# Variety, Spillovers and Market Structure in aModel of Endogenous Technological Change

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## Abstract

I study an economy where oligopolistic firms establish in-house R&D programs to produce a continuous flow of cost-reducing (incremental) innovations. The scale of firms' R&D operations determines the rate of productivity growth. I first study the role of concentration, firm size, and demand, appropriability, and opportunity conditions, when the number of firms is exogenous. I find hump-shaped relationships of knowledge appropriability and the number of firms with steady-state growth that give a first intuition about the forces at work in the model. In symmetric equilibrium, static economies of scale due to variety of input supply and knowledge spillovers yield increasing returns to the number of firms. A larger number of firms leads to higher output, higher (aggregate) R&D, and faster growth. Offsetting this force, market fragmentation leads to smaller firms, smaller R&D programs, and slower growth. Next, I let the number of firms be endogenous and study the balanced-growth path of the economy in two dimensions: productivity growth and the number (variety) of goods. The price, investment, entry, and exit decisions are interdependent. In particular, R&D is a fixed (sunk) cost and in zero-profit equilibrium is negatively related to the number of firms. This additional feed-back reinforces the market fragmentation effect. More importantly, many parameters have no longer the effects predicted by the model with an exogenous number of firms (and the standard models in the literature). For example, the scale effect of population size may be negative. Large markets have many firms, high output, and high aggregate R&D. Market fragmentation may offset this force and result in small firms and slower growth.

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