INTERNATIONAL ECONOMIC REVIEW Vol. 42, No. 2, May 2001 QUOTA-INDUCED CYCLES ∗ By Kaz Miyagiwa and Yuka Ohno † 1 Emory University, U.S.A. Rice University, U.S.A. We present a new framework to compare the dynamic effect of tariffs and quotas in the presence of oligopoly. Suppose that the domestic and the foreign firm play a quantity-setting game over time in a perfectly stationary economy. A Markov-perfect equilibrium has the foreign firm exporting at the constant rate under a tariff. In contrast, under the quota the rate of exports changes monotonically over the course of each year, causing seasonal fluctuations in domestic production. Quota-induced cycles can make dynamic market segmen- tation possible and raise profits for both the firms above what they earn under the equal-import tariff. 1. introduction This article presents a new framework to compare the dynamic effect of tariffs and quotas in the presence of an international oligopoly in a perfectly stationary environment, where the demand functions are time invariant, technologies are con- stant, and government policy is fixed. We suppose that one domestic firm and one foreign firm play a quantity-setting game over an infinite-time horizon and focus on a Markov-perfect equilibrium, which rules out the possibility of implicit collusion that may arise in infinitely repeated games. 2 In a perfectly stationary environment, all subgames are identical under free trade. As a result, firms play a one-shot game at each point in time, meaning that the rate of imports is constant over time. The imposition of a tariff raises the marginal cost for the foreign firm at each point in time but does not alter the stationary nature of the equilibrium: the rate of imports remains constant over time under a tariff. A quota does not increase the foreign firm’s marginal cost directly. Rather, it imposes a limit on the foreign firm’s total exports in a given period (say, a year), so how much the foreign firm is allowed to export for the remainder of a year depends on how much it has sold to date in that year. With its past exports serving as a “state variable,” the foreign firm must design a plan to allocate the quota rights over the year. An optimal strategy is not to export at a constant rate but to vary the rate over ∗ Manuscript received February 1998; revised May 1999. † E-mail: yuka@rice.edu. 1 We are grateful to the referee for detailed comments. We also thank Carl Davidson and seminar participants at various universities for helpful suggestions on the early version of this paper. 2 Rotemberg and Saloner (1989) present a model of tacit collusion in an infinitely repeated game. They find that quotas weaken the firms’ ability to collude so much that the domestic price is actually lower under the quota than under the equal-import tariff. 451