Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth

Fiu W = Aiu tf^βu

^βu i_^βu

= Mi^κ Ii  ^κ Ω tf ^βu

with

βuδu⁰

1-^βu
κ

β_u - κ

^δu⁰

βu δu⁰

β_u - κ

βu
κ

and i ∈ {E, F}.

(60)

(61)

Finally, the cut-off productivity level for each market entry mode is derived as

κ   βu  IE ^δ .   .* K βu IF ^δ

^tfEu  β      M   and  '  = β-MM

(62)

These two equilibrium productivity levels differ from the previous cut-offs under certainty only in

the magnitude of the two parameters δ_u⁰ and βu , which are affected by the productivity uncertainty

σ.¹⁰ The magnitude of βu is derived form the fundamental quadratic equation

Ψ = ¹ σ²βu(βu — 1) + (r - δ_u)β_u - r = 0.

(63)

and decreases in σ

^dβu < 0.
∂σ

(64)

The risk-adjusted discount rate δ_u⁰ turns out to be the negative expression of Ψ. For reason-
able results δ_u⁰ needs to be strictly positive. Therefore, κ must lie between the two roots and
consequently, this last requirement necessitates that

βu > κ > 0.

(65)

Based on these two relationships it is possible to analyze the underlying market entry problem as
in the previous scenarios. The ordinal rank between the two productivity cut-offs is independent
of the growth rate α_u⁰ and the extent of uncertainty σ. It is only influenced by the comparative

¹⁰ For σ = 0 the opportunity cost rate μ — α = δ_u = r — α = δ_c.

27