with c0(∙) > 0. It follows that:
Πi (xi,βi , 0) = xip (xi ,βi) - c(xi)
(2)
where βi = kn=1,k6=i h(xk). In case of perfectly substitute goods, we have
pi = p(xi + βi) and h(xi) = xi .
As a second example let us consider a general class of models of price com-
petition. Any model with direct demand Di = D pi, Pjn=1,j6=i g(pj) where
D1 < 0, D2 < 0, g(p) > 0andg0 (p) < 0, is nested in our general framework
after setting xi ≡ 1/pi and h(x) = g(1/x), so that h0(x) = -g0(1/x)/x2 > 0.
Under constant marginal costs, gross profits become:
Πi(xi,βi,0) =
(ɪ - c)d(⅛ ,βi)
xi xi
(3)
We will assume that strategic complementarity typically holds (Π12 > 0) as it
does under weak conditions. As we will see later on, examples include many well
known demand functions like the constant elasticity demand, the Logit demand
and the demand with constant expenditure, while the linear demand case is not
nested in our general model (indeed, in that case, a free entry equilibrium does
not exist since profits are increasing in the number of firms). Another important
case which is nested in this specification is the model of price competition with
demand a la Dixit and Stiglitz (1977), which has been widely employed in the
new trade theory (Krugman, 1980; Helpman and Krugman, 1985), and is studied
in Appendix D.
In these basic models of the market structure we can introduce different
policies for export promotion. In the rest of this section I will derive the general
results and in the next two sections I will apply them to the typical tools of
trade policies and to the exchange rate policy. The general discussion will be
divided in the two crucial cases: in the first the foreign market is closed, in
the sense that there are barriers to entry, in the second, the foreign market is
competitive in the sense that entry is free.
1.1 Strategic policy for closed markets
Let us briefly summarize the results on the optimal unilateral trade policy for
a foreign market with a fixed number of firms. More specifically, assume that
si =0forallfirms except the domestic one, whose policy s is chosen by the gov-
ernment of its home country at an initial stage. Consider the second stage after
a policy s has been chosen and assume that a unique Nash equilibrium exists
with the same strategy for the foreign firms, say x, and a different strategy for
the domestic one, say z, depending on the policy s. The first order equilibrium