  We consider the extension of a tractable NEG model with a quasi-linear log
utility to continuous space, and investigate the behavior of its solution
mathematically. The model is a system of nonlinear integral and differential
equations describing the market equilibrium and the time evolution of the
spatial distribution of population density. A unique global solution is
constructed and a homogeneous stationary solution with evenly distributed
population is shown to be unstable. Furthermore, it is shown numerically that
the destabilized homogeneous stationary solution eventually forms spiky spatial
distributions. The number of the spikes decreases as the preference for variety
increases or the transport cost decreases.
