Dynamic Walrasian price equilibrium problem: evolutionary variational approach with sensitivity analysis

Abstract

Many authors have been devoted to the study of the static general economic equilibrium problem regulated to Walras’ law (see e.g. Arrow and Debreu in Econometrica 22:265–290, 1954; Arrow and Hahn in General competitive analysis, 1991; Arrow et al. in Econometrica 27:82–109, 1959; Border in Fixed point theorems with application to economics and game theory, Cambridge University Press, Cambridge, 1985; Dafermos in Math Programm 46:391–402, 1990; Dafermos and Zhao in Oper Res Lett 10:396–376, 1991; Donato et al. in J Glob Optim, 2007; Hahn in Stability, North Holland, Amsterdam, 1982; Jofre et al. in Math Oper Res, 2007; Nagurney in Network economics—a variational inequality approach, Kluwer, Dordrecht, 1999; Nagurney and Zhao in Network formalism for pure exchange economic equilibria, World Scientific Press, Singapore, 1993; Walker in J Polit Econ 94(4), 1987; Walras in Elements d’Economique Politique Pure, Corbaz, Lausanne, Switzerland, 1874; Zhao in Variational inequalities in general equilibrium: analysis and computation, PhD thesis, Brown University, 1988; and their bibliography). The aim of this paper is to provide a first approach to a particular dynamic general economic equilibrium problem: a Walrasian price equilibrium problem when the data are time-dependent. The equilibrium conditions that describe this pure exchange economic model are expressed in terms of an evolutionary variational inequality, for which existence and sensitivity results are given. Moreover, our problem can be expressed in a common way to many other equilibrium problems.