Reference no: EM13874788
Suppose that the gross utility of a representative consumer is V = N 1/2 where N is the number of products. Their net utility is U = V (N) - P = N 1/2 - P where P is the equilibrium price when there are N firms. Suppose that P = 1/N , so that as the number of firms increases the equilibrium price falls. Assume that firms divide the market equally. Marginal cost of production is zero, but each firm incurs a fixed cost equal to f = 0.64. Normalize the number of consumers at 1. Suppose that α consumers belong to a buyer group and k is the percentage of firms that belong to a seller group.
(a) What is the monopolistically competitive price and equilibrium number of firms?
(b) Suppose that the buyer group is offered a requirements contract by the seller group for price P1. Under what circumstances would they accept the deal, assuming the number of firms is fixed at the free-entry monopolistically competitive number?
(c) What are the profits of the seller group if the requirements contract is accepted, assuming the number of firms is fixed at the free-entry monopolistically competitive number?
(d) What are the aggregate benefits to the two coalitions from the requirements contract? Is the collective contract a potential Pareto improvement from the perspective of the two coalitions when k = .10? k = .90? What is the minimum value of k for the collective contract to be a potential Pareto improvement for the two coalitions? Assume that the number of firms is fixed at the free-entry monopolistically competitive number.
(e) For this and all following parts assume the following: (i) f is not sunk and the number of firms can adjust; and (ii) that k = .1 and α = 0.99. Show that the profits of a firm not included in the seller coalition are negative. What happens in the long run to the number of firms?
(f) What is the aggregate increase in profits for firms in the coalition?
(g) Does the requirements contract increase the joint surplus of the two coalitions? Would it be for these parameter values if the number of firms was fixed?
(h) Is the requirements contracts socially efficient in the long run? Why?
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