Since the seminal works of Schumpeter (1937) and Arrow (1962), economists have recognised that the innovation process is crucially dependent on the strategic environment in which firms operate and on the institutional arrangements which govern the appropriability of economic returns from innovation In this paper we focus on one particular aspect of the relationship between market structure and innovation, that is the effect of regulation on the incentives to innovate of a regulated monopolistic firm. More precisely, we discuss the influence of price regulation on the economic incentives to undertake costly R&D effort to discover a new technology. After a discussion of positive approaches to regulation and their relevance for the policy debate about the relationship between innovative activity and regulation, the paper develops the analysis of different price regulatory schemes in terms of incentives to undertake R&D effort, comparing a traditional price cap scheme with a downward flexible price-cap scheme. The welfare analysis of these schemes and a discussion of their relative merits shows that a welfare ranking of the alternative forms of regulations is crucially dependent on the properties of the cost reduction distribution function. Finally, it is shown that the incentives effects induced by a flexible price-cap bear some similarities with the incentives to innovate resulting from the so-called 'sliding scales' regulatory schemes.