Process and product innovation in a vertically differentiated industry

We examine a vertically differentiated duopoly where firms invest in process and product innovation and then compete in prices under full market coverage. We show that (i) process and product innovation are complements (substitutes) for the low-quality (high-quality) firm; (ii) the firm which is initially more efficient invests more than the rival in process innovation; (iii) if the initial differential between marginal costs is sufficiently high, the demand for the less efficient firm is nil and the duopoly equilibrium does not exist.