# 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).

## References

- Ago, T., Isono, I., Tabuchi, T.: Locational disadvantage of the hub. Ann. Reg. Sci.
**40**(4), 819–848 (2006)CrossRefGoogle Scholar - Akamatsu, T., Takayama, Y., Ikeda, K.: Spatial discounting, Fourier, and racetrack economy: a recipe for the analysis of spatial agglomeration models. J. Econ. Dyn. Control
**36**, 1729–1759 (2012)CrossRefGoogle Scholar - Baldwin, R., Forslid, R., Martin, P., Ottaviano, G., Robert-Nicoud, F.: Economic Geography and Public Policy. Princeton University Press, Princeton (2004)Google Scholar
- Barbero, J., Zofío, J.L.: The multiregional core–periphery model: the role of the spatial topology. Netw. Sp. Econ.
**16**(2), 196–469 (2012)Google Scholar - Behrens, K., Robert-Nicoud, F.: Tempora mutantur: in search of a new testament for NEG. J. Econ. Geogr.
**11**(2), 215–230 (2011)CrossRefGoogle Scholar - Behrens, K., Thisse, J.-F.: Regional economics: a new economic geography perspective. Reg. Sci. Urban Econ.
**37**(4), 457–465 (2007)CrossRefGoogle Scholar - Behrens, K., Gaigne, C., Ottaviano, G.I., Thisse, J.-F.: Is remoteness a locational disadvantage? J. Econ. Geogr.
**6**(3), 347–368 (2006)CrossRefGoogle Scholar - Berliant, M., Kung, F.: Bifurcations in regional migration dynamics. Reg. Sci. Urban Econ.
**39**, 714–720 (2009)CrossRefGoogle Scholar - Bosker, M., Brakman, S., Garretsen, H., Schramm, M.: Adding geography to the new economic geography: bridging the gap between theory and empirics. J. Econ. Geogr.
**10**(6), 793–823 (2010)CrossRefGoogle Scholar - Castro, S.B.S.D., Correia-da-Silva, J., Mossay, P.: The core–periphery model with three regions and more. Pap. Reg. Sci.
**91**(2), 401–418 (2012)Google Scholar - Commendatore, P., Kubin, I., Sushko, I.: Typical bifurcation scenario in a three region identical new economic geography model. Math. Comput. Simul.
**108**, 63–80 (2015a)CrossRefGoogle Scholar - Commendatore, P., Filoso, V., Grafeneder-Weissteiner, T., Kubin, I.: Towards a multiregional NEG framework: comparing alternative modelling strategies In: Commendatore, P., Kayam, S., Kubin, I. (eds.) Complexity and Geographical Economics. Dynamic modeling and econometrics in economics and finance, vol 19. Springer, ChamGoogle Scholar
- Ellickson, B., Zame, W.R.: A competitive model of economic geography. Econ. Theory
**25**(1), 89–103 (2005)CrossRefGoogle Scholar - Fabinger, M.: Cities as solitons: analytic solutions to models of agglomeration and related numerical approaches (2015). Available at SSRN 2630599Google Scholar
- Forslid, R., Ottaviano, G.: An analytically solvable core–periphery model. J. Econ. Geogr.
**3**, 229–240 (2003)CrossRefGoogle Scholar - Forslid, R., Okubo, T.: On the development strategy of countries of intermediate size—an analysis of heterogeneous firms in a multi-region framework. Eur. Econ. Rev.
**56**(4), 747–756 (2012)CrossRefGoogle Scholar - Fujita, M., Mori, T.: Frontiers of the new economic geography. Pap. Reg. Sci.
**84**(3), 377–405 (2005)CrossRefGoogle Scholar - Fujita, M., Thisse, J.-F.: New economic geography: an appraisal on the occasion of Paul Krugman’s 2008 Nobel Prize in Economic Sciences. Reg. Sci. Urban Econ.
**39**(2), 109–119 (2009)CrossRefGoogle Scholar - Fujita, M., Krugman, P., Venables, A.: The Spatial Economy: Cities. Regions and International Trade. MIT Press, Cambridge (1999)Google Scholar
- Gaspar, J.M., Castro, S.B.S.D., Correia-da-Silva, J.: The footloose entrepreneur model with 3 regions. FEP Working Papers, 496 (2013)Google Scholar
- Ghiglino, C., Nocco, A.: When Veblen meets Krugman: social network and city dynamics. Econ. Theory
**63**(2), 431–470 (2017)CrossRefGoogle Scholar - Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, Berlin (2002)Google Scholar
- Ikeda, K., Akamatsu, T., Kono, T.: Spatial period-doubling agglomeration of a core–periphery model with a system of cities. J. Econ. Dyn. Control
**36**(5), 754–778 (2012)CrossRefGoogle Scholar - Ikeda, K., Murota, K., Akamatsu, T., Kono, T., Takayama, Y.: Self-organization of hexagonal agglomeration patterns in new economic geography models. J. Econ. Behav. Organ.
**99**, 32–52 (2014)CrossRefGoogle Scholar - Krugman, P.: Increasing returns and economic geography. J. Polit. Econ.
**99**(3), 483–499 (1991)CrossRefGoogle Scholar - Krugman, P.: First nature, second nature, and metropolitan location. J. Reg. Sci.
**33**(2), 129–144 (1993)CrossRefGoogle Scholar - Mossay, P.: A theory of rational spatial agglomerations. Reg. Sci. Urban Econ.
**43**(2), 385–394 (2013)CrossRefGoogle Scholar - Ottaviano, G., Tabuchi, T., Thisse, J.-F.: Agglomeration and trade revisited. Int. Econ. Rev.
**43**(2), 40–435 (2002)CrossRefGoogle Scholar - Oyama, D.: Agglomeration under forward-looking expectations: potentials and global stability. Reg. Sci. Urban Econ.
**39**(6), 696–713 (2009)CrossRefGoogle Scholar - Pflüger, M.: A simple, analytically solvable, Chamberlinian agglomeration model. Reg. Sci. Urban Econ.
**34**, 565–573 (2004)CrossRefGoogle Scholar - Pflüger, M., Südekum, J.: A synthesis of footloose-entrepreneur new economic geography models: when is agglomeration smooth and easily reversible? J. Econ. Geogr.
**8**(1), 39–54 (2008a)CrossRefGoogle Scholar - Pflüger, M., Südekum, J.: Integration, agglomeration and welfare. J. Urban Econ.
**63**, 544–566 (2008b)CrossRefGoogle Scholar - Picard, P.M., Tabuchi, T.: Self-organized agglomerations and transport costs. Econ. Theory
**42**(3), 565–589 (2010)CrossRefGoogle Scholar - Puga, D.: The rise and fall of regional inequalities. Eur. Econ. Rev.
**43**, 303–334 (1999)CrossRefGoogle Scholar - Tabuchi, T.: Historical trends of agglomeration to the capital region and new economic geography. Reg. Sci. Urban Econ.
**44**, 50–59 (2014)CrossRefGoogle Scholar - Tabuchi, T., Thisse, J.-F.: A new economic geography model of central places. J. Urban Econ.
**69**(2), 240–252 (2011)CrossRefGoogle Scholar - Tabuchi, T., Thisse, J.-F., Zeng, D.Z.: On the number and size of cities. J. Econ. Geogr.
**5**(4), 423–448 (2005)CrossRefGoogle Scholar - Takahashi, T., Takatsuka, H., Zeng, D.Z.: Spatial inequality, globalization, and footloose capital. Econ. Theory
**53**(1), 213–238 (2013)CrossRefGoogle Scholar