese car companies might have agreed to this?
(g) Suppose the firms cannot get the government to enforce their cartel agreement. Explain how such cartel agreements might be sustained as a sub game perfect equilibrium if, each time the firms produce, they expect there is a high probability that they will again each produce as the only firms in the industry in the future?
(h) If you are a a lawyer with the antitrust division of the Justice Department and were charged with detecting collusion among firms that have entered a cartel agreement — and if you thought that these agreements were typically sustained by trigger strategies, in which market setting (Bertrand, Cournot or Stackelberg) would you expect this to happen most frequently?
B: Suppose again that firms face the demand function x(p) = A −αp, that they both face marginal cost c and neither faces a recurring fixed cost.
(a) For each of the bargaining and economic settings discussed in exercise 25.8, determine the output quotas x1 and x2 for the two firms.
(b) Verify that the fraction of the overall cartel production undertaken by each firm under the different scenarios is what you concluded in a(c).
(c) Suppose A = 1000, c = 20 and α = 40. What is the cartel quota for each of the two firms under each of the economic and bargaining settings you have analyzed?
(d) In terms of payoffs for the firms, is the outcome from the cartel agreement any different than the outcome resulting from the negotiated acquisition price in exercise 25.8?
(e) Suppose the two firms enter a cartel agreement with a view toward an infinite number of interactions. Suppose further that $1 one period from now is worth $δ now. What is the lowest level of δ< $1 for each of the bargaining settings such that the cartel agreement will be respected by both firms if they would otherwise be Cournot competitors?
(f) Repeat (e) for the case of Bertrand and Stackelberg competitors.
(g) Assuming that cartel quotas are assigned using alternating offer bargaining, which cartels are most likely to hold: Those that revert to Bertrand, Cournot or Stackelberg? Can you explain this intuitively? Which is second most likely to hold?