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Henry George Theorem

Joseph Stiglitz: October, 2002, interview

Q: Your academic work led you to formulate what you called "The Henry George Theorem." This demonstrated that public spending — where this was efficient — generated additional rental value that surfaced in the land market. Other distinguished scholars, such as the late Nobel prize winner, William Vickrey, confirmed your findings. You also noted in one of your books, co-written with Anthony Atkinson, that the Henry George Theorem was attractive both because it was the revenue-raiser that did not distort private incentives and because "it is the 'single tax' required to finance the public good." [Anthony B. Atkinson & Joseph E. Stiglitz, Lectures on Public Economics, London: McGraw-Hill, 1980, p. 525] Now, public investment, unless of the wasteful kind designed to serve the privileged interests of rent seekers (the classic type being a land speculator), should be viewed as working in partnership with the private sector and not a drain on the community. How can the reputation of publicly provided services and investments be rescued?

JES: That's a very good question. What we did when I was at the Council of Economic Advisors was some studies to try to show what the social returns would be to public investment in R&D, etc. And we became convinced that the rates of return of those investments are very high. So you ask the question, "what can we do to restore confidence in public investment?" We need to realize how much we depend on them. I keep telling people, "The Internet." That's one example. It was publicly funded. It's now a public-private partnership. The government did the basic research, and the private sector ran off with it. But, arguably, we would never have had the Internet if it were not for government expenditure. So I think a major industry in the United States — biotech — is based on NIH (National Institutes of Health). NIH does all the basic research. ... read the entire interview

Fred E. Foldvary — The Ultimate Tax Reform: Public Revenue from Land Rent

The tax reform presented here is not new. It has been working to some degree in many cities and countries around the world. The idea probably obtained its greatest popularity in the U.S. in the late 1800s, when the economist Henry George analyzed taxing land value and untaxing labor and capital in his book, Progress and Poverty.

Many economists have since then expanded on George’s writing, examining both the theory and the evidence. There is even a “Henry George Theorem,” which proves that in a community with optimal population, the land rent equals the value of the community’s public goods. Modern economics thus affirms George’s theory in a more comprehensive and more rigorous form, although the empirical question of how much revenue could be obtained from rent would benefit from more research. ... read the whole document


Nic Tideman:  The Morality of Taxation: The Local Case

From a moral perspective, taxation is dubious or worse. We tell our fellow citizens that if they do not pay taxes that we say they owe, their property will be seized or they will be sent to prison. Why do we treat people this way? Is there a justification?

The dubiousness of taxation increases when we consider its origins. Government seems to have originated as roving bandits who learned that total destruction was less profitable than protecting their victims from other bandits and allowing them to keep a fraction of what they produced (Olson, 1993). In time, scheduled partial plunder evolved into taxation. Over the centuries, regimes that started as tyrannies evolved into democracies. The public sector evolved from an apparatus for implementing the will of despots into a mechanism for carrying out democratic decisions. But public finance continues to rely on the power of tax collectors, developed under early tyrants, to coerce citizen to pay taxes. The wrath that citizens feel toward tax collectors is probably the strongest antagonistic feeling that citizens have toward a governmental institution. Why do we allow ourselves to do this to one another?

There is a gentler side of taxation that provides some explanation of our tolerance of this coercion. Taxation can be the way that people achieve their common purposes. People may agree to be taxed so that there will be money to pay for public services that they want. From this perspective, taxation may be considered no more than the dues for belonging to a club that provides people with things that they would rather pay their share of than do without. However, to make this "voluntary exchange" theory of taxation relevant, people must be able to choose freely whether or not to "join the club," to be a citizen of the taxing jurisdiction. With all land claimed by some taxing jurisdiction, the choice isn't exactly free.

The problem of morality in taxation is the following:

  • How do we retain the possibility of people pooling their contributions to the cost of services that they agree are worthwhile, while eliminating the possibility of citizens treating their fellow citizens as targets of plunder?
  • What are the limits of obligations that we can justly impose on our fellow citizens?
  • And how do we set up a structure of government that will ensure that these limits are observed? ...
we would probably have a much more efficient public sector if every public expenditure required two-thirds approval in legislative bodies.

But to make taxation truly voluntary, the option to leave must be viable. If people could move costlessly from one jurisdiction to another, taking all of their belongings with them, then competition among jurisdictions would tend to eliminate oppressive taxation. This would leave only the fees that people were prepared to pay to have public services (Tiebout, 1956).

Of course, moving will always have some costs, so the ideal will not be attainable. But what can be imagined is a system in which all taxes were local taxes. Then people would not have to move nearly as far to escape from taxes that they regarded as oppressive. Higher levels of government would not need to disappear; if the services that they provide are desired, they could be financed by levies on lower levels of government. ...

...Thus communities would not be able to raise much revenue from income tax or taxes on capital before they would drive residents and investment away. It might seem that there would be no way that localities could finance themselves.

Such a conclusion would be unwarranted, because there is a very significant source of public revenue that can survive when localities compete for mobile residents. This source is land. When people are taxed in proportion to the land they possess, no land moves to another locality where taxes are lower. Thus two questions arise:

  • Would taxes on land be sufficient to finance the public activities that ought to be undertaken, and
  • would such a system be fair?

Consider first the question of adequacy of revenue. There is a theorem in economics, known as the Henry George Theorem, that addresses this question (Arnott and Stiglitz, 1979). One of the simpler versions of this theorem is:

If the following three conditions are met:

1. Public expenditures provide benefits only over a limited area,
2. People can move costlessly, and
3. The number of persons who value a public service as highly as anyone does exceeds the number of persons who can live in the area where the service provides benefits,

then for any public service that is worth at least as much as it costs to those who receive it, the increase in the rental value of land that results from providing the service exceeds the net cost of the service.

The Henry George Theorem is true because people who can move costlessly will bid up the rental value of land to reflect the value of public services that are not available elsewhere. The assumption that the number of bidders exceeds the number of people who can benefit from the public service guarantees that the upward movement of rents will not end until all the benefits of the public service are reflected in these rents. If some people who receive a public service value it more highly than others, then they will receive a surplus in addition to the rent they pay for land, and some worthwhile increments of public services will not add quite enough to rent to pay for themselves (Tideman 1993). But rent increments will go a very long way toward paying for worthwhile local public services. ...Read the whole article

Fred Foldvary: Geo-Rent: A Plea to Public Economists
Textbooks in public finance and urban economics sometimes contain a topic known as the “Henry George Theorem.” It states that the public revenue that provides for the collective goods of an optimally-sized community equals the land rent of that community. As presented in Atkinson and Stiglitz (1987, 523-5), the representative agent’s utility function is U(G,X), where G is a collective and X a private good. Output Y is a function of N workers:

Y = f(N) = XN + G.
X = {f(N)-G} / N
The wage is the marginal product of labor:
∂f/∂N = X
∂f/∂N = {(f(N)-G)/N}
G = f(N) - Nf’(N)

With land and labor the ultimate and original factors of production, rent (R) is the difference between total product Y and total wages:
R = f(N) - Nf'(N)

R = G.
The Henry George Theorem is so named because it echoes Henry George's (1879) single-tax proposal, that not only should land rent be the only general tax, but that it will be adequate to finance public goods. The theorem is accepted in public finance, but it is not applied. In upper-level public-economics textbooks such as Atkinson and Stiglitz (1987), it is presented, yet not invoked in policy discussions, and it is ignored in scholarly treatments of optimal taxation, tax reform, and public policy.

Edwin Mills (1998) goes further and constructs a comparative static model of a metropolis using a Cobb-Douglas production function with three factors, the third being land, which is a refreshing change from the usual two-factor analysis that tucks land into capital and then forgets that it’s there. One theorem of the model is that a land-value tax has no effect on resource allocation. Yet he concludes (47) that despite is theoretical attractiveness a significant taxing of geo-rent would deprive the owners of their beneficial uses, and would require compensation, leaving the tax “practically almost worthless” (47, 41).
Thomas Nechyba (1998) also has a model with land, calibrated to U.S. parameters. He shows that replacing taxes on capital with taxes on land can actually increase land values, despite the downward capitalization caused by the tax, because of the greater increase in capital and rent. According to the model (p. 196), with an elasticity of substitution between capital and land of 0.5, which is within the estimated range, a revenue-neutral tax shift to land value increases capital goods by 122 percent and raises output by 89 percent. Read the entire article

Richard Arnott, Kenneth Arrow, Anthony B. Atkinson and Jacques H. Dreze, editors, Public Economics: Selected Papers by William Vickrey. Cambridge University Press, 1994.

from the introduction to the section on Urban Economics, p. 336.

"One of the most celebrated results in urban economics is the Henry George Theorem. The best-known variant of the Theorem states that in a city of optimal population size, where the source of agglomeration is a localized pure public good, urban (differential) land rents equal expenditure on the public good. Thus, a confiscatory tax on land rents is the single tax necessary to finance the public good. The explanation for the result is as follows: In a city of optimal population size, the average social cost of providing residents with a given level of utility is minimized. At the point of minimum average cost, there are locally constant returns to scale so that the product exhaustion theorem holds. With marginal-cost pricing, the profits generated from the decreasing returns to scale activities equal the losses fro mthe increasing returns to scale activities. In the current contect, the profits take the form of land rents and the loss is the expenditure on the local public good. The Henry George Theorem was discovered independently by Serck-Hansen (1969), Starrett (1974), Flatters, Henderson and Mieszkowski (1974), and Vickrey. Vickrey delayed publication and was the last into print. Unfortunately, therefore, his 1977 paper on the Theorem, "The City as a Firm" (chapter 17), has not received the recognition it deserves. In any event, the paper provides an elegant formulation of a variant of the Theorem and an insightful explanation and discussion of it."

the Summary to Vickrey's "The City as a Firm"

"While it is dangerous to extrapolate too freely from admittedly oversimplified and even caricatured models (such as the above) to the complexities of the real world, it seems not too rash to draw the conclution that urban land rents are, fundamentally, a reflection of the economies of scale of the activites that are carried on within the city, and that efficient organization of a city, or even of the urban life of a nation as a whole, requires that these land rents, or their equivalent, be devoted primarily to the finacing of the intramarginal residues that represent the difference between revenues derived from prices set at marginal cost and the total cost of the activites characterized by increasing returns. This means that revenues derived from these rents must defray not only those overhead costs of government and public services that are not marginally attributable to specific outputs, but also the intramarginal elements of most public utility costs, as well as thoser of a considerable range of activities ordinarily thought of as belonging to the private sector. Such a subsidy is especially crucial for mass transit and for other forms of transportation where economies of scale are significant, given the special relationship existing between transportation and land values.

Use of land rents, or, at least, of a major fraction of them, for public purposes is therefore not merely an ethical imperative, derived from categorization of these retns as an unearned income derived from private appropriation of publicly created values, but is, even more importantly, a fundamental requirement for economic efficiency. Cities that take the lead in such public use of land rents may find that in the long run the subsidy is self-financing through the enhancement in land values that results, while cities that lag may find that in the long run they are unable to compete in national or world markets with the cities that manage to organize themselves more efficiently through the use of land rents to cover intramarginal residues. There will, of course, be many an agonizing slip between abstract economic analysis and cold political and economic reality. Lack of comprehension, political intervention, strategic recalcitrance, and the inertia associated with heavy commitments of fixed capital in what the French so aptly term immeubles may slow the processes involved to a glacial pace. But the fundamental tendencies and requirements inherent in the very nature of the city can be ignored only at great peril to its economic health."

Henry George: The Condition of Labor — An Open Letter to Pope Leo XIII in response to Rerum Novarum (1891)

God’s laws do not change. Though their applications may alter with altering conditions, the same principles of right and wrong that hold when men are few and industry is rude also hold amid teeming populations and complex industries. In our cities of millions and our states of scores of millions, in a civilization where the division of labor has gone so far that large numbers are hardly conscious that they are land-users, it still remains true that we are all land animals and can live only on land, and that land is God’s bounty to all, of which no one can be deprived without being murdered, and for which no one can be compelled to pay another without being robbed. But even in a state of society where the elaboration of industry and the increase of permanent improvements have made the need for private possession of land wide-spread, there is no difficulty in conforming individual possession with the equal right to land. For as soon as any piece of land will yield to the possessor a larger return than is had by similar labor on other land a value attaches to it which is shown when it is sold or rented. Thus, the value of the land itself, irrespective of the value of any improvements in or on it, always indicates the precise value of the benefit to which all are entitled in its use, as distinguished from the value which, as producer or successor of a producer, belongs to the possessor in individual right.

To combine the advantages of private possession with the justice of common ownership it is only necessary therefore to take for common uses what value attaches to land irrespective of any exertion of labor on it. The principle is the same as in the case referred to, where a human father leaves equally to his children things not susceptible of specific division or common use. In that case such things would be sold or rented and the value equally applied.

It is on this common-sense principle that we, who term ourselves single-tax men, would have the community act.

We do not propose to assert equal rights to land by keeping land common, letting any one use any part of it at any time. We do not propose the task, impossible in the present state of society, of dividing land in equal shares; still less the yet more impossible task of keeping it so divided.

We propose — leaving land in the private possession of individuals, with full liberty on their part to give, sell or bequeath it — simply to levy on it for public uses a tax that shall equal the annual value of the land itself, irrespective of the use made of it or the improvements on it. And since this would provide amply for the need of public revenues, we would accompany this tax on land values with the repeal of all taxes now levied on the products and processes of industry — which taxes, since they take from the earnings of labor, we hold to be infringements of the right of property.

This we propose, not as a cunning device of human ingenuity, but as a conforming of human regulations to the will of God.

God cannot contradict himself nor impose on his creatures laws that clash.

If it be God’s command to men that they should not steal — that is to say, that they should respect the right of property which each one has in the fruits of his labor;

And if he be also the Father of all men, who in his common bounty has intended all to have equal opportunities for sharing;

Then, in any possible stage of civilization, however elaborate, there must be some way in which the exclusive right to the products of industry may be reconciled with the equal right to land.

If the Almighty be consistent with himself, it cannot be, as say those socialists referred to by you, that in order to secure the equal participation of men in the opportunities of life and labor we must ignore the right of private property. Nor yet can it be, as you yourself in the Encyclical seem to argue, that to secure the right of private property we must ignore the equality of right in the opportunities of life and labor. To say the one thing or the other is equally to deny the harmony of God’s laws.

But, the private possession of land, subject to the payment to the community of the value of any special advantage thus given to the individual, satisfies both laws, securing to all equal participation in the bounty of the Creator and to each the full ownership of the products of his labor.


... read the whole letter


Nic Tideman: The Structure of an Inquiry into the Attractiveness of A Social Order Inspired by the Ideas of Henry George
 I. Ethical Principles

A. People own themselves and therefore own what they produce.
B. People have obligations to share equally the opportunities that are provided by nature.
C. People are free to interact with other competent adults on whatever terms are mutually agreed.
D. People have obligations to pay the costs that their intrusive behaviors impose on others.
II. Ethical Questions
A. What is the relationship between justice (as embodied in the ethical principles) and community (or peace or harmony)?
B. How are the weak to be provided for?
C. How should natural opportunities be shared?
D. Who should be included in the group among whom rent should be shared equally?
E. Is there an obligation to compensate those whose presently recognized titles to land and other exclusive natural opportunities will lose value when rent is shared equally?
F. Can a person who is occupying a per capita share of land reasonably ask to be left undisturbed indefinitely on that land?
G. What is the moral status of "intellectual property?"
H. What standards of environmental respect can people reasonably require of others?
I. What forms of land use control are consistent with the philosophy of Henry George?
III. Efficiency Questions
A. Would public collection of the rent of land provide enough revenue for an appropriate public sector?
B. How much revenue could public collection of rent raise?
C. Is it possible to assess land with sufficient accuracy?
D. How much growth can a community expect if it shifts taxes from improvements to land?
E. To what extent does the benefit that one community receives from shifting taxes from buildings to land come at the expense of other communities?
F. What is the impact of land taxes on land speculation?
G. How, if at all, does the impact of shifting the source of public revenue to land change if it is a whole nation rather than just a community that makes the shift?
H. Is there a danger that the application of Henry George's ideas would lead to a world of over-development?
I. How would natural resources be managed appropriately if they were regarded as the common heritage of humanity?    Read the whole article




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Wealth and Want
... because democracy alone hasn't yet led to a society in which all can prosper