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1.2 Strategic policy for competitive markets

I will now assume that the number of potential entrants is great enough that a
zero profit condition pins down the effective number of firms competing in the
foreign market. The equilibrium conditions are the two first order conditions,
(4) and (5), and the zero profit condition which binds on the international firms
(since these do not profit from the optimal export policy):

Π [x, (n - 2)h(x) + h(z), 0] = F

(7)


Totally differentiating the system (4)-(5)-(7) we obtain a fundamental result for
what follows:

proposition 2. Under free entry in the foreign market, a change
in the domestic policy does not affect the equilibrium strategy of all
the other firms but only their equilibrium number.

Proof: see Appendix A.

The intuition behind Prop. 2 is simple. Optimization by the foreign firms
and the free entry condition constraining their number pin down the first and
the second argument of their profit functions: their strategic variable and the
level of spillovers from the other international firms and the domestic firm. This
implies that only the number of international firms changes with the strategic
variable of the domestic firm and hence with the strategic policy, while the
strategy of the international firms is independent from the policy. Moreover, we
have:

dn    h0(zH3/h(x) <c dz            ΠHi

R 0 if Π1H3 R 0


dS = ∏H1 - h0(z)∏H2 Q and dS = £ПН - h0(z)∏H>]

In the initial stage, the government will choose the policy to maximize wel-
fare. Using the envelope theorem and the previous results, we obtain the strate-
gic incentive to promote exports:

h0(z)Π2HΠ1H3
H1 - h0(z)∏H2

(8)


Its sign is the sign of Π13, hence:

Proposition 3. Under free entry in the foreign market, when the
export policy increases (decreases) the marginal profitability of the
domestic firm, there is (not) a strategic incentive to export promo-
tion.

Notice that the result would not change in presence of more than one do-
mestic firm, as long as some entry of foreign firms takes place in equilibrium.
11

11Actually, it is immediate to verify that with nH domestic firms, the equilibrium strategy



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