Whenever (27) is violated, the outside option of the MNE dominates its out-
sourcing payoff. This occurs when trade costs are small (τ large) and the bar-
gaining power of the MNE is weak (β large). Intuitively, outsourcing is un-
appealing with respect to intermediate export when exporting intermediates is
cheap and when the hold-up problem for the supplier is big (since in such a case
intermediate production is small).
5 Choice of supply mode
In this section we determine the number of Y -firms that choose modes X , E ,
or O in equilibrium. We start with considering a situation in which no firm will
ever choose mode O. This is the case when (27) is violated. The opposite case
is addressed next.
5.1 Case 1: Intermediate exports dominate outsourcing
When (27) does not hold, mode O is dominated by mode E. Recalling that
m and n are the numbers of firms adopting modes E and O respectively, the
violation of (27) implies n = 0 for all parameter values. Then (m,n) = (m*, 0)
is an equilibrium distribution of firms between modes E and X whenever no
firm wants to change its mode. This happens for interior outcomes m ∈ (0, 1)
whenever:
∆χ,E(m) ≡ Πχ - ∏e = 4A(m, 0) τ - б4A2(m, 0) τ2 = 0 (28)
and for corner outcomes m =1 (m =0) whenever ∆X,E (m) < 0 (> 0). In (28)
the market potential measure is obtained by solving (3) after substituting for
the equilibrium prices (6) and (14):
A(m, 0) = ∣ - 2m + m2 + mL) - (1 - m). (29)
τm
Solving (28) for m then yields:
m* = L — 1. (30)
which can be shown to be a stable equilibrium since ∂∆χ,E/∂rn∖m=m∙ > 0.
When L> 16 (L<8)allfirms choose mode E (X), that is, m =1 (m =0).
To sum up, we have:
Proposition 1 When β < τ/2 FDI plus outsourcing (mode O) is never chosen.
The choice between final exports (mode X) and FDI plus intermediate exports
(mode E) is unaffected by trade costs and depends only on market size. In
particular, the share of firms choosing FDI increases with market size.
Trade costs are immaterial for the choice of mode because their changes
affect modes X and E in the same way.
12
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