Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth

By using the Girsanov theorem¹² it is possible to derive the probability density function of Ti* as

2

1     1 2 ʌ τ^, * ʌ

^-(^α-1^σ )T_i I

2σ2T *
i

√2πσ²T*³

which is also referred to as the Inverse Gaussian distribution.¹³ The Laplace transform of T_i^* is
then given by (see Ross, 1996; Proposition 8.4.1)

e(TV = о =

∞            if α ≤ 2 σ²

with ■&* >⅜ and i ∈{E,F}.

Equation (72) shows that for σ ∈ (0, √2α) there exists a finite market entry time. However, if
productivity growth α is lower than 2σ² or equal to zero, market entry might not be realized
since E(T_i^*) diverges.¹⁴

Within the proximity-concentration trade-off framework it is again possible to derive a relation-
ship between relative fixed and variable costs which determines whether the expected market

¹² A detailed derivation is offered by Karatzas and Shreve (1991, p.196) or by Karlin and Taylor (1975, p.363).

¹³ The name ”inverse gaussian distribution” stems form the inverse relationship between the cumulant generating
functions of these distributions and those of Gaussian distributions.

¹⁴ A detailed discussion about the peculiarities of the inverse gaussian distribution can be found in Johnson, Kotz,
and Balakrishnan (1995) or Dixit (1993).

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