Outsourcing, Complementary Innovations and Growth

occurs at ω = a. When assemblers’ R&D costs are relatively small, their profit margin relatively
large, and supplier bargaining power weak, the majority of entrants are final assemblers reducing
their chances of being matched (η (?) < 1). In this situation, the impact of ω on the propensity to
outsource becomes unambiguously positive. The reason is that, by fostering intermediate entry and
hampering final entry, stronger supplier bargaining power (larger ω) raises the matching probability
of final assemblers.

4 The Speed of Innovation

4.1 Vertical Integration

When condition (26) does not hold, no labor is allocated to specialized innovation (L¹_s = L¹_m = 0),
so no new specialized patent is ever created: s = m = 0 and asymptotically f = 0. Along a balance
•

growth path, we have v∕v = g_v and E = 0.⁸ This allows us to write the full employment condition
(23) and the Euler condition (2) as:

L = kv (gv + J) + aE

and

(1 - a) E
kv

These can be solved to yield the equilibrium values of expenditures and the speed of innovation:

^e^ — ^{l +} p^kv^{, g<}v — ^{(1 - a})~₇    ^aP ^- δ-                         ⁽²7⁾

kv

Under vertical integration innovation is boosted by weak time preference (small p), slow depreciation
(small J), large size of the economy (large L), small R&D cost (small k_v), and pronounced product
differentiation (small a). While a large size of the economy also gives large expenditures, weak
time preference and small R&D costs depress them. A high rate of depreciation hence lowers both
the speed of innovation and expenditure by reducing the incentive to innovate and diverting labor
⁸The initial stock of specialized blueprints depreciates through time and asymptotically disappears since it is not
refilled. See Naghavi and Ottaviano (2008a) for details.

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