A footloose entrepreneur model in a continuous space

Abstract

This paper studies a footloose entrepreneur model in a continuous space. In an appropriate function space, the model is formulated as an initial value problem for an infinite-dimensional ordinary differential equation. A unique global solution is constructed based on the Banach fixed point theorem. The stability of a homogeneous stationary solution is then investigated, and numerical simulations of the asymptotic behavior of global solutions under different parameter values are performed. Numerical solutions starting near the unstable homogeneous stationary solution converge to spike-shaped non-homogeneous stationary solutions, and the number of spikes decreases with declining transport costs. An analysis of the stability of non-homogeneous stationary solutions supports this observation.

54 pages, 49 figures