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.
This paper is a revised version of Kawano (2014).
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Notes
- 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.
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Kawano, M. (2022). Dynamic Model of Urbanization with Public Goods. In: Kawano, M., Kourtit, K., Nijkamp, P., Higano, Y. (eds) Theory and History in Regional Perspective. New Frontiers in Regional Science: Asian Perspectives, vol 56. Springer, Singapore. https://doi.org/10.1007/978-981-16-6695-7_8
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