A network model of migration equilibrium with movement costs

Abstract

In this paper we introduce a new network equilibrium model of human migration in the presence of movement costs. The equilibrium conditions state that migration continues until the net gain in utility between the destination locations and each particular origin location minus the movement cost is equal, maximal and nonnegative, if there is a positive outward flow from that origin to the particular destinations. We then consider the case of linear utility functions and fixed movement costs and demonstrate that the equilibrium conditions can be reformulated as the solution to an equivalent quadratic programming problem. This approach is in line with the classical approaches to both traffic network equilibrium and spatial price equilibrium problems. We then present an equilibration algorithm which explicitly exploits the special structure of the underlying network. The algorithm proceeds from location to location, at each step equilibrating the migration flow out of a location. The numerical results demonstrate the robustness and efficacy of this approach on large-scale migration network equilibrium problems.