# Agglomeration patterns in a multi-regional economy without income effects

## Abstract

We study the long-run spatial distribution of industry using a multi-region core–periphery model with quasi-linear log utility Pflüger (Reg Sci Urban Econ 34:565–573, 2004). We show that a distribution in which industry is evenly dispersed among some of the regions, while the other regions have no industry, cannot be stable. A spatial distribution where industry is evenly distributed among all regions except one can be stable, but only if that region is significantly more industrialized than the other regions. When trade costs decrease, the type of transition from dispersion to agglomeration depends on the fraction of workers that are mobile. If this fraction is low, the transition from dispersion to agglomeration is catastrophic once dispersion becomes unstable. If it is high, there is a discontinuous jump to partial agglomeration in one region and then a smooth transition until full agglomeration. Finally, we find that mobile workers benefit from more agglomerated spatial distributions, whereas immobile workers prefer more dispersed distributions. The economy as a whole shows a tendency towards overagglomeration for intermediate levels of trade costs.

### Keywords

Core–periphery model Footloose entrepreneur Multiple regions Welfare### JEL Classification

R10 R12 R23## Notes

### Acknowledgements

We are grateful to Pascal Mossay, Sergey Kokovin, and two anonymous referees for very useful comments and suggestions. We also thank the audience at the 2014 “Industrial Organization and Spatial Economics” conference in Saint Petersburg (Center for Market Studies and Spatial Economics and Higher School of Economics, National Research University). José Gaspar gratefully acknowledges support from CEF.UP. This research was financed by the European Regional Development Fund through COMPETE 2020\(\textendash \)Programa Operacional Competitividade e Internacionalização (POCI) and by Portuguese Public Funds through Fundação para a Ciência e Tecnologia in the framework of Projects POCI-01-0145-FEDER-006890, PEst-OE/EGE/UI4105/2014, PEst-C/MAT/UI0144/2011, and Ph.D. scholarship SFRH/BD/90953/2012. Part of this work was developed, while João Correia-da-Silva was a Marie Curie Fellow at Toulouse School of Economics, financed by the European Commission (H2020-MSCA-IF-2014-657283).

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