Academic journal article The American Journal of Economics and Sociology

Does the Henry George Theorem Provide a Practical Guide to Optimal City Size?

Academic journal article The American Journal of Economics and Sociology

Does the Henry George Theorem Provide a Practical Guide to Optimal City Size?

Article excerpt

I

Introduction

THE BASIC HENRY GEORGE THEOREM states that, with identical individuals, in a city of optimal population size, differential land rents (the aggregate over the city of urban land rent less the opportunity cost of land in nonurban use) equal expenditure on pure local public goods. The Theorem is so named because it characterizes a situation in which only Henry George's "single tax"--a confiscatory tax on land rents--is needed to finance urban public expenditures. In the models for which the Theorem holds, there are two opposing effects that interact to determine optimal city size. As population size increases, the fixed cost of the pure local public goods can be shared between a larger number of residents; this is the single source of spatially localized increasing returns to scale that encourages the agglomeration of economic activity. But as population size increases, marginal travel costs and hence the marginal cost of "producing" lots increases; this is the single source of spatially localized decreasing returns to scale that encourages the spatial dispersion of economic activity. With optimal population size, at the margin the increasing returns to scale due to the local public goods just balance the decreasing returns to scale due to land scarcity. At the corresponding locally constant returns to scale allocation, the average cost of providing residents with an exogenous level of utility is minimized.

With heterogenous individuals who may differ according to tastes or production characteristics, optimal population size is not well defined. In these circumstances, the Henry George Theorem states that in any Pareto optimal allocation differential land rents equal expenditures on pure local public goods.

The generalized Henry George Theorem allows for multiple sources of spatially localized increasing returns to scale and of spatially localized decreasing returns to scale. Sources of spatially localized increasing returns to scale include, in addition to pure local public goods, increasing returns to scale in production (which can be internal to the firm, external to the firm but internal to the industry (so-called localization economies), or external to the firm but internal to the city (so-called urbanization economies)) and localized congestible facilities with decreasing long-run average costs. Sources of spatially localized decreasing returns to scale, in addition to land scarcity, include localized disamenities such as air pollution and localized congestible facilities with increasing long-run average costs. The generalized Henry George Theorem also allows for distortions. The generalized Henry George Theorem states that in any constrained Pareto optimal (which allows for unalterable distortions) and nontrivial (neither indeterminate, completely agglomerated, nor completely dispersed) allocation of population in a spatial economy, the aggregate shadow losses from the increasing returns to scale activities (losses evaluated at social opportunity costs or shadow prices) just equal the aggregate shadow profits from the decreasing returns to scale activities.

This paper has two aims. The first is to provide an intuitive and nontechnical presentation of the Theorem and to demonstrate how very general the Theorem is. The second is to address the question that forms the title of the paper: Does the Henry George Theorem provide a practical guide to optimal city size? This question entails two subquestions: Can the Theorem in principle be applied to infer in what ways the distribution of population over a system of cities is distorted? And if the answer to this question is affirmative, are the data available that would be needed to calculate whether an actual city is over- or underpopulated, or could these data be collected? In addressing these questions, the paper will draw heavily on Kanemoto, Ohkawara, and Suzuki (1996a), which uses the Henry George Theorem as the conceptual basis in estimating whether Tokyo is too large. …

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