Outsourcing, Complementary Innovations and Growth



where r is the bundling parameter defined in (24). Both its sides being constant, (25) is satisfied
only for a zero-measure set of parameter values. Therefore, in general, specialized and vertically
integrated blueprints are not invented together in equilibrium. In particular, only the former are
created when

ks vp (1 - a) 1 1 “
kυ fo (1 - ω) η(r)

(26)


and only the latter when the reverse is true. Hence, we have:

Proposition 1 Firms choose outsourcing rather than vertical integration if and only if A > A.

Higher initial experience in vertically integrated (vo) or in specialized processes (fo) makes new
blueprints of the same type less costly to invent. Outsourcing is hence selected when there is relatively
higher initial experience in outsourcing (small
Vo/ fo); when specialized final assemblers have a high
chance of finding specialized intermediate suppliers (high
η(r)); when product differentiation is weak
so that the profit share of revenues of vertically integrated firms is small (small
1 a) relative to the
share appropriated by final assemblers through bargaining (large
1 ω); when vertical revenues are
relatively low due to large gains from specialization (large
A) and little intermediate underproduction
is caused due to sufficient supplier bargaining power (large
ω) ; and when the blueprints for specialized
assembly are relatively cheap compared with those for vertically integrated production (small
ks∕kυ ).

The matching probability of specialized assemblers itself depends on the relative R&D costs
(ks∕km), the relative profit margin of final assemblers and intermediate suppliers ((1 a) /(1 ω)),
and the supplier bargaining power (
ω). When assemblers’ R&D costs are relatively large, profit
margin relatively small, and supplier bargaining power strong, the minority of entrants are final
assemblers, so they are surely matched (
η (r) = 1). In this case, their matching probability is unaf-
fected by marginal parameter changes. Here, stronger supplier bargaining power has two opposite
effects: it promotes intermediate production but at the same time discourages final production.
While the first effect fosters outsourcing, the second hampers it. Higher product differentiation
(small
a) reinforces the second effect because it makes demand more elastic, hence more sensitive to
small price differences. High intermediate prices due to a large
ω thus map into small final quantities
sold. The best scenario for outsourcing strikes the optimal balance between those two effects, which

14



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