Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs. (11th July 2017)

• Record Type: Journal Article
• Authors: Tabata, Minoru; Eshima, Nobuoki
• Other Names: Rehak Pavel Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2017(2017)
• Publication Date: 2017-07-11
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2017/9341502
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : In spatial economics, the distribution of wages is described by a solution to the wage equation of Dixit-Stiglitz-Krugman model . The wage equation is a discrete equation that has a double nonlinear singular structure in the sense that the equation contains a discrete nonlinear operator whose kernel itself is expressed by another discrete nonlinear operator with a singularity. In this article, no restrictions are imposed on the maximum of transport costs of the model and on the number of regions where economic activities are conducted. Applying Brouwer fixed point theorem to this discrete double nonlinear singular operator, we prove sufficient conditions for the wage equation to have a solution and a unique one.