Paul Krugman (1991, JPE) developed a spatial model in which a country can endogenously become differentiated into an industrialized ``core" and an agricultural "periphery". It is known that the model can give rise to multiple (instantaneous) equilibria at which manufacturing production concentrates or disperses. To make the basically static model dynamic, we introduce a iscrete-time adjustment process that leads the workers who earn lower real wage than the average to migrate to the other regions which pay higher real wage. Numerical simulations show not only how a certain equilibrium steady state is selected along the dynamics but also that persistent or transient complicated fluctuations in the relevant variables are possible.