Exchange Rate Economics: Theories and Evidence

The economics of the PPP puzzle 79
By substituting the demand functions into the profit function and maximising
this with respect to the price charged in each market gives the following set of
first-order conditions:
p it = c t
(
εit
ε it − 1
)
i = 1, ..., N t = 1, ..., T (3.21)
where c t denotes the marginal cost of production in period t (= C ′ δ) and ε it is the
elasticity of demand with respect to local currency price in destination market i.
The system of equations in (3.21) captures the basic result of price discrimination:
the price in the exporter’s currency is a mark-up over marginal cost,where
the mark-up is determined by the elasticity of demand in the various destination
markets.
On the basis of (3.21) if the exporter faces a constant elasticity of demand schedule
then the price charged over marginal cost will be a constant mark-up and
in this case there will be complete pass-through; that is,the price in terms of the
exporters currency will stay unchanged as the exchange rate depreciates and so the
price in terms of the destination market will fully reflect the exchange rate change.
However,in this example although marginal cost is common across destinations,
it may nonetheless vary over time and the mark-up can therefore vary across
destinations. For a monopolist who discriminates across export markets,demand
schedules that are less convex (i.e. more elastic) than a constant-elasticity schedule
will produce a stabilisation of local currency price and therefore pricing to market:
as the exchange rate depreciates the mark-up will fall. However,if the monopolist’s
demand schedule is more convex (inelastic) than a constant-elasticity schedule
will produce the opposite effect – mark-ups increase as the buyer’s currency
depreciates.
The specific form of PTM in which sellers reduce the mark-up to buyers
whose currencies have depreciated,thereby stabilising the price,is known as local
currency price stability (LCPS).
Equation (3.21) could also be used to represent export behaviour in a perfectly
competitive environment. In this case the demand elasticities are infinite and independent
of destination and the firm chooses the level of output at which marginal
cost is equated to world price.
In the model considered above,the price of the good is invoiced in the exporters
own currency. What are the implications when the exporter invoices the price in
the importers currency? One implication is that if the firm is risk averse it will
try to offload at least some of the risk of currency movements by hedging in the
forward market. Feenstra and Kendall (1997) proposed a variant of the model
considered above to capture the different invoicing possibilities and also the cost of
hedging. In this model the exporter sets price (in the importers currency) in period
t − 1 for period t but the period-t exchange rate is unknown,making the currency
revenue from trade uncertain. The uncertainty,though,can be offset by selling
the importers currency on the forward market. More specifically,when invoicing