tell us that after a devaluation the domestic firm will increase its production
level. Under barriers to entry, as long as strategic substitutability holds, the
other firms will decrease production so that the market share of the domestic
firm increases (as it was shown by Dornbush, 1987): this creates a strategic
incentive to devaluate.20 Also under free entry the domestic firm expands its
market share, but the other firms produce the same as before the devaluation,
while some of them exit the market.21 Summarizing, we have:
Proposition 6. Under quantity competition, a) when the number
of firms is exogenous there is a strategic incentive for competitive
devaluations if strategic substitutability holds and b) when entry is
free there is always a strategic incentive for competitive devaluations.
Notice that a devaluation always increases exports. When entry is free and
goods are perfect substitutes, the elasticity of domestic production with respect
to the exchange rate is simply (σ + μ) 1, that is decreasing in the elasticity
of the marginal cost σ and in the mark up μ = [Ep — c(z)] /c(z). Since the
devaluation does not affect the equilibrium price, the elasticity of exports Ezp
to the exchange rate is just 1 + (σ + μ) 1 > 1.
3.2 Competitive devaluations with Bertrand competition
The case of price competition is the most interesting, since it is the usual case
under study in macroeconomic models on the exchange rate and probably the
most realistic for our purposes.
Imagine again an initial situation where all the exchange rates are unitary.
In particular, the price of the foreign currency in terms of domestic currency, E,
is initially unitary. This implies that if pH is the price of the domestic good in
foreign currency, the price of the same good in domestic currency is рн = EpH.
If the latter is constant, a devaluation (an increase in E) will reduce the price
in foreign currency, and an appreciation of the exchange rate will increase it.
However, prices in domestic currency for foreign segmented markets can be
changed after a devaluation and our purpose is exactly to check how they are
changed.
Since production takes place at home and demand depends on prices in
foreign currency, the relevant profit function for the domestic firm is:
∏H = (ph — c) D hpHH-, X g(pj)i =(EpH — c) D (pH,βH) (18)
which can be rewritten in our framework with z = 1/pH and s = E — 1. With
such a change of variables, the strategic variable for each firm becomes the price
20 But it also creates a negative terms of trade effect which can eliminate the strategic
incentive to devaluate if there are many domestic firms.
21 In this case, when there are many domestic firms, there is not a terms of trade effect and
a devaluation remains desirable from a strategic point of view.
17