Working paper

The Lindahl equilibrium in Schumpeterian growth models: Knowledge diffusion, social value of innovations and optimal R&D incentives

Elie Gray, and André Grimaud


What is the social value of innovations in Schumpeterian growth models? This issue is tackled by introducing the concept of Lindahl equilibrium in a standard endogenous growth model with vertical innovations which is extended by explicitly considering knowledge diffusion. Assuming that knowledge diffuses on a Salop (1979) circle allows us to formalize the creation of the pools of knowledge in which research and development (R&D) activities draw from to produce innovations. Within this model, we compare two equilibria. The standard Schumpeterian equilibrium à la Aghion & Howitt (1992) is mainly characterized by incomplete markets since knowledge is not priced. It provides the usual private value of innovations. The Lindahl equilibrium is a benchmark enabling us to compute the system of prices that sustains the first-best social optimum, and thus to define and to determine analytically the social value of innovations. It provides a suitable methodology for revisiting issues involving the presence of knowledge, often studied in the industrial organization and endogenous growth literatures. This comparison sheds a new light on the consequences of non-rivalry of knowledge and of market incompleteness on innovators’ behavior in the Schumpeterian equilibrium. We notably revisit the issues of Pareto sub-optimality and of R&D incentives in presence of cumulative innovations. Basically, the key externality triggered by market incompleteness implies that knowledge creation is indirectly funded by means of intellectual property rights on rival goods embodying knowledge. Therefore, because the private value of innovations differs from the social one, innovators are not given the optimal incentives.


Schumpeterian growth theory - Lindahl equilibrium - Social value of innovations - Pareto sub-optimality - Cumulative innovations - Knowledge spillovers;

JEL codes

  • D52: Incomplete Markets
  • O31: Innovation and Invention: Processes and Incentives
  • O33: Technological Change: Choices and Consequences • Diffusion Processes
  • O40: General
  • O41: One, Two, and Multisector Growth Models

Replaced by

Elie Gray, and André Grimaud, The Lindahl equilibrium in Schumpeterian growth models: (Knowledge diffusion, social value of innovations and optimal R&D incentives), Journal of Evolutionary Economics, vol. 26, n. 1, March 2016, pp. 101–142.

See also

Published in

TSE Working Paper, n. 14-469, January 2014