We analytically study a discrete-space version of the spatial model of agglomeration proposed by Allen and Arkolakis.
1) Employing the bifurcation analysis method developed by Akamatsu
et al.,
14) we show that the model exhibits, if any, only
mono-centric or unimodal spatial concentration patterns of mobile agents. The properties we reveale in this paper pose one simple but significant issue: Can we justify fitting the model to the actual spatial patterns, which are typically not mono-centric but poly-centric? We argue that, the
unobserved amenity approach, which Allen and Arkolakis and other recent studies employ to circumvent the issue, is an inappropriate one as it can replicate any observed data with any model.
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