Working paper

Using the Salop Circle to Study Scale Effects in Schumpeterian Growth Models: Why Inter-sectoral Knowledge Diffusion Matters

Elie Gray, and André Grimaud


This paper analyzes the link between the fact that fully endogenous growth models exhibit (or not) the non-desirable scale effects property and assumptions regarding the intensity of knowledge diffusion. In that respect, we extend a standard Schumpeterian growth model by introducing explicitly knowledge diffusion over a Salop (1979) circle: a continuum of sectors simultaneously sending and receiving knowledge is located over the circle. The link between knowledge diffusion and scale effects stems from the fact that the more diffusion spreads with the size of the economy, the larger the pools of knowledge used by each sector’s R&D activity are, the higher the marginal productivity of labor in R&D is, and eventually the higher the growth rate is. The paper tackles the apparent following paradox. Knowledge diffusion seems to lead to scale effects; however, the former is empirically desirable while the latter is not. Our first basic result is that a sufficient condition to have a scale-invariant fully endogenous growth model is to assume no inter-sectoral knowledge diffusion. However, this assumption is not empirically reasonable. We overcome the aforementioned paradox by showing that the absence of diffusion is not a necessary condition to suppress scale effects. More precisely, we determine sets of reasonable assumptions on knowledge diffusion under which one can obtain fully endogenous growth models complying with most undeniable empirical facts - namely the absence of significant scale effects, the impact of public policies on the growth rate, and somehow realistic interactions among sectors R&D activities (including the occurrence of GPTs).


Schumpeterian growth theory / Scale effects / Inter-sectoral knowledge diffusion / Knowledge spillovers / Non rivalry;

JEL codes

  • O30: General
  • O31: Innovation and Invention: Processes and Incentives
  • O33: Technological Change: Choices and Consequences • Diffusion Processes
  • O40: General
  • O41: One, Two, and Multisector Growth Models


Elie Gray, and André Grimaud, Using the Salop Circle to Study Scale Effects in Schumpeterian Growth Models: Why Inter-sectoral Knowledge Diffusion Matters, TSE Working Paper, n. 16-676, July 2016.

See also

Published in

TSE Working Paper, n. 16-676, July 2016