The main motivation of the paper is to determine the social value of innovations in a standard scale-invariant Schumpeterian growth model, which explicitly introduces knowledge diffusion over a Salop (1979) circle. The social value of an innovation is defined as the optimal value of the knowledge inherent in this innovation. We thus have to price optimally knowledge. For that purpose, contrary to what is done in standard growth theory, we complete the markets using Lindahl prices for knowledge. The Lindahl equilibrium, which provides the system of prices that sustains the first-best social optimum in an economy with non rival goods, appears as a benchmark. First, its comparison with the standard Schumpeterian equilibrium à la Aghion & Howitt (1992) enables us to shed a new light on the issue of non-optimality of the latter. Second, the Lindahl equilibrium also allows us to revisit the issue of R&D incentives in presence of cumulative innovations. Finally, this benchmark may be a first step to understand how knowledge is exchanged in new technology sectors.

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).

This paper presents an endogenous growth model à la Aghion & Howitt (1992) in which we explicitly formalize knowledge spillovers in the innovation process. We revisit the issue of the Pareto non-optimality of the Schumpeterian equilibrium by revealing the part played by the intensity of knowledge spillovers. Basically, we highlight that the market incompleteness characterizing this type of decentralized economy (knowledge is not priced) is all the more likely to lead to an under-optimal (resp. over-optimal) R&D effort as the intensity of knowledge spillovers is high (resp. low). The reason behind this is that the effects of the distortion of R&D incentives resulting from market incompleteness are amplified all the more as this intensity is strong. Complementarily, we derive the optimal tool dedicated to correct the market failure caused by market incompleteness, and we demonstrate that it clearly depends on the intensity of knowledge spillovers: the higher (resp. lower) the intensity of knowledge spillovers is, the more likely this policy tool should consist in a subsidy (resp. tax). Moreover, if this optimal tool happens to be a subsidy, then this subsidy will be all the larger as the intensity is high.