A Simple Model of Functional Specialization of Cities

Nagamachi, Kohei (2015): A Simple Model of Functional Specialization of Cities.

Abstract

Resorting to the method proposed by Matsuyama (2013), this paper develops a static equi- librium model of a system of cities in which ex ante identical locations specialize in stages of production different in the degree of dependence on routine and nonroutine local services sec- tors, the latter of which is tied to an agglomeration force due to monopolistic competition a ́ la Dixit and Stiglitz (1977). The model is simple in that the system is summarized by a second-order differential equation, which has a unique non-degenerate city size distribution with the comove- ment of income, population, factor prices, and urban diversity as observed for the U.S. cities. Two examples of use of the model are then illustrated: analyses of welfare gain from functional specialization and optimal income redistribution, the latter of which provides an important impli- cation of an increasing importance of interactive activities in a modern developed economy for income redistribution. Although extending the model makes the model analytically intractable, it is still characterized by a differential equation easily solved with a numerical method and thus useful for further analyses.

• Item Type: MPRA Paper
• Language: English
• Keywords: functional specialization, system of cities, optimal income redistribution policy
• Subjects: F - International Economics > F1 - Trade > F12 - Models of Trade with Imperfect Competition and Scale Economies ; Fragmentation; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R13 - General Equilibrium and Welfare Economic Analysis of Regional Economies

References

ALBOUY, D. AND G. EHRLICH, “Metropolitan Land Values and Housing Productivity,” NBER Working Papers 18110, National Bureau of Economic Research, Inc, May 2012.

ANDERSON, J. E. AND E. VAN WINCOOP, “Trade Costs,” Journal of Economic Literature 42 (September 2004), 691–751.

BEHRENS, K., G. DURANTON AND F. ROBERT-NICOUD, “Productive Cities: Sorting, Selection, and Agglomeration,” Journal of Political Economy 122 (2014a), 507 – 553.

BEHRENS, K., G. MION, Y. MURATA AND J. SUEDEKUM, “Spatial frictions,” Technical Report, 2014b.

DAVIS, J. C. AND J. V. HENDERSON, “The agglomeration of headquarters,” Regional Science and Urban Economics 38 (September 2008), 445–460.

DAVIS, M. A. AND F. ORTALO-MAGNE, “Household Expenditures, Wages, Rents,” Review of Eco- nomic Dynamics 14 (April 2011), 248–261.

DESMET, K. AND E. ROSSI-HANSBERG, “Urban Accounting and Welfare,” American Economic Review (2013), forthcoming.

DHINGRA, S. AND J. MORROW, “Monopolistic competition and optimum product diversity under firm heterogeneity,” London School of Economics, mimeograph (2012).

DIXIT, A. K. AND G. M. GROSSMAN, “Trade and Protection with Multistage Production,” Review of Economic Studies 49 (October 1982), 583–94.

DIXIT, A. K. AND J. E. STIGLITZ, “Monopolistic Competition and Optimum Product Diversity,” American Economic Review 67 (June 1977), 297–308.

DORNBUSCH, R., S. FISCHER AND P. A. SAMUELSON, “Comparative Advantage, Trade, and Pay- ments in a Ricardian Model with a Continuum of Goods,” American Economic Review 67 (Decem- ber 1977), 823–839.

DURANTON, G., “Urban Evolutions: The Fast, the Slow, and the Still,” American Economic Review 97 (March 2007), 197–221.

DURANTON, G. AND D. PUGA, “Nursery Cities: Urban Diversity, Process Innovation, and the Life Cycle of Products,” American Economic Review 91 (December 2001), 1454–1477.

———, “From sectoral to functional urban specialisation,” Journal of Urban Economics 57 (March 2005), 343–370.

EECKHOUT, J., “Gibrat’s Law for (All) Cities,” American Economic Review 94 (December 2004), 1429–1451.

FEENSTRA, R. C. AND G. H. HANSON, “Foreign Investment, Outsourcing, and Relative Wages,” in R. C. Feenstra, G. M. Grossman and D. A. Irwin, eds., The Political Economy of Trade Policy: Papers in Honor of Jagdish Bhagwati (Cambridge, MA: MIT Press, 1996), 89–127.

FELDMAN, M. P. AND D. B. AUDRETSCH, “Innovation in cities: Science-based diversity, special- ization and localized competition,” European Economic Review 43 (February 1999), 409–429.

GABAIX, X., “Power Laws in Economics and Finance,” Annual Review of Economics 1 (05 2009), 255–294.

GABAIX, X. AND Y. M. IOANNIDES, “The evolution of city size distributions,” in J. V. Henderson and J. F. Thisse, eds., Handbook of Regional and Urban Economicsvolume 4 of Handbook of Regional and Urban Economics, chapter 53 (Elsevier, 2004), 2341–2378.

GROSSMAN, G. M. AND E. ROSSI-HANSBERG, “Trading Tasks: A Simple Theory of Offshoring,” American Economic Review 98 (December 2008), 1978–97.

HELPMAN, E., “The size of regions,” in D. Pines, E. Sadka and I. Zilcha, eds., Topics in Public Economics Theoretical and Applied Analysis (Cambridge: Cambridge University Press, 1998), 33–54.

HENDERSON, J. V., “The Sizes and Types of Cities,” American Economic Review 64 (September 1974), 640–56.

HSU, W., “Central Place Theory and City Size Distribution,” Economic Journal 122 (09 2012), 903– 932.

JACOBS, J., The economy of cities, Vintage international (Random House, 1969).

KOHLER, W., “International outsourcing and factor prices with multistage production,” Economic Journal 114 (03 2004), C166–C185.

MATSUYAMA, K., “Endogenous Ranking and Equilibrium Lorenz Curve Across (ex ante) Identical Countries,” Econometrica 81 (09 2013), 2009–2031.

MICHAELS, G., F. RAUCH AND S. J. REDDING, “Task Specialization in U.S. Cities from 1880- 2000,” CEP Discussion Papers dp1186, Centre for Economic Performance, LSE, February 2013. PFLU ̈ GER, M. AND T. TABUCHI, “The size of regions with land use for production,” Regional Science and Urban Economics 40 (November 2010), 481–489.

ROSSI-HANSBERG, E. AND M. L. J. WRIGHT, “Urban Structure and Growth,” Review of Economic Studies 74 (04 2007), 597–624.

VALENTINYI, A. AND B. HERRENDORF, “Measuring Factor Income Shares at the Sector Level,” Review of Economic Dynamics 11 (October 2008), 820–835.

YI, K.-M., “Can Vertical Specialization Explain the Growth of World Trade?,” Journal of Political Economy 111 (February 2003), 52–102.