Price rigidity, collusion, and booms. (This follows Rotemberg and Saloner 1986.) Suppose that a sector, with N firms, faces the demand function, p = e - bq, where e is Li.d. and uniform on [0, IJ. The marginal cost of production is equal to zero. (a) Suppose that the N firms collude to achieve the monopoly outcome. Determine the monopoly price and quantity (assuming that prices are set after e is realized). (b) Determine the profit of each firm if the sector behaves as a monopolist. (c) What is the relation between e and the incentive to cheat, that is, the incentive for any of the N firms to post a price e lower than the others?
(a) Suppose that the N firms collude to achieve the
(b) Determine the profit of each firm if the sector behaves as a monopolist.
(c) What is the relation between e and the incentive to cheat, that is, the incentive for any of the N firms to post a price e lower than the others?
(d) Suppose that there is a fixed punishment K for firms that do not cooperate. Write down e·, the value of the shock such that firms are indifferent between colluding and cheating. Derive the price charged by the sector as a function of e. What is the highest sustainable price when e exceeds e*
(e) Suppose that the punishment is that if a firm charges a price lower than other firms in the current period, the market reverts to competitive pricing in all future periods. Is this punishment credible? Assuming that firms discount the future at rate D, derive K as a function of D and N.
(f) "This model explains why markups of prices over marginal costs are countercyclicaL" Discuss this statement. (f) Suppose that firms, instead of having zero marginal cost, have zero marginal cost up to some capacity leveL at which point marginal cost becomes vertical. How would this affect the conclusions derived above?
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