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The Existence and Uniqueness of Global Solutions to the Initial Value Problem for the System of Nonlinear Integropartial Differential Equations in Spatial Economics: The Dynamic Continuous Dixit‐Stiglitz‐Krugman Model in an Urban‐Rural Setting

Author

Listed:
  • Minoru Tabata
  • Nobuoki Eshima

Abstract

Assume that economic activities are conducted in a bounded continuous domain where workers move toward regions that offer higher real wages and away from regions that offer below‐average real wages. The density of real wages is calculated by solving the nominal wage equation of the continuous Dixit‐Stiglitz‐Krugman model in an urban‐rural setting. The evolution of the density of workers is described by an unknown function of the replicator equation whose growth rate is equal to the difference between the density of real wages and the average real wage. Hence, the evolution of the densities of workers and real wages is described by the system of the nominal wage equation and the replicator equation. This system of equations is an essentially new kind of system of nonlinear integropartial differential equations in the theory of functional equations. The purpose of this paper is to obtain a sufficient condition for the initial value problem for this system to have a unique global solution.

Suggested Citation

  • Minoru Tabata & Nobuoki Eshima, 2015. "The Existence and Uniqueness of Global Solutions to the Initial Value Problem for the System of Nonlinear Integropartial Differential Equations in Spatial Economics: The Dynamic Continuous Dixit‐Stiglitz‐Krugman Model in an Urban‐Rural Setting," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:760136
    DOI: 10.1155/2015/760136
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    References listed on IDEAS

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    1. Mossay, Pascal, 2006. "The core-periphery model: A note on the existence and uniqueness of short-run equilibrium," Journal of Urban Economics, Elsevier, vol. 59(3), pages 389-393, May.
    2. Masahisa Fujita, 2010. "The Evolution Of Spatial Economics: From Thünen To The New Economic Geography," The Japanese Economic Review, Japanese Economic Association, vol. 61(1), pages 1-32, March.
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