Cyclically oscillating product quality: A simple model of the product life cycle

This paper presents a dynamic model of the firm, where the firm can exert influence on demand by setting the price and by controlling the quality index. Assuming profit maximization, it is shown by means of the Hopf Bifurcation theorem that persistent oscillations of the variables may occur if there is positive growth at the steady state together with a high discount rate. Oscillations may also occur if the influence of an additional unit of the quality index on demand and price is sufficiently large, thus yielding a special version of the product life cycle. A numerical example is used in order to illustrate the results derived in the general framework. Valuable comments from an anonymous referee are gratefully acknowledged.