Uncertain Productivity Growth
the investor will neglect the export market entry for the sake of the FDI mode. The distance
between E(TFF) and E(TE) in figure 8 represents the prolongation of market entry by negligence.
Inversely, it can be concluded that for relative cost patterns which lead to a productivity cut-off
ranking with i?F. < ¾, the FDI mode has a first-order stochastic dominance over the export
mode and there will be no market entry prolongation.
4 TIMING & COMPARATIVE STATICS
By considering the partial derivative of equation (71) with respect to σ it is possible to assess the
impact of a volatility change in productivity on the expected market entry time. The differential
results as
∂E(T*) 1 ∕tf*λ 1 1 ∂tf*
(75)
-- i = σ-------l ln — +-------
dσ (α - 1 )2 Vo∕ (α - 1 σ2) tf* dσ
, C , 1 O
with ~l > 1 and α > 2σ2.
Thus, whether a change in uncertainty results in a positive or negative effect on the expected
market entry time, decisively depends on the partial differential on the right hand side of equation
(75). A change in uncertainty affects the optimal productivity levels tf* through two channels.
The first effect of an increase in σ is a rise in the option value of each market entry mode which
is captured by
∂σ
>0
for
κ ≥ 1.
(76)
The intuition for this monotonic positive effect is that an increase in uncertainty, incentivises the
postponement of the investment decision into the future (higher #*) in order to gain additional
information on the productivity development.
The second effect is a change in the expected investment value ½(tf) which itself depends on the
adjusted discount rate δu0 .
For linear periodical cash-flows (κ = 1) the discount rate becomes independent of σ with
∂δu = 0. (77)
∂σ
Summing up theses two effects, in this particular case both market entry modes’ expected market
entry time strictly increases in σ . Furthermore, since the productivity cut-offs of both entry
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