Question: Discussed a players "strategic incentive" to alter his first-period actions in order to change his own second-period incentives and thus alter the second-period equilibrium. A player may also have a strategic incentive to alter the second-period incentives of others. One application of this idea is the literature on strategic trade policies (e.g. Brander and Spencer 1985; Eaton and Grossman 1986-see Helpman and Krugman 1989, chapters 5 and 6, for a clear review of the arguments). Consider two countries, A and B, and a single good which is consumed only in country B. The inverse demand function is p = P(Q), where Q is the total output produced by firms in countries A and B. Let c denote the constant marginal cost of production and Qm the monopoly output (Qm maximizes Q(P(Q) - c)).
(a) Suppose that country B does not produce the good. The 1 (> 1) firms in country A are Cournot competitors. Find conditions under which an optimal policy for the government of country A is to levy a unit export tax equal to - P'(Qm)(I - 1)Qm/1. (The objective of country A's government is to maximize the sum of its own receipts and the profit of its firm.) Give an externality interpretation.
(b) Suppose now that there are two producers, one in each country. The game has two periods. In period 1, the government of country A chooses an export tax or subsidy (per unit of exports); in period 2, the two firms, which have observed the government's choice, simultaneously choose quantities. Suppose that the Cournot reaction curves are downward sloping and intersect only once, at a point at which country A's firm's reaction curve is steeper than country B's firm's reaction curve in the (qA qB) space. Show that an export subsidy is optimal.
(c) What would happen in question (b) if there were more than one firm in country A? If the strategic variables of period 2 gave rise to upward-sloping reaction curves? Caution: The answer to the latter depends on a "stability condition" of the kind discussed in subsection 1.2.5.