Dynamic control of a firm's process innovation with knowledge accumulation in a vertically differentiated monopoly

This paper explores a multiproduct firm's process innovation of high-and low-quality goods with knowledge accumulation in a vertically differentiated monopoly. We show that: (i) the system admits a saddle-point steady-state equilibrium under firm decision-making and social planner adjustment, respectively; (ii) the firm's learning rates of knowledge accumulation of process innovation call for more intense efforts in both directions; (iii) there is a substitution between the process innovation for these two kinds of goods; (iv) the social incentive towards both kinds of innovation efforts is always larger than the private incentive characterizing the profit-seeking firm. Our contribution extends the dynamic innovation literature that focuses on single-good and considers the effects of corresponding knowledge accumulation on process innovation of these two kinds of goods. Further, this theoretical work contributes to the design of efficient innovation effort strategies for firms' process innovation with corresponding knowledge accumulation in a vertically differentiated monopoly market.