The Lindahl equilibrium in Schumpeterian growth models

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 (Bell J Econ 10(1):141-156 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 A la Aghion and Howitt (Econometrica (60)2:323-351 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.