DYNAMIC PRICING AND PRODUCT/PROCESS R&D WITH REFERENCE QUALITY EFFECT IN A MONOPOLY

In this article, we construct a dynamic optimal control model where the price and R&D portfolio are simultaneously determined by a monopolist with the consumers' reference effect about product quality. We extend the conventional model by describing the product and process R&D with non-linear dynamic equations and considering the signal effect of price on the change rate of reference quality. Our analysis mainly suggests that: (i) the non-linear system admits at most two steady-state saddle-point equilibria under both monopoly and social planning; (ii) the product price is increasing (decreasing) in the effort for quality improvement in the beginning (ending) period of the time horizon, while the price is always decreasing in the effort for marginal production cost reduction; (iii) in the neighbourhood of consumers' memory parameter, the two dimensions of R&D portfolio are substitutes (complements) if and only if the signal effect of the price is strong (weak); (iv) the change rates of the efforts in product and process R&D are increasing (decreasing) in memory parameter if and only if the signal effect of the price is below (above) some threshold; (v) by examining the extreme case of key parameters, we find that the system cannot converge to the steady-state equilibrium when consumers' adjustment speed about reference quality is low under both monopoly and social planning.