A new analytical framework for urban size and policies

ABSTRACT

This study develops a new comprehensive analytical framework for use in achieving optimal city size and conducting policy studies. The EE–EC framework simultaneously considers economic productivity, environmental pollution, and traffic congestion. We take Beijing as an example and perform a simulation analysis using this framework. We find that, in 2010, Beijing was 10% oversized and transportation and industrial policies were more effective than environmental policies for maximizing Beijing’s net urban agglomeration economies. The framework presented in this study is not only flexible in the sense that it can be easily applied to other cities, but also urgently needed by policy makers.

KEYWORDS:

• City size
• urban policy
• environmental quality
• analytical framework

JEL CLASSIFICATION:

• R11
• R12
• O18

Disclosure statement

No potential conflict of interest was reported by the authors.

Data sharing availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Notes

¹ See Appendix A.1 for the derivation.

² See Appendix A.2 for the derivation.

³ $1-tR>0$, that is, despite living on the periphery of a city, a labourer can get a job.

⁴ In other words, it is not sufficient for a city to focus only on environmental quality or economic growth.

⁵ See Appendixes A.3–A.6 for the proof.

⁶ According to Equation (7)(7) ${\mathrm{\Omega }}_j=Z_{4j}{L}_j^{\mathrm{{\rm Y}}}{N}_j^{-1},$(7) , $\mathrm{{\rm Y}}$ can be viewed as the output elasticity of effective labour.

⁷ See Appendix B for the comparison of the EE–EC framework and some urbanization theories.

⁸ See Appendix C for the empirical steps and data.

⁹ $\mathrm{\partial }\mathrm{E}\mathrm{E}/\mathrm{\partial }\mathrm{{\rm Y}}<0$ and ${\mathrm{\partial }}^2\mathrm{E}\mathrm{E}/\mathrm{\partial }{\mathrm{{\rm Y}}}^2>0$.

¹⁰ By the Dixit–Stiglitz model, the price elasticity of intermediate good demand is $1/\left(\rho -1\right)$, so by the Lerner equation $\left(p_{x,j}-{\omega }_j{c}_x\right)/p_{x,j}=1-\rho$ and $p_{x,j}={\omega }_j{c}_x/\rho$.

¹¹ Substituting Equations (A4)(A4) $\alpha \frac{\sigma -1}{\sigma }p\left(j,\varsigma \right)\frac{Y_{j\varsigma }+c_{j\varsigma }}{k_{j\varsigma }}=r_j,$(A4) –(A7)(A5) $\beta \frac{\sigma -1}{\sigma }p\left(j,\varsigma \right)\frac{Y_{j\varsigma }+c_{j\varsigma }}{l_{j\varsigma }}={\omega }_j,$(A5) in to (5) yields $\pi \left(j,\varsigma \right)=Y_{j\varsigma }p\left(j,\varsigma \right)-\left(1-1/\sigma \right)p\left(j,\varsigma \right)\left(Y_{j\varsigma }+c_{j\varsigma }\right)\left(\gamma +\vartheta +\beta +\alpha \right)$. Let $\pi \left(j,\varsigma \right)=0$, then $Y_{j\varsigma }=\mathrm{\Gamma }\left(1-1/\sigma \right)c_{j\varsigma }/\left[1-\mathrm{\Gamma }\left(1-1/\sigma \right)\right]$.

¹² It can also be proved by more rigorous mathematical derivation similar to the proof of Corollary 2.

¹³ That is, all the labourers live in the periphery of the city.

¹⁴ They used the data of 286 Chinese cities for regression analysis to get the parameter $\mathrm{{\rm Y}}$ for each city. Because the regression process is complex, it is not included in this article.

¹⁵ Further details about the estimation of $t$ will be made available upon request to the authors.

¹⁶ We let $B=\mathrm{e}\mathrm{x}\mathrm{p}\left(0.5\right)$ and $b=1/R^u$ ($R^u$ denotes the city radius under the uniform distribution as required by Au and Henderson (2006)), and hence, $f\left(x\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left(0.5-x/R^u\right)$, which has three advantages. First, population density becomes higher with the distance to the central business district (CBD) reduces. Second, large cities have a higher population density, which is more reasonable. Third, $f\left(x\right)>1$ when $R<R^u$, $f\left(x\right)=1$ when $R=R^u$, and $f\left(x\right)<1$ when $R>R^u$, hence the exponential distribution is an improvement of the uniform distribution that sets $f\left(x\right)\equiv 1$.

Additional information

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.Zhongqi Deng acknowledges Sichuan Planning Project of Philosophy and Social Sciences.