Exchange Rate Economics: Theories and Evidence

The new open economy macroeconomics part 2 279
exporter’s (importer’s) currency is preferred when E is globally convex (concave)
with respect to S because profits are larger (smaller).
Exchange rate variability will clearly affect the variance and expectation of
profits but since the first-order derivative of profits with respect to the exchange
rate is identical under the two invoicing strategies,the first-order effect on the
variance will be the same and so risk aversion does not matter. The effects on
expected profits are,of course,different under the two pricing strategies. Pricing
in the importer’s currency,the profit function is linear in the exchange rate and
expected profits are not affected. There are two effects on expected profits when
the firm prices in exporter’s currency. First,when the elasticity of demand is
greater than unity the cost function is convex and a rise in demand will raise costs
more than a decline in demand lowers costs and so expected profits will be lower
and there will be an incentive to price in the importer’s currency. However,to set
against this the expected level of demand will also rise,since demand is a convex
function of the exchange rate and is proportional to S µ ,where µ is the elasticity
of demand; this will raise expected profits when pricing in the exporter’s currency.
The first effect dominates when (η − 1)µ > 1,where η defines the convexity of
the cost function.
Bacchetta and van Wincoop extend this base-line model to the situation where
the domestic firm is competing with a number of other firms in the same country
and in other countries. In the case where all of the firms are in the same country they
consider a particular industry where N exporting firms from the home country sell
in the market of the foreign country,which is assumed to have N ∗ exporting firms
and the market share of the exporting country is defined as: n = N /(N + N ∗ ).
Assuming CES preferences with elasticity µ>1 among the different products
then the demand for firm j is:
D(p, P ∗ ) =
1
N + N ∗ (
pj
P ∗ ) −µ
d ∗ ,(11.13)
where p j is the price set by the firm measured in the importer’s currency and d ∗ is
the level of foreign spending on goods in the industry (equal to the nominal level
of spending divided by the industry price index). If it is assumed that a fraction, f ,
of home country firms sets a price, p E ,in their own (i.e. exporter’s) currency,and
a fraction 1 − f sets price in the importer’s currency, p I ,and foreign firms set a
price p H ∗ ,it can be shown that the overall price index faced by the consumers is
given by: 1
P ∗ = (( 1 − n) ( p H ∗) 1−µ + nf
(
p E /S ) 1−µ + n(1 − f )
(
p
I ) 1−µ) 1/1−µ. (11.14)
Bacchetta and van Wincoop consider two types of equilibrium: a Nash equilibrium
in which each firm makes an optimal invoicing decision conditional on
the invoicing decisions of all other firms and,since there will be multiple Nash
equilibria,a coordination equilibrium which is the Parato optimal Nash equilibria
for the exporting country’s firms. The coordination equilibrium is found by