Comments on "Echoes of Henry George in Modern Analysis"

American Journal of Economics and Sociology, The,  Nov, 2004  by Fred E. Foldvary

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Public Finance and Urban Economics: Optimal City Size

RICHARD ARNOTT'S PAPER ASKS, "Does the Henry George Theorem Provide a Practical Guide to Optimal City Size?" The paper invokes the Henry George Theorem (HGT), which states that at the optimal city population, the total civic land rent (aggregate rent minus the nonurban rent) equals the cost of providing public goods. The public good is fully paid for by the rent, with no user fee, since the marginal cost of providing one more user is zero. This modern Theorem echoes and vindicates Henry George's proposal for a single tax that finances public goods. The HGT thus applies to public finance as well as to urban economics.

Arnott's model uses a featureless plain where labor is exerted at one point. With identical individuals, utility is maximized at a population for which the expenditure for the public good equals half the commuting costs. The Theorem generalizes to heterogenous individuals and holds for any level of the public good. Applied to a market economy, developers compete in the creation of cities, choosing the level of public goods, and collecting the rents to pay for them. Since rent is the revenue and the costs are the expense of the optimal amount of the public good, a zero economic profit implies the HGT, an efficiency result from minimizing the average cost in competition.

Arnott extends the HGT to contestable facilities, where the sum of land rents and Pigouvian user fees (i.e., payments equal to the social cost of the externality) cover the costs of constructing the facilities of optimal capacity. The HGT can also handle the complexity of metropolitan areas (club complexes), where different public goods (e.g., opera houses and swimming pools) can be efficiently provided in different but overlapping territories or "spatial units of replication." Arnott adds that the Henry George Theorem continues to hold in distorted economies when resources are evaluated at their shadow prices, in other words, their social opportunity costs.

Arnott states that the Georgian single tax is on "market rents" rather than on shadow rents, but actually, George intended that it be applied to the economic rent, what the land would fetch in its highest use, and so the single tax on site rentals is properly applied to the shadow rents or land values, reflecting the real costs, the social opportunity costs.

According to Arnott, the theory of optimal city size does not encompass the possibility of land speculation. However, if all the rent is collected to pay for the public good, there would be no land speculation, since future rents would all be tapped by the provider of the good. As to the question posed by the title of the paper, Arnott's answer is "hopefully in time." But the most useful application of the HGT is not to compute the optimal city size, but to confirm George's theory that site rentals not only offer the most efficient source of revenue for public goods but are also adequate to finance them. Do this, and profit-seeking developers as well as utility-seeking land users will sort themselves out in response to the rental payments and benefits.