Associate Professor, Graduate School of Economics and Management, Tohoku University

In this note, we consider dynamically optimal pricing of a network good, when consumers’ demand adjusts only gradually. We find a Lyapunov function that characterizes where and how the platform size converges under the dynamically optimal pricing. Given the current platform size, we compare the value of the Lyapunov function with the profit under static pricing that keeps this current size at a Nash equilibrium of consumers’ entry game. We show that the difference between them can be interpreted as adjustment costs and we justify this interpretation by regarding a myopic pricing scheme as an approximation. This justification suggests that recurrent adjustment of the myopic pricing scheme brings the platform to the same size in the long run as the dynamically optimal pricing.