Beyond the Arrow effect: a Schumpeterian theory of multi-quality firms

This paper introduces multi-quality firms within a Schumpeterian framework. Featuring non-homothetic preferences and income disparities in an otherwise standard quality-ladder model, we show that the resulting differences in the willingness to pay for quality among consumers generate both positive investments in R&D by industry leaders and positive market shares for more than one quality, hence allowing for the emergence of multi-product firms within a vertical innovation framework. This positive investment in R&D by incumbents is obtained with complete equal treatment in the R&D field between the incumbent patentholder and the challengers: in our framework , the incentive for a leader to invest in R&D stems from the possibility for an incumbent having innovated twice in a row to efficiently discriminate between rich and poor consumers displaying differences in their willingness to pay for quality. We hence exemplify a so far overlooked demand-driven rationale for innovation by incumbents. Such a framework also makes it possible to analyze the impact of inequality both on long-term growth and on the allocation of R&D activities between challengers and incumbents. We find that an increase in the income gap positively impacts an econ-omy's growth rate, partly shifting R&D activities from challengers to incumbents. On the other hand, a greater income concentration is detrimental for growth, diminishing both the incumbents' and the challengers' R&D activities.