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

Summary

This 2004 paper by Richard Arnott — co-author, with Joseph Stiglitz, of the canonical 1979 formalization of the Henry George Theorem (HGT) — appeared in The American Journal of Economics and Sociology (Vol. 63, No. 5, November 2004, pp. 1057–1090), as part of a symposium titled "Echoes of Henry George's Economics in Modern Analysis." Arnott is Distinguished Professor of Economics at Boston College (previously Boston University), a leading figure in urban and public economics, and at the time of writing edited Regional Science and Urban Economics. This is not an outside critique: it is the theorem's own principal architect asking, twenty-five years after Arnott & Stiglitz (1979), whether the result he helped prove is actually usable — that is, whether it can tell us whether an actual city (the paper's running example is Tokyo) is too big or too small. The paper has two stated aims: first, to give an intuitive, nontechnical exposition of the HGT and show "how very general" it is; second, to assess whether it provides a promising empirical/conceptual foundation for estimating over- or under-population of cities.

The Core Argument and Findings

1. The basic HGT, restated. With identical individuals, in a city of optimal population size, aggregate differential land rent (aggregate urban land rent net of the opportunity cost of land in non-urban use) equals aggregate expenditure on pure local public goods. Population size balances two opposing spatial forces: increasing returns to scale from spreading the fixed cost of local public goods over more residents, against decreasing returns from rising marginal commuting costs as the city grows. At the optimum, the two exactly offset, and — as a corollary of the Product Exhaustion Theorem applied to a constant-returns economy — aggregate land rent equals aggregate public-goods spending (pp. 1057–1066).

2. Arnott is explicit that George did not anticipate this theorem. He writes plainly that "there is... no suggestion in George's writings that a confiscatory tax on land raises just the right amount of revenue to finance pure public goods in a city of optimal population," concluding that "George's writings did not anticipate the Henry George Theorem" — it provides "a different argument for the single tax" than George's own (p. 1068). This is a Type-A/C factual-historical clarification: the theorem bears George's name because it formalizes his intuition that public investment is capitalized into land value, not because George stated or proved it.

3. The theorem generalizes very broadly ("the generalized HGT"). Arnott shows the result survives far beyond the toy identical-individuals model: it holds with heterogeneous individuals and multiple goods (applying then to any Pareto-optimal allocation, not just a single optimal city size); with alternative sources of increasing returns to scale (Marshallian agglomeration economies internal or external to firms, congestible facilities, not just local public goods); with durable capital and infrastructure in dynamic/intertemporal settings (extending the static rent identity to a present-value-of-land-values identity); and — critically — even in the presence of real-world distortions such as unpriced congestion externalities and agglomeration spillovers, provided aggregates are measured at shadow prices rather than market prices (pp. 1068–1075). This generality is the paper's strongest and most citable theoretical contribution: the HGT is not a fragile artifact of one stylized model.

4. But the generalized theorem's practical bite is blunted by several specific problems, which Arnott enumerates directly: - Heterogeneity implies a system of differently-sized cities, not one number. With heterogeneous tastes, production characteristics, or industries, "optimal population size is not well defined" for a single city; the theorem instead describes an optimal spatial unit of replication — potentially a whole multi-city industrial cluster — making "optimal city size" for any one city an ambiguous target (pp. 1058, 1071). - The integer problem. A country's population will rarely be an exact multiple of the average-cost-minimizing spatial unit, and the resulting constrained optimum can have multiple local minima at non-integer multiples — so "one cannot say a priori" whether efficient allocation implies aggregate shadow profits above or below zero for the economy as whole. Arnott states plainly that "the degree to which the integer problem causes the HGT to be violated has not been investigated empirically" (pp. 1071–1072). - Land heterogeneity (Ricardian differences) is unmodeled. The theorem assumes homogeneous land, but real locations differ in fertility, amenity, and natural accessibility; Arnott notes "to my knowledge, this question has not been investigated in the literature" (p. 1072). - Market vs. shadow prices diverge under real distortions, and the direction/size of the gap is generally indeterminate. Arnott walks through two major real-world distortions — uninternalized agglomeration externalities and unpriced transport congestion — plus land-use controls and property (rather than pure land-rent) taxation, concluding: "in a constrained Pareto optimal economy... little can be said in general concerning how close the generalized Henry George Theorem, with the corresponding aggregates valued at market rather than shadow prices, comes to holding" (p. 1075).

5. The one empirical application available is Kanemoto, Ohkawara & Suzuki (1996), and Arnott gives it a qualified but real endorsement. That unpublished study used a market-price version of the HGT to test whether Tokyo — famous for extreme land values, reaching an estimated 5.35 times Japanese GNP in 1990 — is overpopulated relative to other Japanese cities. Arnott identifies a "long chain of questionable assumptions" the study must make to get from the generalized theorem to a testable procedure (ignoring heterogeneity and the integer problem, assuming the theorem holds city-by-city rather than per spatial-replication-unit, assuming a constant ratio of aggregate land values to shadow production losses across the urban hierarchy). Their finding: the ratio of aggregate market land value to shadow production losses is not systematically larger for Tokyo than for other Japanese cities — implying that if Tokyo is overpopulated, "it is no more overpopulated than the average Japanese city." Arnott's assessment is careful and non-dismissive: that it "would be easy to dismiss" the Kanemoto–Ohkawara–Suzuki conclusion given "the long chain of questionable assumptions… But quantification is an essential element of enlightened policy making, and if the procedure employed… is the soundest available, its conclusion should be respected until a sounder procedure is developed" (p. 1083).

6. Arnott compares the HGT approach against the alternative "marginal social cost vs. private cost" approach to over/underpopulation, concluding the two are conceptually complementary rather than competing: the HGT approach requires markedly less data (city-level land values, output, and estimated local returns-to-scale) but implicitly assumes away the integer problem and requires the disputable market-shadow-price equivalence; the marginal-cost/benefit approach is more data-hungry and requires a value judgment that "a dollar is a dollar" regardless of who holds it, but sidesteps the integer problem and the need for land-rent data (pp. 1083–1084).

Relation to the Georgist Case

This paper both strengthens and disciplines the theoretical case tied to the Henry George Theorem. It strengthens it by showing — from the theorem's own principal author — that the HGT rent-equals-public-goods-spending result is far more robust and general than the textbook identical-individuals derivation suggests, extending to heterogeneous populations, multiple sources of agglomeration, dynamic economies with durable infrastructure, and (at shadow prices) even distorted real-world economies. This directly reinforces Behrens, Kanemoto & Murata (2015), a later paper in the same "second-best generalization" tradition that Arnott's 2004 survey anticipates and partially previews.

But the paper disciplines any claim that the HGT is a ready-made practical policy tool. Arnott is candid that turning the theorem into an operational test of whether an actual city, or the actual share of public revenue land rent could fund, is over- or under-sized remains unresolved: valuing aggregates at the market prices any policymaker would actually observe (rather than the unobservable shadow prices the theorem strictly requires) generally introduces an indeterminate bias once agglomeration externalities, congestion, land-use controls, and property (as opposed to pure land-rent) taxation are present. His summary verdict — "Does the Henry George Theorem provide a practical guide to optimal city size? The jury is not yet in, but the approach is sufficiently promising to merit further exploration" (p. 1087) — is a considered "not yet," not a "no." For the outcome that public goods can be funded from the land rent they create, this paper is best read as evidence for the theoretical robustness of that claim's mechanism, while being an explicit caution against over-claiming that the theorem alone can currently size real-world land-rent-funded budgets or verify empirically whether any given city or jurisdiction has "got it right."

Nuances and Limits

• This is a theory-and-methodology survey, not a new empirical result. Arnott derives no new numbers about any actual city; the paper's empirical content is entirely a critical review of one prior unpublished study (Kanemoto, Ohkawara & Suzuki 1996).
• The generalized HGT's validity at market prices in distorted economies is explicitly left open — Arnott shows it holds in the Kanemoto-Ohkawara-Suzuki model's particular distortion structure (a single Marshallian production externality) but states no general result holds once congestion, land-use controls, and property taxation are added simultaneously.
• The theorem is about efficient population allocation, not about the level or fairness of revenue. It says aggregate rent equals aggregate optimal public-goods spending at the optimum — it does not by itself establish that observed rent equals observed spending in any real city today, nor does it address distributional questions (Arnott separately notes the marginal-cost/benefit alternative "approach" embeds a distributional judgment that the HGT approach does not).
• Data availability is a first-order constraint. Arnott notes that "data on land values" (as opposed to land rents) are available for very few jurisdictions — Japan is one of the few exceptions, which is why Tokyo, rather than a US or European city, was the test case available in 1996–2004.
• The integer problem and land heterogeneity are flagged by Arnott himself as unresolved research gaps, not settled matters — both remain, to his knowledge at the time of writing, empirically uninvestigated.

Bears On

• Outcome: Public goods can be funded from the land rent they create — reinforces the theoretical robustness of the rent-equals-public-goods mechanism across many generalizations, while cautioning that using it as an operational empirical/policy test of real-world land-rent adequacy is still an open research question, not a solved one.
• Concept: Henry George Theorem — this is the theorem's co-founder's own account of how far the result generalizes and where its practical application currently stalls.
• Objection: Land value can't be assessed accurately — Arnott's point that land value (not rent) data are rare outside jurisdictions like Japan, and that market vs. shadow land values diverge unpredictably under real distortions, is a mainstream-economist statement of a closely related measurement problem.
• Research: Arnott & Stiglitz (1979) — this paper is Arnott's own retrospective extension and stress-test of that founding result.
• Research: Behrens, Kanemoto & Murata (2015) — the later "second-best" generalization this 2004 paper anticipates in spirit (both ask how far the HGT survives real-world frictions).

See Also

• Kanemoto, Ohkawara & Suzuki (1996) — the Japanese optimal-city-size test the practical-guide question builds on
• Richard Arnott
• Henry George Theorem
• Arnott & Stiglitz (1979): Aggregate Land Rents, Expenditure on Public Goods, and Optimal City Size
• The Henry George Theorem in a Second-Best World (Behrens, Kanemoto & Murata 2015)
• The Theory of Local Public Goods (Stiglitz 1977)
• Objection: Land value can't be assessed accurately

Sources

1. Richard Arnott (2004), "Does the Henry George Theorem Provide a Practical Guide to Optimal City Size?" The American Journal of Economics and Sociology 63(5): 1057–1090. JSTOR · Full-text PDF — used for all claims, findings, and quotations above; full text read directly.
2. Richard Arnott & Joseph Stiglitz (1979), "Aggregate Land Rents, Expenditure on Public Goods, and Optimal City Size," Quarterly Journal of Economics 93(4): 471–500 — used for background on the original theorem this paper revisits; see wiki summary.
3. Yoshitsugu Kanemoto, Toru Ohkawara & Tsutomu Suzuki (1996a), "Agglomeration Economies and a Test for Optimal City Sizes in Japan" (unpublished ms.); related published version: Kanemoto, Ohkawara & Suzuki (1996b), Journal of the Japanese and International Economies 10: 379–398 — the empirical Tokyo application discussed and critically assessed in Arnott's §IV; cited as reviewed by Arnott, not independently verified in this session.
4. Boston College, Richard Arnott faculty profile — used to verify Arnott's institutional affiliation and field. [VERIFY: current faculty-page URL, as this session's fetch relied on the paper's own author footnote (p. 1057) rather than a live BC directory page.]