in foreign currency (but on the basis of its value in terms of domestic currency,
which is what matters in the profit function). Clearly, for all the international
firms except the domestic one, the price is the same in foreign and domestic
currency, pj = pj for j = H.
Defining with μi = (pi — c) /c the mark-up of firm i, and with ei = —p* Di / D >
1 its perceived price elasticity of demand, we can express the equilibrium first
order conditions as:
while the second order conditions require ηi < 2ei, where ηi ≡ — p*D11∕D1 is
the price elasticity of the slope of demand and represents the degree of convexity
of the demand function.22
μi =
ei -
As usual, the incentives to change strategy for the domestic firm depend on
the cross effect ΠiH3 = —p*H2 [D +p*HDi], which is positive in equilibrium. Hence,
the price of the domestic firm in foreign currency p*H is always decreasing in the
exchange rate, that is after a devaluation. In general, Prop. 1 implies that a
competitive devaluation is not desirable under barriers to entry. Such a policy
forces the domestic firm to decrease its price in foreign currency, which induces
also the other firms to do the same, reducing profits for all firms in the market.
Actually, there is a strategic incentive to appreciate the currency, which induces
the domestic firm to increase its own price in foreign currency and the other
firms to do the same.23
When entry is free, the domestic firm does not obtain a strategic advantage
when induced to increase its own price because this would promote entry in the
foreign market. According to Prop. 3, there is a strategic incentive to devaluate
the exchange rate. This would reduce the price of the domestic firm in the
foreign currency. Foreign firms would not change their own prices, but fewer
would enter in the market so that the market share of the domestic firm would
expand. In this case, a devaluation has also a direct beneficial effect, since it
increases revenues of the domestic firm in domestic currency; the positive direct
and strategic effects of a devaluation should be compared with the costs in
terms of a higher price of imports, which is beyond the scope of this discussion.
What matters here, is that the usual claim that devaluations give a strategic
22Notice that a devaluation has always a direct positive effect on the profit of the domestic
firm, since it increases revenues in domestic currency. At the same time, there are direct costs
from a devaluation, for instance in terms of higher prices of imports. However, these are not
the effects we are interested in, since the case for a strategic advantage for the domestic firm
depends on the indirect effect on the equilibrium strategies.
23Again, this is just the strategic incentive for the government: an appreciation would
also have a negative direct effect on profits, reducing the mark-up of the domestic firm, and
finally, it will induce other effects for the society like a reduction in the price of imports.
The comparison between these direct effects and the strategic effect provides the optimal
unilateral policy, but the crucial point, here, is that there is not a strategic incentive to
implement competitive devaluations when domestic firms export in markets with barriers to
entry.
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