Product and quality innovations: an optimal control approach

In the suggested paper an attempt to combine two different aspects of innovative activity which are known as product and process innovations is made. The main objective of the paper is to demonstrate the importance of interdependence between these two types of innovative activity through means of a simple one agent model. Research questions which are studied in the paper are as following: 1. Whether it is possible to analyze simultaneously two different aspects of innovations on a continious and dynamical basis. To our knowledge there are no models which would suggest the dynamical analysis of such type. 2. What is the interaction between product and quality innovations and how it may in uence both processes. 3. What is the effect of the degree of diversity of products on the innovative activity. The suggested model contains no uncertainty and only one agent (monopolist) which may invest in expansion of variety of products available on the market and into the development of quality of every product which already exists. To develop such a model in continuous time I make use of infinite-dimensional Optimal Control methods. Main finding of the paper is that interaction between different types of innovative activity significantly changes the dynamics of product emergence to the market as well as the quality of products on the market as incentives of investor are changed. Another important finding is that heterogeneity of products and its nature are fundamental for the outcome of the model. The complementarity of product and process innovations changes our view on technology management and competition in this field.