Product innovation, expected quality and network externality: A dynamic analysis

This paper investigates the dynamic optimal control problem of a monopolist's product innovation in a market exhibiting network externality. The main features of our article are: (ⅰ) consider the problems of customers' expected quality (reference quality) and consumers' withdrawal from the network system; (ⅱ) network size and expected quality are state equations; and (ⅲ) the demand function depends on the product quality, expected quality, product price, and network size. Our main results show: (ⅰ) the system admits an unique saddle-point steady-state equilibrium; (ⅱ) the path of price shows positive correlation with the network size; (ⅲ) the unit variable strength of network externality is more sensitive to network size than price and innovation effort, while the consumer's memory parameter is more sensitive to price and innovation effort than network size; and (ⅳ) there is a positive price-quality relationship.