Do process innovations induce product ones?

We study the relationship between process and product innovations in vertically differentiated duopolies. A process innovation can lead two competing firms to improve the quality of their goods introducing a product innovation. In fact, a cost reducing innovation has two effects: it spurs production and it enhances price competition. The former effect induces both firms to increase quality. The latter encourages differentiation, inducing low quality firm to decrease it. Therefore, high quality firm always improves its quality, while the other may or may not. The prevailing effect depends on the nature of quality costs (fixed or variable).