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.