Firm price-cost markups may reflect (a) bigger step sizes from quality innovations that confer significant knowledge spillovers onto other firms, and/or (b) higher process efficiency than competing firms or other factors which bear no obvious knowledge externality. We write down an endogenous growth model with innovation step size and process efficiency as alternative sources of markup heterogeneity. Compared with the laissez-faire equilibrium, the social planner wants to reallocate research towards high step size firms but not high process efficiency firms. We then use price and productivity data across firms in French manufacturing to infer firm step sizes and process efficiency. We find that the planner could achieve faster growth by reallocating research toward high step size firms, and more so if high step size firms could freely license their innovations to high process efficiency firms.
Aghion et al. (2025) studied this question.