We determine the properties of the core-periphery model with three regions and compare our results with those of the standard 2-region model. The conditions for the stability of dispersion and concentration are established. As in the 2-region model, dispersion and concentration can be simultaneously stable. We show that the 3-region (2-region) model favours the concentration (dispersion) of economic activity. Furthermore, we provide some results for the n-region model. We show that the stability of concentration of the 2-region model implies that of any model with an even number of regions.
JEL classification: R12, R23
I would like to thank Jacques Thisse for useful help and suggestions. The usual disclaimer applies. Financial support from the Commission of the European Communities, under grant HPMD-CT-2000-00010, is acknowledged.
We extend Beckmann's spatial model of social interactions to the case of a two-dimensional spatial economy involving a large class of utility functions, accessing costs, and space-dependent amenities. We show that spatial equilibria derive from a potential functional. By proving the existence of a minimiser of the functional, we obtain that of spatial equilibrium. Under mild conditions on the primitives of the economy, the functional is shown to satisfy displacement convexity, a concept used in the theory of optimal transportation. This provides a variational characterisation of spatial equilibria. Moreover, the strict displacement convexity of the functional ensures the uniqueness of spatial equilibrium. Also, the spatial symmetry of equilibrium is derived from that of the spatial primitives of the economy. Several examples illustrate the scope of our results. In particular, the emergence of multiplicity of equilibria in the circular economy is interpreted as a lack of convexity of the problem.
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