NON-UNIQUENESS AND STABILITY OF EQUILIBRIUM URBAN CONFIGURATION FOR BECKMANN&rdsquo;S SPATIAL INTERACTION MODEL

Abstract

  Since the pioneering work of Beckmann³⁾, a considerable number of studies have been made to explain emergence of the city center in urban economics. These studies presuppose symmetric urban configuration to analyze equilibrium and social optimal. However, uniqueness and stability of the equilibrium have never been examined. For this reason, we first provide a method to examine uniqueness and stability of equilibrium solution of Beckmann&rdsquo;s model. We then disclose that equilibrium configuration is not unique and there are asymmetric equilibrium configurations. Finally, we demonstrate that urban configurations of social optimal is also asymmetric as well as symmetric.