conditions are:9
Π1 [x, (n - 2)h(x) + h(z), 0] = 0
Π1H [z, (n - 1)h(x), s] = 0
(4)
(5)
Totally differentiating this system, we have x0(s) T 0 if Π12Π1H3 T 0and
z0 (s) T 0 if Π1H3 T 0. In the initial stage the government will choose the policy
to maximize welfare. Using the envelope theorem and the previous results, we
obtain the strategic incentive to export promotion as:
where ∆ > 0 is the determinant of the equilibrium system. When Π13 > 0,
which (as we will see) is always the case when the policy is subsidization, this
effect is positive under strategic substitutability (Π12 < 0) and negative under
strategic complementarity (Π12 > 0), while the result is inverted when Π13 < 0.
It is now immediate to conclude with:
SI =
(n - 1)h0(x)h0(z)Π2HΠ12Π1H3
(6)
Proposition 1. Under barriers to entry in the foreign market, a)
when the export policy increases the marginal profitability of the do-
mestic firm, there is (not) a strategic incentive to export promotion
if strategic substitutability (complementarity) holds, b) when the ex-
port policy decreases the marginal profitability of the domestic firm,
the opposite holds.
Notice that with just one domestic firm, the kind of policy does not depend
on the number of international firms. The optimal policy implies an aggressive
firm under strategic substitutability and an accomodating firm under strategic
complementarity. However, the result is sensitive to the number of domestic
firms: if this is large enough, there is a bias against export promotion (Dixit,
1984, and Klette, 1994).
Nevertheless, we can conclude with an unambiguous implication: in standard
models of quantity and price competition, the foreign market gains from an
increase in the number of international firms (since this will increase production
and lower the equilibrium price), hence, it becomes crucial to investigate what
happens under free entry.10
9 Given the symmetric equilibrium, I will drop the index i for the international firms and
use the index H for the domestic one.
10 One should keep in mind that free entry may not be always the relevant assumption.
Empirically, few firms are actually able to export. It seems that there are indeed very large
barriers to exporting, that typically take the form of fixed costs (on top of the variable cost
of shipping goods, tariffs and others). Nevertheless it appears reasonable that in a global
context, there are potential entrants in most international markets.