Abstract
The main purpose of this study is to estimate the optimal city size which would attain maximum total surplus and sustainability, or a city size in which total benefits would equal total costs. We apply regressions to the total benefit function and the total cost function for 269 employment metropolitan areas for the year 2000 in Japan. Our study can be distinguished from others in that we include in total costs such social costs as environmental pollution. Our findings are that the optimal city size is 393–433 thousand persons. The sustainable limit for city size is 1,057–1,150 thousand.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Empirical studies related to city size include the following: an evaluation of Chinese city size by Au and Henderson (2006); an exploration of the relationship between labor productivity and such structural features of a city as its size, sprawl, and traffic speed by Prud’homme and Lee (1999); an investigation into the effect of a compact city by Burton (2000); a study of factors associated with worker productivity by Cervero (2001); and a study of the compact city as a sustainable urban form by Holden and Norland (2005).
We also apply the SUR (Seemingly Unrelated Regression) model for both total benefit and total cost functions in order to test the robustness of key coefficients.
We estimate commuting subsidies, following Zheng (2007).
$$\begin{aligned} CMS =CMSA \cdot [( ARU)^{1/2 }/ (ARAU)^{1/2}]\cdot L, \end{aligned}$$where CMS (commuting subsidies), CMSA (average commuting subsidies per person), ARU (habitable areas in metropolitan area), ARAU (average habitable areas in metropolitan area), \(L\) (number of employees).
For some cities, data are not available for total annual incomes per household. Therefore, we estimate total annual incomes by using taxable incomes. The estimated results are as follows:
$$\begin{aligned}&AR/N = 1217.31 + 0.747(YT/N)\\&\qquad \qquad \quad (14.532) \quad \quad (11.010) \qquad R^{2} = 0.205, \end{aligned}$$where YT (taxable incomes), numbers in parentheses are t-statistics, \(R^{2}\) (coefficient of determination) and sample size is 471.
Because the portion of total annual incomes that must be estimated accounts for less than 10% in a metropolitan area, we consider it acceptable to supply missing data by using this method.
Missing data for some cities on monthly general consumption expenditure per household are also estimated by the following function:
$$\begin{aligned} ln (CNS/N)&= 6.729 + 0.034\,\, ln (COM/N)\\&(57.219) (2.031) \qquad R^{2} = 0.009, \end{aligned}$$where COM (annual commercial sales), numbers in parentheses are t-statistics, \(R^{2}\) (coefficient of determination) and sample size is 471. Again, the portion of general consumption expenditures that must be estimated accounts for less than 10% in a metropolitan area.
The coefficient of emission type-\(i\) for travel length is obtained from Namikawa et al. (2003).
Figures on total travel length by cars are obtained with the following equation:
$$\begin{aligned} V = 365\, \textit{TRP} \cdot \textit{AREA} \cdot \textit{ATRL}, \end{aligned}$$where TRP (number of trip generations and attractions per area per day), AREA (total areas of a city), ATRL (average trip length per trip). Figures for trip generation and attractions per area per day, and average trip length are obtained from Road Transport Census (Doro Kotsu Sensasu), by the Ministry of Land, Infrastructure and Transport. To calculate these numbers, we assume that average traffic speed is 35 km/h.
We apply the Wald test. Null hypothesis \(\hbox {H}_\mathrm{o}\): the coefficients of population in total benefit and total cost functions of the SUR model are one simultaneously. The chi-squares between the restricted and unrestricted regressions are \(\chi ^{2}\)=27.382. Therefore, the null hypothesis is rejected at 1% significance.
This attains the following equation:
$$\begin{aligned}&\hbox {EXP}[\alpha + \beta ln\, N + \mu _{1}ln TR_{1}+\mu _{2}ln TR_{2 }+ ln\, p] (\beta /N) \\&-\hbox {EXP}[\delta + \gamma ln\, N + \pi ln\, p + \rho ln\, r + \tau ln\, t] (\gamma /N) = 0. \end{aligned}$$
References
Alonso W (1971) The economics of urban size. Pap Reg Sci Assoc 26:67–83
Arnott R (1979) Optimal city size in a spatial economy. J Urb Econ 6(1):65–89
Arnott R (2004) Does the Henry George theorem provide a practical guide to optimal city size? Am J Econ Sociol 63(5):1057–1090
Au C-C, Henderson JV (2006) Are Chinese cities too small? Rev Econ Stud 73(3):549–576
Burton E (2000) The compact city: just or just compact? A preliminary analysis. Urb Stud 37(11):1969–2001
Capello R, Camagni R (2000) Beyond optimal city size: an evaluation of alternative urban growth patterns. Urb Stud 37(9):1479–1496
Cervero R (2001) Efficient urbanisation: economic performance and the shape of the metropolis. Urb Stud 38(10):1651–1671
Fujita M (1989) Urban economic theory: land use and city size. Cambridge University Press, Cambridge
Henderson JV (1974a) Optimum city size: the external diseconomy question. J Polit Econ 82(2):373–388
Henderson JV (1974b) The size and types of cities. Am Econ Rev 64(4):640–656
Henderson JV (1986) Efficiency of resource usage and city size. J Urb Econ 19(1):47–70
Holden E, Norland IT (2005) Three challenges for the compact city as a sustainable urban form: household consumption of energy and transport in eight residential areas in the greater Oslo region. Urb Stud 42(12):2145–2166
Kanemoto Y (1980) Theories of urban externalities. North-Holland, Amsterdam
Kanemoto Y, Ohkawara T, Suzuki T (1996) Agglomeration economies and a test for optimal city sizes in Japan. J Jpn Int Econ 10(4):379–398
Kanemoto Y, Saito H (1998) Is Tokyo too big? a test of the Henry George theorem (Tokyo wa kadai ka: Henry George teiri ni yoru kensho). Hous Land Econ (Jutaku Tochi Keizai) 29:9–17 (in Japanese)
Kanemoto Y, Tokuoka K (2002) Proposal for the standards of metropolitan areas of Japan (Nihon no toshiken settei kijun). J Appl Reg Sci (Ouyo Chiikigaku Kenkyu) 7:1–15 (in Japanese)
Kelly KC (1977) Urban disamenities and the measure of economic welfare. J Urb Econ 4(4):379–388
Mizuno K, Mizutani F, Nakayama N (2006) Industrial diversity and metropolitan unemployment rate. Ann Reg Sci 40(1):157–172
Mizutani F, Suzuki Y, Sakai H (2011) Estimation of social costs of transport in Japan. Urb Stud 48(16): 3537–3559
Moomaw RL (1981) Productivity and city size: a critique of the evidence. Quart J Econ 96(4):675–688
Nakamura H (1997) Social and economic appraisal of road investment (Doro toshi no shakai keizai hyoka). Toyo Keizai Shinposya, Tokyo
Nakamura R, Kaneuchi M (2001) Efficient city size in terms of population: empirical study by cost and benefit approach (Jinko kara mita toshi no kouritsuteki kibo: hiyou beneki apurochi ni yoru jishoteki kenkyu). DBJ Kansai discussion paper series 0101 (in Japanese).
Namikawa R, Takai Y, Oshiro N (2003) Calculation basis for coefficient of emission by car (Jidosha haishutsu keisu no santei konkyo). National Institute for Land and Infrastructure Management, Ministry of Land, Infrastructure and Transport, Tokyo (in Japanese)
Prud’homme R, Lee C-W (1999) Size, sprawl, speed and the efficiency of cities. Urb Stud 36(11):1849–1858
Small AK, Kazimi C (1995) On the costs of air pollution from motor vehicles. J Transp Econ Policy 29(1):7–32
Yezer AMJ, Goldfarb RS (1978) An indirect test of efficient city size. J Urb Econ 5(1):46–65
Zheng X (2007) Measure of optimal city sizes in Japan: a surplus function approach. Urb Stud 44(5/6): 939–951
Acknowledgments
We would like to thank the anonymous referees and the editor for their valuable comments and suggestions. This paper has been supported by a Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mizutani, F., Tanaka, T. & Nakayama, N. Estimation of optimal metropolitan size in Japan with consideration of social costs. Empir Econ 48, 1713–1730 (2015). https://doi.org/10.1007/s00181-014-0850-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00181-014-0850-6