The Invariance of R&D to the Number of Firms in the Industry: Equilibrium and Efficiency under Bertrand Competition

RAND Journal of Economics, Vol. 18, No. 1, 1987

Yale University, School of Organization & Management. Economics of organization, Working paper series D, Working paper number 11

15 Pages Posted: 20 Jun 2012

See all articles by Raaj Kumar Sah

Raaj Kumar Sah

University of Chicago

Joseph E. Stiglitz

Columbia Business School - Finance and Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: June 1985

Abstract

This paper presents certain results, of remarkable simplicity, concerning the market allocation of resources of research and development (R&D) and its comparison to socially efficient allocations. In contrast to many previous studies, we posit that a firm can undertake more than one project (at desired levels of intensity) aimed at the same innovation, if it is profitable to do so. The market is characterized by a Bertrand equilibrium in the product market. We show that the marginal private decisions are independent of the number of firms in the industry; as a result, the equilibrium R&D (that is, the number of projects undertaken in the market, and the level of effort spent on each project) is invariant to the number of firms. The equilibrium level of effort per project is also invariant to the magnitude of (appropriable) rents from successful innovation.

The number of firms affects the gains from innovation to consumers and firms; for any research program, a larger number of firms entail larger gains to consumers, smaller gains to firms, and larger aggregate social benefits. While the market equilibrium level of effort per project is shown to coincide with the socially efficient level, the market undertakes fewer projects than is desirable.

Suggested Citation

Sah, Raaj Kumar and Stiglitz, Joseph E., The Invariance of R&D to the Number of Firms in the Industry: Equilibrium and Efficiency under Bertrand Competition (June 1985). Yale University, School of Organization & Management. Economics of organization, Working paper series D, Working paper number 11. Available at SSRN: https://ssrn.com/abstract=2086951

Raaj Kumar Sah (Contact Author)

University of Chicago ( email )

Chicago, IL 60637
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Joseph E. Stiglitz

Columbia Business School - Finance and Economics ( email )

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HOME PAGE: http://www.josephstiglitz.com

National Bureau of Economic Research (NBER) ( email )

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