A dynamic analysis of investment in process and product innovation with learning-by-doing

•Develop a dynamic control model of a monopolist's investments in process and product innovation under learning-by-doing.•Derive the optimal investment levels in the saddle stable steady state under monopolist optimum and social optimum.•Investigate the effects of learning-by-doing on the process and product innovation investments and their the complementarity (substitutability) relationship.•Compare the social incentive towards both product and process innovation against the private incentive that characterizes the profit-seeking monopolist.

This paper investigates the optimal control problem of a monopolist's investments in process and product innovation under learning-by-doing in a dynamic setting. We show that: (i) there exists the saddle stable steady state under monopolist optimum and social optimum; (ii) the learning rates of product and process innovation affect not only the monopolist's process or product innovation investments, but also the complementarity (substitutability) relationship between product and process innovation; (iii) the social incentive towards both product and process innovation is always larger than the private incentive characterizing the profit-seeking monopolist. These results are valuable complement and development to the results drawn from the standard product and process innovation model.