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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 9341502, 7 pages
Research Article

Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs

1Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
2Center for Educational Outreach and Admissions, Kyoto University, Kyoto 606-8501, Japan

Correspondence should be addressed to Minoru Tabata; pj.en.nco.kcul@atabatrnm

Received 18 April 2017; Revised 6 June 2017; Accepted 7 June 2017; Published 11 July 2017

Academic Editor: Pavel Rehak

Copyright © 2017 Minoru Tabata and Nobuoki Eshima. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.