Output Diffusion of the Monopolist Over Time and Space

In this paper, we develop an output diffusion model in which a monopoly firm faces a cost of adjusting output over time and across geographic regions. First, we investigate a dynamic monopoly model and a simple spatial model with only regional adjustment costs. Then, we explore how the firm maximizes profits over time and space, a calculus of variation problem. The Euler equation yields a partial differential equation which forms our output diffusion model. It extends the traditional intertemporal output path into output diffusion over time and space. As long as regional adjustment costs exist, steady-state output in the diffusion model is less than the static monopoly output level. This model suggests that a policy designed to lower regional adjustment costs can increase supply in all geographic regions.