Output Diffusion of the Monopolist Over Time and Space

Hyungho Youn (), Patrick De Leenheer () and Victor Tremblay ()
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Hyungho Youn: Seoul Institute
Patrick De Leenheer: Oregon State University
Victor Tremblay: Oregon State University

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 1, No 14, 290-298

Abstract: Abstract 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 inter-temporal 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.

Keywords: Profit maximization; Output diffusion; Calculus of variation; Partial differential equation; 35K05; 35K20; 49K20 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0837-2

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