Spatial discounting, Fourier, and racetrack economy: a recipe for the analysis of spatial agglomeration models. (English) Zbl 1345.91052
Summary: We provide an analytical approach that facilitates understanding the bifurcation mechanism of a wide class of economic models involving spatial agglomeration of economic activities. The proposed method overcomes the limitations of the A. M. Turing approach [“The chemical basis of morphogenesis”, Philos. Trans. R. Soc. Lond., Ser. B, Biol. Sci. 237, No. 641, 37–72 (1952; doi:10.1098/rstb.1952.0012)] that has been used to analyze the emergence of agglomeration in the multi-regional core-periphery (CP) model of P. R. Krugman [“On the number and location of cities”, Europ. Econ. Rev. 37, No. 2–3, 293–298 (1993; doi:10.1016/0014-2921(93)90017-5)] and [The self organizing economy. Blackwell Publishers (1996)]. In other words, the proposed method allows us to examine whether agglomeration of mobile factors emerges from a uniform distribution and to analytically trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as a uniform pattern) that these models exhibit when the values of some structural parameters change steadily. Applying the proposed method to a multi-regional CP model, we uncover a number of previously unknown properties of the CP model, and notably, the occurrence of “spatial period doubling bifurcation” in the CP model is proved.
MSC:
| 91B72 | Spatial models in economics |
| 91B55 | Economic dynamics |
| 37N40 | Dynamical systems in optimization and economics |
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