Outsourcing, Complementary Innovations and Growth



As under vertical integration, in both cases innovation is fostered by weak time preference (small
p), slow depreciation (small J), large size of the economy (large L), small R&D cost (small
ks or km),
and pronounced product differentiation (small a). A large size of the economy also supports large
expenditures whereas weak time preference as well as small R&D costs depress them. The impact of
product differentiation on expenditure is different under the two matching cases. The reason is that
the annuity value of the initial stock of blueprints depends positively on the dividends to assembler
patents and negatively on the matching probability of new assembler entrants. When matching is
certain
(r > 1), little differentiation (large a) depresses dividends and thus expenditures. When
matching is uncertain (r < 1), little differentiation depresses the matching probability more than
the dividends, which sustains expenditures. Finally, when assemblers are uncertain about finding
a partner, higher supplier bargaining power (larger
ω) increases assemblers’ matching probability
by encouraging supplier entry. This reduces expenditures and promotes innovation
(dgm∕dω > 0
provided that
gm > 0). On the other hand, when assemblers are surely matched (r > 1) a larger ω
is associated with larger expenditures and slower rate of innovation. This is because the matching
probability no longer plays a role, while the return to assembly falls, thus discouraging the creation
of new assembler blueprints.

4.3 Bargaining Power

We now analyze the role of the bargaining weight ω on our results. Particularly, we highlight a direct
link between innovation and the proportion of suppliers over assemblers that enter the market, r,
which is in turn determined by the bargaining weight granted to each side. The top panel of Figure
2 displays the matching probability of final assemblers a a function of ω. It shows that a higher
ω encourages supplier entry thereby raising assembler matching probability until there is an equal
number of the two types of entrants. A higher number of suppliers thereafter only reduces their own
matching probability, while leaving the assemblers’ unchanged.

The middle panel of Figure 2 shows the impact of ω on the speed of innovation. The flat line
represents the innovation rate under vertical integration, which shows that outsourcing yields a

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