Outsourcing, Complementary Innovations and Growth

weight of intermediate suppliers is also large (resp.small) with respect to the bargaining weight of
final assemblers. These results are amplified in sectors with pronounced product differentiation.

The rest of the paper is organized as follows. Section 2 presents the basics of our model. Section
3 investigates the industry equilibrium. Section 4 discusses the consequences of firms’ organizational
choices on the speed of innovation. Section 5 concludes.

2 The Model

2.1 Consumption and Saving

There are L infinitely-lived households with identical preferences defined over the consumption of a
horizontally differentiated good C. The utility function is assumed to be CES with unit elasticity of

intertemporal substitution:

where p > 0 is the rate of time preference and

is a quantity index in which c(i,t) is the consumption of variety i, n(t) is the number of varieties
produced, and a is an inverse measure of the degree of product differentiation between varieties.
Households have perfect foresight and they can borrow and lend freely in a perfect capital market
at instantaneous interest rate R(t).

Using multi-stage budgeting to solve their utility maximization problem, households first allocate
their income flow between savings and expenditures. This yields a time path of total expenditures
E(t) that obeys the Euler equation of a standard Ramsey problem:

E(t)

—— = R(t) — p,

E(t)       ^{( ) p,}

where we have used the fact that the intertemporal elasticity of substitution equals unity. By
definition, E(t) = P(t)C(t) where P(t) is the exact price index associated with the quantity index

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