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Published in:
Geodemographics and Urban Planning Analysis: An Historical Review Read chapter Read first chapter

2022 | OriginalPaper | Chapter

8. Dynamic Model of Urbanization with Public Goods

Author : Masamichi Kawano

Published in: Theory and History in Regional Perspective

Publisher: Springer Nature Singapore

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Abstract

We try to examine the optimal number of the regions or the optimal number of the population would be? The Henry George theorem is about the optimal supply of local public goods. The theorem asserts that the optimal population of a region is attained when the total expenditure on the public goods equals the total revenue of the land rents. This theorem had been discussed in static frameworks. We examine this theorem in a dynamic framework. We used an overlapping-generations model and derived the optimal dynamic path of the economy, and we try to examine the theorem. As the result, it is shown that the theorem holds in a steady state, but does not hold on the optimal path which is converging to the steady state.

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previous chapter The Formation Process and Logic of the Spin-off Governance Mode: A Case Analysis of the Morimura Zaibatsu
next chapter Optimal Openness
Footnotes
1
The term region in this paper implies the area where people live together and jointly consume the service of the same public goods.
 
2
In China, people in agricultural sector are moving to urban sector. About 51% of the total population live in urban area now. However, there are 16% of the non-registered residents in urban regions, and they cannot receive enough public services from the governments. This is an important urbanization problem in China. See Ehara (2013), Kaniwa (2013). However, we cannot discuss this kind of problem and we limit our discussion in purely economic field in this paper.
 
3
Especially, Chapter 1 of his dissertation, “Dynamic Henry George Theorem and Optimal City Sizes.”
 
4
Fujita (1989) and others derived the physical size of the city endogenously. We assume the physical size is fixed for the sake of simplicity. This assumption does not affect the result crucially.
 
5
At each period, two generations co-exist, so the total population is 2p.
 
6
The bliss is introduced for a mathematical purpose, that is, for the objective function not to expand to an infinity, and it does not have essentially important meaning economically. See Ramsey (1928).
 
7
This can be said as {Gt} and {nt}.
 
8
If we assume symmetric utility function, \( {U}_t={\beta}_1\ln {C}_t^1+{\beta}_2\ln {C}_{t+1}^2+{\beta}_3\ln \left(\frac{G_t{N}_t}{p}\right) \), then we cannot derive steady state equilibrium.
 
9
P and P−1 can be derived as \( P=\left(\begin{array}{cc}1& 1\\ {}\frac{-25\sqrt{417}-425}{64}& \frac{25\sqrt{417}-425}{64}\end{array}\right) \), and \( {P}^{-1}=\left(\begin{array}{cc}\frac{417-17\sqrt{417}}{837}& \frac{-32}{25\sqrt{417}}\\ {}\frac{417+17\sqrt{417}}{837}& \frac{32}{25\sqrt{417}}\end{array}\right) \), respectively.
 
10
In order for the Henry George theorem to hold, HG = 0 must be satisfied, hence, from (8.54), we have \( \frac{\mathrm{d}\mu }{\mathrm{d}G}=\frac{-3}{50}=-0.06 \). On the other hand, however, on the optimal path \( \frac{\mathrm{d}\mu }{\mathrm{d}G}\approx -0.068 \) holds. There exists a gap.
 
Literature
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Kaniwa Y (2013) Possibility of the growth of Chinese economy by urbanization (in Japanese). Monthly Report, Sumitomo Mitsui Trust Bank
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Metadata
Title
Dynamic Model of Urbanization with Public Goods
Author
Masamichi Kawano
Copyright Year
2022
Publisher
Springer Nature Singapore
Book
Theory and History in Regional Perspective

Print ISBN: 978-981-16-6694-0

Electronic ISBN: 978-981-16-6695-7

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-981-16-6695-7_8