R&D for green technologies in a dynamic oligopoly: Schumpeter, Arrow and inverted-U's

We extend a well known differential oligopoly game to encompass the possibility for production to generate a negative environmental externality, regulated through Pigouvian taxation and price caps. We show that, if the price cap is set so as to fix the tolerable maximum amount of emissions, the resulting equilibrium investment in green R&D is indeed concave in the structure of the industry. Our analysis appears to indicate that inverted-U-shaped investment curves are generated by regulatory measures instead of being a "natural" feature of firms' decisions.