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One or infinite optimal city sizes? In search of an equilibrium size for cities

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Abstract

In this paper, the stylized assumption that one single “optimal” city size exists for all cities—achieved when marginal location costs equal marginal location benefits—is abandoned, as well as the opposite view that each city operates on its own cost and production curves, defining a specific optimal size. Instead, this work maintains the comparability among cities and demonstrates that urban specificities in functions performed, quality of life, industrial diversity and social conflicts shift up and down the benefits and costs linked to pure physical size, leading to different “equilibrium” sizes for cities. In order to achieve this result, a model of equilibrium urban size is set up, based on urban costs and urban benefits, merging elements suggested both by the traditional urban economics literature as well as by updated approaches considering also environmental quality, urban form and inter-urban cooperation networks. The model is then estimated on a sample of 59 European cities with data at FUA level. Empirical results allow the identification of city-specific “equilibrium” sizes. The error term, that is, the difference between actual urban population and the “equilibrium” one predicted by the model can be explained, beyond a measure of our ignorance, by good or bad governance, thereby suggesting future strategies for more efficient urban planning.

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Notes

  1. The optimal city size theory tackles the issue of optimal urban dimensions in terms of population; this is also the approach followed in this paper.

  2. Advocating a multiplicity of specialized cities, each with its own production function (as in Henderson 1974, 1985) looks as a rather ad hoc solution inside this kind of abstract models. On the other hand, showing urban heterogeneity as a consequence of a casual identity of urban production and cost functions, with increasing returns (as in Fujita and Krugman 1995, p. 163), or as a consequence of the choice of different wage rates by different developers/managers of new towns, instead of the normal national wage rate (as in Fujita and Krugman 1995, p. 166), means relying on strange, casual cases rather than on theoretically relevant conditions. Introducing a consistent mix of urban externalities, quality public goods and rankings of services and functions into a modelling paradigm based substantially on the accessibility principle represent still a widely open theoretical challenge.

  3. Alonso stressed the mistaken tendency of many authors to look for “optimal city size” only by minimizing the location cost function. As he argued, this would be sensible only if output per capita was constant (Alonso 1971, pp. 70).

  4. Data presented by Alonso were previously analysed by Douglas (1967).

  5. A doubt remains though with these results: in larger cities, higher per capita expenses may be due to a higher willingness to pay for public services than to diseconomies of scale. Moreover, the difference in per capita income between large and small cities exceeds the difference in average costs; therefore, if an optimal dimension exists, this is characterized more by productivity than by average costs.

  6. Carlino (1980) provides a criticism of Chinitz’ analysis and demonstrates on a sample of 65 American towns that economies of scale, both internal and external to the firm, play a role in the definition of urban productivity. See on this debate also Kawashima (1975).

  7. On the concept of urban milieu, see Camagni (1991). For empirical evidence on the existence of “urban milieu effects”, see Capello (2001).

  8. Richardson (1972) suggests replacing the concept of optimal city size with an efficient interval of urban size in which urban marginal benefits are greater than marginal location costs.

  9. The two cities will differ, though, in dynamic terms: the one belonging to the lower rank (R1) will not grow further, having reached the maximum size of its interval, while the other one having developed the higher functions (linked to rank 2) will grow, due to the presence of new and wide net urban benefits (profits).

  10. Camagni (1993) theorized the concept applying it to urban systems. The same concept was already utilized in other fields, such as the behaviour of the firm and macroeconomic organizational behaviour. For a review of the concept, see Capello and Rietveld (1998).

  11. The controversial issue concerning the capability of a pure market mechanism to lead to an optimal allocation of population in cities—evident in the stylized theoretical model of urban land-use but not confirmed by more complex formulations with externalities and public goods (Henderson 1985, p. 262; Fujita 1989, p. 284)— is not crucial for the model presented here.

  12. A similar result in a different theoretical context was achieved by Fujita (1989, p. 151) treating “the open city model with absentee landowners” inside the land-use equilibrium theory. Assuming two cities with two communities maximizing their utilities, with similar productivity curves but, in one case, a superior level of amenities, the model proves that the city with amenities, being more attractive, reaches a higher equilibrium size (which is also optimal). This result shows convergence between our approach and the one of the New Urban Economics.

  13. Capital cities in the EU27 countries are 22, as Brussels, Dublin, Valletta, Nicosia, and Luxembourg are excluded from the sample because of missing values.

  14. “The LUZ approximate as much as possible the functional urban region taking into account the commuting of the work force into the core city. The LUZ are built as follows:

    1. The building blocks for the LUZ are the Local Area Units (i.e. communes). However, not always data are available for the LAUs, and in some cases, NUTS level 3 regions were used as building blocks.

    2. The commuting rate is calculated as the share of the out commuters of the working population. The commuting rate threshold for including or excluding areas of the hinterland in the LUZ is set between 10 and 20 %.

    3. Criteria of spatial contiguity helped in adjusting the definition of the LUZ, although some exception was made.

    The definition of the LUZ is then adjusted taking into account the requirement of spatial contiguity. Moreover, it should be underlined that the boundaries of all LUZ were developed in close cooperation with national experts of the country concerned. This approach assures that realistic choices were made, paying attention to the view of experts who know the city in question very well” (EUROSTAT 2010).

  15. See “Appendix 2” for more details.

  16. Country fixed effects have also been used, although these results are not presented in this paper. They strongly confirm the main message of the paper, without, however, adding much insight into the main relations between independent and dependent variables.

  17. The EVS is a comprehensive survey on Europeans and their beliefs about broad life categories, including trust, religion, politics and society. Citizens have been asked, respectively, “Would you agree that most people can be trusted?”, Do you spend some [spare] time in voluntary organizations?”, “Is politics important in your life?”, “Would you justify cheating on taxes?”, “Have you ever signed a petition for political action?” and “How do you react to a major change in life?”. For more information on data collection methods, see www.europeanvaluesstudy.eu.

  18. In particular, for the latter variable, the answers were used to the questions “Is casual sex justifiable?”, “Do you think that a woman has to have children in order to be fulfilled or is this not necessary?” and “If a woman wants to have a child as a single parent but she does not want to have a stable relationship with a man, do you approve or disapprove?”. On the other hand, trust is measured as the percentage of people replying that they highly trust connationals.

  19. Raw data are available at http://www.arwu.org/ARWU2003.jsp.

  20. Stadtluft macht frei, as predicted by a mediaeval saying.

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Authors and Affiliations

  1. Architecture, Building Environment and Construction Engineering Department, Politecnico di Milano, Piazza Leonardo 32, 20133,  Milan, MI, Italy

    Roberto Camagni, Roberta Capello & Andrea Caragliu

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  1. Roberto Camagni
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  2. Roberta Capello
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  3. Andrea Caragliu
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Correspondence to Andrea Caragliu.

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A first version of this article has been conceived within the ESPON POLYCE project, coordinated by the Vienna Technical University, under the supervision of Prof. Rudolf Giffinger.

Appendices

Appendix 1

Table 4 presents the administrative regions used by EUROSTAT in the creation of LUZ.

Table 4 Administrative regions employed in the construction of LUZ
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Appendix 2

Table 5 presents the sources for land rent data used in the empirical verification of the model.

Table 5 Land rent sources
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Camagni, R., Capello, R. & Caragliu, A. One or infinite optimal city sizes? In search of an equilibrium size for cities. Ann Reg Sci 51, 309–341 (2013). https://doi.org/10.1007/s00168-012-0548-7

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