the optimal production is unaffected by these restrictions as well. Hence, the optimal
output is the same irrespective of whether the firm’s flexibility is restricted or not. This
is due to the fact that marginal revenue with respect to the exchange rate is independent
of the restrictions. That is why Broll and Wahl (1997) derive an equivalent result for a
fully flexible firm. In contrast to the production decision, the optimal hedge portfolio,
(H*, z*), depends on the restrictions as will become clear later.
Proposition 1 states that the distribution of the exchange rate does not affect optimal
production. This statement, however, has to be interpreted with care since it only holds
for a given call option premium C . As is well-known from the option pricing literature,
an increase in the volatility of the exchange rate makes currency options more valuable
(see, e.g., Sercu and Uppal, 1995). Thus, it will result in an increase in the call option
premium C. Then, cz(Q*) = Pd + Pf C and the convexity of the cost function imply that
the firm’s optimal output increases in C and, hence, in the volatility of the exchange rate.
This is summarized in the following statement.
Corollary 2 When currency call options with strike price Pd/Pf are available, the re-
stricted export flexible firm’s optimal output, Q*, increases in the call option premium
C which in turn increases in the volatility of the exchange rate. It follows that the firm
produces more as the exchange rate becomes more volatile.
An immediate implication of Corollary 2 is that export volume and exchange rate
volatility should be positively related in countries where export flexibility prevails.9
We now turn to the question of how the firm’s optimal production decision is affected
by the existence of exp ort flexibility. As shown by Benninga et al. (1985), Kawai and
Zilcha (1986) and others, the optimal output of an export-inflexible firm, Qi*nflex, which
is obliged to export its entire output is implicitly given by c,(Q*nflex) = FPf. Comparing
this optimality condition and the one given in Proposition 1 yields cz(Qi*nflex) = FPf <
9Together with the theoretical results of Franke (1991), Dellas and Zilberfarb (1993) and Broll and
Eckwert (1999), Corollary 2 might therefore explain the positive empirical relation between exchange
rate volatility and the volume of international trade found in a number of studies that are surveyed by
McKenzie (1999).
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