Outsourcing, Complementary Innovations and Growth

final products are sold to households together with those supplied by vertically integrated firms.

3 Industrial Organization

3.1 Production

At time t the instantaneous equilibrium is found by solving the model backwards from final produc-
tion to R&D given the number of blueprints invented for each organizational mode. Varieties can
be sold to final customers by two types of firms: vertically integrated firms and final assemblers. A
typical vertically integrated firm faces a demand curve derived from (4) and a marginal cost equal
to λ. It chooses its scale by maximizing its operating profit

‰ = PυУу - -X

where x_υ is the amount of the intermediate input produced and y_υ = x_υ is the final output. Optimal
output and price are then given by:

1

a ɪɪɑ

Xυ = Уу = A ^-
and

Pυ = ^-∙                                           (8)

a

Replacing these values in (6) results in operating profit equal to

a

'' = (1 - a) a(-) ¹~^a ,                                       (9)

which is an increasing function of product differentiation (1 — a) and a decreasing function of the
marginal cost (λ).

Turning to the outsourcing mode, there is a one-to-one equilibrium relationship between the
number of matched assemblers, the number of matched intermediate suppliers, and the number of
outsourced varieties; they are all equal to f. The joint surplus of a matched pair of entrants is given
by the revenues from the final sales of the corresponding variety p_sy_s. This is divided according to
the bargaining weights of the two parties. Accordingly, a share (1 — ω) goes to the final assembler

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