Bill Vickrey was a major figure among contemporary Georgists. He died, en route to a meeting of Georgist scholars, a few days after learning he was to be a joint recipient of the Nobel Prize in Economics in 1996. Here is a collection of tributes which will give you a sense of both the man and his ideas.

http://henry-george.org.au/gaffney.1996.10.html

[ed note: William Vickrey, Columbia University, New York, born Victoria, British Columbia, June 21, 1914; died October 11, 1996, aged 82; joint winner of the 1996 Nobel Prize for Economics with James Mirrlees of Cambridge University].

The evening of the day Bill Vickrey won his Nobel I impulsively, hesitantly dialed his home. His phone surprised me by ringing unbusy, and Bill surprised me more by answering, and sounding unhurried. After congratulations, I asked "Bill, was this for a lifetime of achievement, or some specific work?" "I don't know," he replied. "Well," I persisted, "Is there a citation? What does it say?" "Yes," he said, "there is one, but I can't understand it." If you and I find it a puzzle, we have good company.

Mission performed, I hastened to ring off, but Bill kept me on the line. To Bill, the transaction was incomplete -- too one-sided. He turned things around and said "Tell me about yourself. What are you working on now?" I told him as briefly as I could, and he immediately offered to help. It was not a perfunctory sham offer, he's helped me before. "How are the wife and children?" He really wanted to know, and report back to Cele. That was Bill, thinking of others, in the time of his greatest triumph, at the end of a long, wearying day of praise and celebration. What a saint! And I thank that other saint, my wife, who nudged me to call right away: two days later Bill left us forever.

Bill was born in Victoria, B.C., his mother's home. His middle name was Spencer, as in Spencer's Stores; they had merged with, I believe he said, Eaton's. From the Spencer side he got his sense of how business works. His father was a preacher from Illinois who raised money for starving Armenians -- literally. From him Bill got his firm sense of social justice, plus a reflex against spending money on his own creature comforts. At professional meetings he sought out cheaper lodgings than anyone else, though his expenses were covered. He did it inconspicuously so as not to make others uncomfortable: his humility was not for flaunting, he just lived it. Again, what a saint!

Bill had a degree in mathematics from Yale, before turning to economics at Columbia. He was not one to hide behind phony math, as most economists do now, nor to intimidate others; but none could snow or intimidate him, although many tried. In spite of the phonies, genuine math can be truly useful, and that's when he drew on this skill plus his insight and talent, which went far deeper than mere skill. He gave freely of them. At one point he dashed off a mathematical appendix to an article I had struggled over for months. His page of squiggles pretty well comprehended and tied together and validated all the points I had spread over 50 pages. He gave it to me gratis -- that was Bill. For him, it was effortless: "Just a matter of inverting the order of integration," he explained casually. What a saint!

Bill had high standards, but no false standards. He feared no contamination or loss of caste by consorting with less renowned economists, or supporting ideas that lacked mainline "respectability" and "prestige." If he had a fault, it was projecting his own virtues onto others. He was delightfully ingenuous in personal dealings, and could not impute base, careerist motives to social and professional climbers.

It was in 1964 or so that I called Bill impulsively and hesitantly the first time. Art Becker and Weld Carter and I were growing a committee of economists to meet annually and produce a modern Georgist literature, but who were we in the world? Bill had published works on financing mass transit that breathed a distinct sweet odor of Georgism. Like a bee to a flower, I buzzed him. It was a good impulse; he accepted, suddenly we were somebodies, and other somebodies joined up, too. Soon we had our academic-Georgist Camelot, if only for one brief shining moment. Our committee, named TRED, produced about ten volumes of neo-Georgist literature, published by the University of Wisconsin Press. Bill had a chapter in our first volume, and also helped me, as editor, straighten out a headstrong contributor who insisted on turning rents into earned incomes. When Bill wrote, people heeded, and Bill was ever ready to lend a hand. I thought of him as a big brother to call on in need. How I shall miss my big brother!

At Columbia, Bill rubbed elbows with Harold Hotelling, the most brilliant and creative economist of his generation. Hotelling was a closet Georgist who never fully came out, even after a lifetime of professional acclaim for his technical triumphs - a measure of the pressure used to squelch academic Georgists. The nearest he came was to let Will Lissner include him on a roster of "Editorial Advisers" to the AJES. Francis A. Walker, first President of the American Economic Association in 1885, had written "I will not insult my readers by discussing a project so steeped in infamy" as taxing land values. Bill Vickrey, President of the same Association 106 years later, wrote on the same subject that we should tax 'em to the max. He joined Nic Tideman in composing a letter to Gorbachev advising the then-Soviets to base their privatization strategy on taxing land values. Together they signed up 20-30 highly visible economists, including four earlier Nobel laureates. This did not stop Bill from winning his Nobel in 1996. Perhaps our cause has progressed within the ivied walls, after all; or perhaps that is just a measure of Vickrey's personal courage and conscience, and the power of courage and conscience to overcome fear and win confidence -- even of Nobel prize committees.

A reporter asked Bill what he would do with his prize money. Bill said he didn't care about the money, and he spoke truly, for his conscience would not let him live it up while others were down. He said he valued the "bully pulpit" the prize gave him to spread his ideas. He didn't say which ideas; he had many. I am morally certain, however, that near the top of his list was implementing George's proposal to raise public revenues by taxing land values. The last thing he asked me before hanging up was, "Will I see you at the TRED meeting?" Bill never missed.

Bill died, as you know by now, en route to that meeting. He drove at night, true to his principle of easing peak-hour congestion. Had he arrived, I know he would have raised his head from the doze he affected and told some unwary journeyman, "This paper would benefit from an application of Henry George's idea of taxing land values." How do I know? Because he always did. I imagine by now he has mentioned it to God, too; and God has said "Actually, Bill, that's how we've always done it here; but thank you for urging folks to have my will done on earth as it is in Heaven."

http://www.econ.vt.edu/tideman/nobel.pdf

 Nicolaus Tideman

 The 1996 Nobel Prize in Economics was awarded to two public finance economists, James Mirrlees and William Vickrey. James Mirrlees is Professor of Economics at the University of Cambridge, in England. Until his death just three days after receiving the Noble Prize, William Vickrey was Professor of Economics Emeritus at Columbia University.

 Both of this year's winners have made numerous contributions to economics.

 Prof. Mirrlees is most famous for his analysis of "optimal income taxation." In this analysis, Prof. Mirrlees treats the problem of the choice of an income tax schedule as one of maximizing the aggregate utility of the members of a society. One might expect an economist to shun such an approach, on the ground that it requires interpersonal comparisons of utility, which economists generally regard to be unfounded. Instead, Prof. Mirrlees said, "Let's solve the problem in general, and then see what results from different assumptions about the way that the marginal utility of income varies with income." As Prof. Mirrlees conceives the problem, those who choose the income tax schedule must deal with the fact that, the greater the tax that is imposed on income, the less people will earn. The identification of the optimal income tax schedule is then a problem in the calculus of variation, a branch of advanced mathematics. Besides being a very impressive example of the application of mathematics to an economic problem, the analysis offers some interesting insights. One is that under most reasonably plausible assumptions about the way that the utility of income varies with income, the rate schedule that would maximize total utility entails rather modest maximum income tax rates. Another is that, under the rate schedule that maximized total utility, the marginal tax rate of the richest person on his last dollar of income would be zero! (You want to motivate him to work that last minute, and you don't lose any taxes on previous work, because that is all taxed at higher rates.)

 Prof. Vickrey wrote a book in the 1940s, suggesting that instead of having just an income tax, it would be sensible for a country to use a combination of an income tax, a consumption tax and a wealth tax. One of his suggestions was for a system of lifetime income averaging. Instead of paying a tax each year on that year's income, one would add this year's income to the sum of previous years' incomes, divide by the number of years to get average income, compute the tax on that amount of income, multiply by the number of years to get the total tax, and finally subtract the total of taxes paid in previous year to get the tax owed this year. Prof. Vickrey was also renown for his suggestions of public pricing schemes that more closely approximated marginal social costs. He may have been the first advocate of the practice of the airlines of seeking (paid) volunteers to wait for the next flight, instead of bumping the last persons to arrive. He was an early advocate of peak-load pricing for electricity, public transit, bridges, tunnels, and for city streets! He estimated that the social cost of an hour of driving in Manhattan at busy times (taking account of the value of the time of all the people who were slowed down by the presence of one more car on the streets) was $20,000! He did not want to charge people this much; he felt that a price of $20 to $50 per hour for driving in Manhattan would probably have brought the amount of driving down to where the benefit matched the cost. Prof. Vickrey was most famous in recent years for a 1961 paper that went virtually unnoticed for the first dozen or so years after it was published, but then came to be seen as the foundation of the theory of efficient auctions. In this paper, Prof. Vickrey introduced the idea of an auction in which each person makes just one bid, the item is sold to the person who makes the highest bid, but that person is only required to pay the second-highest bid. The characteristic of such an auction that has fascinated economists is that, with such a rule, it is in the interest of every bidder to bid exactly what the item is worth to him or her.

In choosing to honor Professors Mirrlees and Vickrey, the Nobel committee has highlighted the contribution that economics can make to the creation of a more productive public sector.

http://www.geocities.com/Athens/Acropolis/5148/netzer_vickrey_bio.html

William Vickrey died on October 11, three days after the announcement of his being awarded the Nobel Prize in Economics, while on his way to the Lincoln Institute for the annual research conference of the Committee on Taxation, Resources and Economic Development (TRED).

TRED meetings have been sponsored by the Institute for 20 years, and Bill Vickrey was at every one of those meetings. Indeed, his connection with TRED goes back even further, for he was one of the committee's founding members more than 35 years ago. TRED began in discussions among academic economists who were interested in contemporary applications of the ideas of Henry George and were also concerned with land and natural resources. Over the years, TRED's membership expanded to include public finance and urban economists interested in the use of land and economic phenomena related to how things are arranged over space.

Bill Vickrey was the ultimate intellectual sparkplug of TRED from the beginning. His wonderful inventiveness and irreverence came out in inspired, seemingly off-the-cuff interventions in the discussion, some of which have changed thinking about economics and economic policy forever. For example, in one sally he imagined a linear city in which all structures were truly mobile. This image made it possible to think clearly about location, the effects of the durability and immobility of structures, and appropriate land policies, without being trapped by peripheral issues. No one could cut to the quick like Vickrey.

TRED member Ed Mills of Northwestern University spoke to our assembled group at the Institute shortly after hearing the news of Bill's untimely death. "Bill Vickrey lived his life exactly as he wished, right to the end," Mills said. "He died with his boots on." Those of us who have been honored to know Bill for some time have been shaped by our contact with him, and we will miss him.

Dick Netzer
TRED member and visiting senior fellow of the Lincoln Institute

Here are a few more bits and pieces picked up online that will give you a sense of who Bill Vickrey was:

http://pw2.netcom.com/~masonc/vickrey.html#PEOPLE

Am I wrong, or is William Vickrey the old fellow that we often see hanging around at Post Keynesian sessions, say at the meetings of the EEA?

A stunned Marc Lavoie!

To Marc Lavoie about Bill Vickrey:

The answer is, Mais Oui! He is, and gave all of us young whippersnappers a good dose of his more old-fashioned Keynesian concern with achieving full employment no matter what at the Post Keynesian session at the EEA, as did Ingrid Rima.

Actually I have been somewhat amused to observe over a number of years people at the EEA treating him with less than proper respect. Two years ago I chaired a session for the nonlinear crowd that does its thing at the EEA and Vickrey was "imposed" on it by the EEA with a paper on deficit financing to achieve full employment, which he presented. I knew that the sub-organizers were kind of annoyed, so I made sure that I was the discussant, and treated the presentation with proper respect, if not necessarily full agreement (I expressed concern about the impact of unlimited foreign indebtedness, to which he cannily smiled, obviously looking like one who had heard that one before!).

I have noticed in previous years that he would sometimes show up for odd sessions with very small audiences, but which were actually extremely innovative and interesting. He is a very original and innovative thinker who remains close to the edge of the profession at a deeper level, even if not what is generally accepted as such by the mainstream. He has accomplished much and I applaud his selection. For once the Nobelers have been not so bad.

Barkley Rosser

Date: Thu, 10 Oct 1996
From: Max B. Sawicky
To: POST-KEYNESIAN THOUGHT
Subject: Bill Vickrey -- Live Like Him

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Response by Max B Sawicky:

The very same. He also used to frequent National Tax Association meetings, although I haven't seen him at the last few. If you chanced to meet him on the street, you might feel the urge to buy him a sandwich.

As Peter Passell wrote in the NY Times, Vickrey is famous for appearing to snooze through seminars, then rise at the end to edify the group with "razor-sharp questions."

My best Vickrey story comes from a tax meeting a couple of years ago. He was sitting alone down in front doing a crossword puzzle while corporate types babbled tediously about the international aspects of the Federal corporate income tax. When Q&A time came, he gets up in his gruff voice and says, "Don't you think you're just rearranging deck chairs on the Titanic?"

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Response by Max B Sawicky:

The work on which Vickrey's reputation is based defies the prejudices of many on this list: he is rigorously neoclassical in his microeconomics, but his choice of subject and application of n-c theory are of great help to anyone doing applied public finance from a liberal or progressive viewpoint. Other examples of such people are William Baumol, the pre-CEA Joseph Stiglitz, and a few people on this list whom I will decline to embarrass by naming them. To be sure, this has some un-progressive features: Vickrey and some others are dedicated free-traders and tend to take a jaundiced view of "labor monopolies" (e.g., trade unions).

Vickrey's macroeconomic views are certainly heterodox. He was quoted in the Washington Post to the effect that "balancing the budget is insane and would drive the economy into a depression." He also thinks the unemployment rate can be driven down to two percent, and that the NAIRU theory is positively evil. Vickrey has written a little on his scheme for "inflation warrants" which would levy a tax on firms that raised their prices; it resembles a value-added tax and would not be designed to collect much revenue -- only to enable the Fed and the Fisc to drive unemployment to perdition. On the whole, however, Vickrey has not done scholarly papers on macro; it's more like an avocation for him, though you would never know it judging by the strength of his feelings.

It is worth noting (and not surprizing, if you know Passell) that while Passell's piece in the Times was complimentary, he gave no hint of Vickrey's views on macro policy.

Date: Thu, 10 Oct 1996
From: James K. Galbraith
Subject: Nobel to Vickrey

I want to echo Paul Davidson and to congratulate Professor William Vickrey on his Nobel prize, which ought to raise the visibility of Post Keynesian economics in the wider world. Vickrey is a dogged and stalward progressive who remembers exactly what the unemployment rate was in 1926 (1.9 percent in peacetime) and thinks that was a pretty good example. He also has no patience for the balanced budget nonsense that has once again taken over economic policy discussion in this country. Congratulations, Bill, and see you at the next meeting wherever it may be!

James K. Galbraith
LBJ School of Public Affairs
The University of Texas at Austin
Austin TX 78713

Date: Mon, 14 Oct 1996
From: Timothy A. Canova
University of Miami School of Law
Subject: Re: The Vickrey loss

See: William Vickrey, "Today's Task For Economists", Challenge, March-April 1993:

According to Vickrey:

"There is no reason inherent in the real resources available to us why we cannot move rapidly within the next two or three years to a state of genuine full employment." Vickrey goes on to define genuine full employment as "a rate of unemployment, as currently measured, of between 1 and 2 percent. Practically, the desirable situation ought to be one in which any reasonably responsible person willing to accept available employment can find a job paying a living wage within 48 hours."

See also Vickrey's article in American Economic Review 83 (March 1993).

Vickrey was an advisory board member and active with the National Jobs For All Coalition, a coalition of scholars and advocacy groups based in New York. Vickrey proposed tradeable or "marketable growth markup warrants", with penalties or taxes for those corporations retaining fewer warrants than the excess of sales revenues over amounts paid for non-prime inputs in the preceding period. This was a variant of Abba Lerner's plan to control inflation by creating a market in rights to raise prices. For discussion of the above, see: Jobs For All, by Sheila D. Collins, Helen Ginsburg, and Gertrude Goldberg (Apex Press, 1994), p. 55.

http://www.nap.edu/html/biomems/wvickrey.html

WILLIAM VICKREY DIED ON October 11, 1996, three days after the announcement that the 1996 Bank of Sweden prize in economic sciences in memory of Alfred Nobel was being awarded to him and to Professor James Mirrlees of Cambridge "for their fundamental contributions to the economic theory of incentives under asymmetric information." Vickrey was eighty-two years old and had been a member of the National Academy of Sciences since April 1996. The press release from the Royal Swedish Academy of Sciences refers specifically to his work in the mid-forties on income taxation, then in the early sixties on auctions. With characteristic independence, Vickrey reacted by privileging instead his work of the late thirties on cumulative averaging of income for tax purposes and his then current concern with unemployment. Early insights, lifetime dedication, and late recognition are unmistakable traits of a truly remarkable career devoted to economics in the service of the public sector.

William Vickrey was born in 1914 in Victoria, British Columbia (Canada). He attended Yale, obtaining a science B.S. degree in 1935 and then went to Columbia University for graduate work in economics, obtaining an M.A. in 1937. The Ph.D. degree was awarded there in 1947 after completion of the "Agenda for Progressive Taxation," his 496-page doctoral dissertation included in 1972 among the Reprints of Economic Classics. The intervening ten years, including World War II, had been spent in various research or advisory positions related to taxation.

Vickrey joined the faculty of Columbia University in 1946 and never left, except for a few sabbaticals. His working life was devoted mostly to teaching and research, but it also included a significant amount of advisory and consulting services on behalf of public institutions and utilities, and a fair amount of non-specialist writing and lecturing.

The advisory and consulting missions encompass the major areas of Vickrey's applied research: taxation, public utilities, transportation, and urban problems. In 1949 he and his Columbia colleague Carl Shoup laid the foundation for the postwar tax structure of Japan. This was followed by a number of tax missions, notably to Puerto Rico, Venezuela, and Liberia. Vickrey also spent a year as an adviser on fiscal matters for the United Nations, working in Singapore, Malaysia, Iran, Zambia, Ivory Coast, Libya, and Surinam.

The work on public utilities started with the electric power industry in 1939 and gained momentum in 1951 with the famous study of subway fares performed for the Mayor's Committee for Management Survey of the City of New York. In 1959 he studied traffic congestion in Washington. Further studies on urban planning and transportation took him to India, Argentina, and Venezuela. Over the years, he developed ideas for efficient pricing of electricity, telephone services, urban transportation, street and road use, municipal services, and airlines. He also kept up with every conceivable technological development in these areas, visiting experimental designs on-site and attending specialized conferences.

The quest for efficiency of public services made him a crusader, advocating innovations not only through lectures for the National Tax Association, the NBER, public utility conferences, and transportation symposia, but also through testimony at hearings and letters to the New York Times. Often there is an expression of impatience at the slow acceptance of new ideas by regulatory and operating agencies. In recent years this impatience with blatant inefficiencies has been focused on the macroeconomic field. But the crusade goes on. Irrational budget accounting, excessive concern with inflation, and insufficient attention to wasteful unemployment had become favorite themes on which Vickrey hoped to capture more attention because of the notoriety of the Nobel award.

Response to practical challenges is only one facet of our late friend's intellectual curiosity. His interest in ethics and philosophy led to several publications. Interdisciplinary contacts always appealed to him, in particular through seminars. Bill Vickrey's fearsome participation in seminars was part of his legend, and in particular earned him the Rip van Winkle award from the Center for Advanced Study in the Behavioral Sciences "for deep and uninterrupted concentration while attending seminars." At Columbia, he showed up at seminars in many fields, and invariably attended the interdisciplinary ones.

Vickrey was a distinguished fellow of the American Economic Association (president, 1992) and a fellow of the Econometric Society. He was a past president of the Metropolitan Economic Association and the Atlantic Economic Association. Among various honors he received were the F. E. Seidman Distinguished Award in Political Economy and a doctor of humane letters degree from the University of Chicago.

William Vickrey's career was exceptionally rich, having extended over a full sixty years. His work included highly original contributions over a broad spectrum and displayed some distinctive methodological traits. His publications included eight books and some 140 articles, of which a selection with introductory reviews was published in 1994 by Cambridge University Press under the title Public Economics. The following illustrates the originality with reference to incentives and information, suggests the spectrum in regard to public economics, and concludes on methodological traits.

A central concern of economics is the extent to which decentralized decisions by a myriad of economic agents (consumers, workers, producers, asset holders, and public authorities) are compatible with efficiency and equity. Efficiency is a property of economic situations where it would not be possible to improve any one individual's circumstances without impairing those of another; in short, there is no waste. Equity is a more demanding and more controversial property; it relates the distribution of benefits across individuals to ethical premises.

Efficiency of decentralized decisions becomes possible when individual decisions are based on information and incentives reflecting correctly common values. In relatively simple situations, competitive prices for commodities (goods and services) provide correct information and incentives, as was recognized in 1776 by Adam Smith in The Wealth of Nations:

the marginal relative values of commodities are the same for all, since all face the same prices (information), which they cannot manipulate (incentives); further exchanges could not benefit both parties.

The "simple" situations correspond to a surprisingly broad range of economic activities, yet fall substantially short of universality. For instance, public services, like transportation and utilities, are produced under scale economies, which suggest a single producer (monopoly). Decreasing marginal costs lead to losses under competitive pricing. Either prices are not competitive or losses are covered by taxes and transfers. But taxes distort relative prices and affect incentives. Also, taxation raises at once equity issues.

In 1938 Carl Shoup, professor of public finance at Columbia University, and his research assistant Vickrey were discussing methods of taxing capital gains (i.e., wealth increments due to appreciation of assets, such as houses and shares of stock):

The idea emerged that ideally, at least, the method of taxation should be such that the tax should be completely neutral with respect to the time at which a gain is realized (i.e., that the tax payer should have no incentive in the long run for preferring to realize at one time rather than another on account of the tax). From this it was a short step to requiring neutrality with respect to the time of realization or reporting of all forms of income. It then remained only to work out the implications of this requirement for the formulation of the tax, and to devise procedures for the assessment of the tax that would be administratively feasible (1972).

The procedure devised by Vickrey, cumulative averaging, is quite simple once you think about it. It considers "all payments of income tax, with respect to income reported since some base starting date, as interest-bearing deposits in a taxpayer's account with the treasury. The accumulated balance on this account would then be available as a credit against whatever tax is found to be due for the entire period to date, on the basis of the total income thus far reported for the period . . . inclusive of the interest credited on the tax deposit account (which is, in effect, to be treated no differently from interest earned on any other type of deposit)" (1972). This simple scheme would achieve the required neutrality with respect to the time at which a gain is realized, that is, the tax system would become incentive-compatible with efficient economic decisions.

Cumulative averaging has not been applied on a significant scale, for the same reason perhaps that major revisions or simplifications of the income tax, whatever their nature, do not come into being. Still, the merits stand: neutrality, equity with regard to fluctuations and sources of income, simplification of the tax law, and elimination of loopholes.

A few years later, Vickrey was concerned with the proper graduation of progressive taxation. He investigated the prospect for implementing the so-called utilitarian approach outlined by Francis Edgeworth in 1897. Assume that the benefits of a higher real income could be measured by a function of income, labeled utility. Edgeworth posed the problem of income taxation as that of maximizing, through taxes and transfers, the total utility derived by a population from a given fixed aggregate income. Vickrey's contribution was twofold. First, he sought a way of defining and measuring utility that would be germane to the problem. Second, he recognized that income tax distorts incentives to earn income, so that the aggregate income cannot be treated as given and fixed.

The first contribution consisted of adopting the method of representing choices among risky alternatives by comparisons of expected utilities, a method introduced in the eighteenth century by Daniel Bernoulli and axiomatized in 1945 by John von Neumann and Oskar Morgenstern in their Theory of Games and Economic Behaviour. If a person is indifferent between an income prospect of $50,000 and a fifty-fifty chance of either $20,000 or $100,000, the utility difference between 50,000 and 20,000 is set equal to the utility difference between 100,000 and 50,000. Vickrey recognized as follows the relevance of this construction to the Edgeworth problem: "If utility is defined as that quantity the mathematical expectation of which is maximized by an individual making choices involving risk, then to maximize the aggregate of such utility over the population is equivalent to choosing that distribution of income which such an individual would select were he asked which of various variants of the economy he would like to become a member of, assuming that once he selects a given economy with a given distribution of income he has an equal chance of landing in the shoes of each member of it" (1945). The gedanken- experiment introduced by Vickrey is the basis of modern utilitarianism, an important branch of contemporary social choice theory. It is also used, under the name of "original position, behind the veil of ignorance" in Theory of Justice by John Rawls.

The second contribution is well described by the Swedish Academy:

Vickrey's analysis emphasized that a progressive tax schedule would affect individuals' incentives to exert themselves. He therefore reformulated the problem with respect to both incentive problems--that each individual takes the tax schedule into account when choosing his work effort--and asymmetric information, that in practice, the productivity of individuals is not known to the government.

Vickrey formulated the mathematical problem associated with optimal taxation and derived an appropriate Euler equation, but he went no further, and left it to James Mirrlees to give an explicit characterization twenty-five years later.

The Swedish Academy emphasized the link thus established between incentives and information. It stressed the role of that link in lively developments of contemporary economic research and also related it to Vickrey's work on auctions.

Asymmetric information is also an essential component of auctions, where potential buyers have limited knowledge about the value of the asset or rights up for sale. Vickrey analyzed the properties of different kinds of auctions in two papers in 1961 and 1962. He attached particular importance to the second-price auction or, as it is now often called, the Vickrey auction. In such an auction, an object is auctioned off in sealed bidding, where the highest bidder gets to buy the item, but only pays the next highest price offered. This is an example of a mechanism which elicits an individual's true willingness to pay. By bidding above his own willingness to pay, an individual runs the risk that someone else will bid likewise, and he is forced to buy the object at a loss. And vice-versa, if an individual bids below his own willingness to pay, he runs the risk of someone else buying the item at a lower price than the amount he himself is willing to pay. Therefore, in this kind of auction, it is in the individual's best interest to state a truthful bid. The auction is also socially efficient. The object goes to the person with the highest willingness to pay, and the person in question pays the social opportunity cost which is the second highest bid. Other researchers have later developed analogous principles, for example in order to elicit the true willingness to pay for public projects. Thus, Vickrey's analysis has not only been momentous for the theory of auctions; it has also conveyed fundamental insights into the design of resource allocation mechanisms aimed at providing socially desirable incentives.

Recent years have witnessed spectacular application of auctions theory, in particular to bidding for band spectrum licenses. It is surprising that, to the very end, Vickrey would label this work "one of my digressions into abstract economics, at best of minor significance in terms of human welfare."

Concern about human welfare pervades the sixty years of Vickrey's professional life. Considered in retrospect, with the benefit of hindsight, his numerous and widely scattered contributions come close to retracing the history of the field of public economics as it evolved over the last forty years. The field is concerned with the economics of the public sector, with government's effect on the economy. It is today a broad field, where microeconomic theory is applied on the one hand to the revenue side, in particular taxation; and on the other hand to the sphere of real activities carried out or regulated by the public sector. It is a difficult, complex field. On the revenue side, efficiency calls for second best analysis (i.e., minimizing the dead-weight burden of taxation), whereas equity goes straight to the ethical roots of social choice theory. On the real side, if public intervention makes sense, there must be a reason why the market mechanism is not fully operative--like externalities, non-convexities, or information asymmetries. The challenge is thus to invent mechanisms that somehow succeed where the market fails--a challenge that is never trivial.

Reference has been made above to William Vickrey's seminal role in the emergence of modern utilitarianism. Shortly thereafter, he had the good fortune of supervising Kenneth Arrow's doctoral dissertation "Social Choices and Individual Values." Vickrey himself devoted several papers to the area. As early as 1960, he discussed in that context strategic misrepresentation of preferences, a topic that figures prominently in the work on auctions and in an extensive literature on demand-revealing mechanisms.

Reference has also been made to cumulative averaging, Vickrey's "proudest accomplishment" in the area of taxation. It was, however, only one out of twenty-one specific recommendations listed in the Agenda for Progressive Taxation (1947). One particularly innovative chapter deals with inheritance taxes, resting again on a neutrality principle (1944). In the ensuing years, the tax treatments of corporate income, government interest, land values, and charitable contributions retained Vickrey's attention. An overall evaluation of these contributions is worded as follows by Anthony Atkinson, a leading British specialist: "Bill Vickrey occupies a unique position among public finance economists. His contributions to taxation, simultaneously analytical and policy-relevant, are characterized by an inventiveness which is unrivaled. They derive from a powerful, yet essentially simple, view of the logic of taxation, a logic which has quizzed his writing over more than half a century."

On the real side of public economics, Vickrey's work is equally extensive. Much of it derives from his interest in marginal cost pricing, "a device for improving the efficiency with which we use various facilities" (1970). The principle is straightforward in simple situations, for instance, when a specific good or service is consumed at a constant rate over time and produced under conditions of constant or increasing marginal cost. Marginal cost is then well defined and defines in turn the efficient, competitive price. Fluctuations in demand or cost over time and space or in response to imperfectly foreseen circumstances, decreasing marginal costs or heterogeneous production complicate matters. Marginal cost pricing then becomes a subtle art, calling for skillful application of theoretical guidelines. The relevant concept is that of short run marginal social cost (SRMSC) to the proper definition of which Vickrey has contributed several useful precisions. This is not the place to review theoretical intricacies, but it is possible to give a flavor of some of the more innovative applications devised by Vickrey in the areas of public utilities and urban transportation. Here are some illustrations, listed in chronological order to bring out the extent to which they anticipated current developments.

In 1948 Vickrey was concerned with the assessment of SRMSC over time, when the demand for a service at a given future date is imperfectly predicted by the seller, but is known to some buyers apt to make advance reservations. Seats on long-distance flights or rooms at vacation resorts provide examples. He suggested "a fairly elaborate pricing scheme in which the price quoted would vary according to the proportion of seats on a given flight already sold and the time remaining to departure, in simulation of what an ideal speculator's market might produce, the price at any time being an estimate of the price, which, if maintained thereafter, would result in all the remaining seats being just sold out at departure time" (1948). Today, some airlines and tour operators follow precisely this advice, using a technique known as yield management, for which elaborate software is produced commercially.

In 1950-51 Vickrey was consulting for the Mayor's Committee for Management Survey of the City of New York. He was assigned the problem of subway fares, with the aim of reducing the drain of the transit deficit on the city's finances. Evaluation of the SRMSC led him to suggest replacing the prevailing 15-cent flat fare with an efficient set of fares varying from 5 cents to 25 cents according to time of day and trip definition (origin and destination). He even designed a new electromechanical turnstile permitting automatic implementation. Today, such differentiated fares are commonplace in many cities, with implementation facilitated by magnetic cards and electronic processing.

Subways operate under marginal costs that decrease with overall traffic. Pricing at SRMSC entails losses. If budgetary considerations place a ceiling on these losses, a second-best solution calls for raising prices above SRMSC to an extent determined by demand elasticities (and just sufficient to meet the ceiling). That principle had been discovered and translated into mathematical formulae by Frank P. Ramsey in 1927. That contribution had fallen into oblivion, however. Spurred by the practical subway challenge, Vickrey computed the Ramsey solution and extended it in one important respect. Instead of accepting an arbitrary ceiling on the losses, he evaluated the social cost of the distortions associated with revenue raising by the city, summarized in a marginal cost of public funds (MCPF). He then proposed a fare structure such that the marginal inefficiencies associated with reducing the losses matched exactly the MCPF. The subway study stands out as a classic in applied public economics, the reading of which is still instructive today.

In 1959 Vickrey studied road transportation in Washington, D.C., stressing the quantitative importance of the underpricing of rush-hour auto travel. He estimated that, if a suburbanite gave up bus commuting to drive a $3,500 automobile into town, it would cost $23,000 in infrastructure investment to keep road congestion unchanged. The solution was to impose road tolls in amounts corresponding to SRMSC. These tolls would vary with the time of day, culminating at the rush hours. They would help spread the peak and encourage bus travel.

Here again Vickrey faced a technical problem of implementation: toll booths slow down the flow of traffic. He proposed instead the use of vehicle identifiers that could be read electronically without slowing down the traffic and obtained a prototype and cost estimate from a manufacturer. Today, that system has been fully developed, is being used in a few places, and is seen as the way of the future.

Further investigation of the optimal tolls led ten years later to a paper described by specialist Richard Arnott as "almost certainly the most important in urban transport economics over the last quarter century."That paper models the dynamics of rush-hour congestion by treating the departure-time decisions of commuters as endogenous variables. The extended problem is made tractable by modeling congestion as a queue behind a bottleneck. That model has received strong empirical support from detailed traffic flow studies, and has changed the way traffic engineers think about the problem. An interesting property of equilibrium is that it leaves commuters at least as well off as before, so that the toll revenues come free. Road tolls are an example of responsive pricing (i.e., prices varied from moment to moment in response to observed congestion levels). The concept has been applied repeatedly by Vickrey to public utilities, like telephone and electricity, but also water supply.

In 1963 Vickrey published a first paper on pricing and financing of urban services, such as fire protection, water provision, parks and recreational facilities, and education. Fire protection (which accounted at the time for 8% of all general expenditures by cities) is an interesting illustration. Vickrey noted that a given grade of fire protection is a matter of providing an engine company within a suitable number of minutes of travel time, and concluded that the appropriate charge should be a matter of land area (rather than property value under current practice).

The interest of Vickrey for urban problems spread to other areas, like land value taxation. Here again he extended and clarified the theoretical basis by showing how, in equilibrium, "the aggregate of the land rents generated by the urban agglomeration produced by the existence of activities with economies of scale within the city will equal the subsidies required to enable these activities to sell their output at prices equal to their respective marginal costs" (1977). (This is a modern extension of an approach introduced by Henry George, of which several variants were published in the 1970s.) That result sets the problem of land value taxation and financing of public services in a general equilibrium framework.

The review above is partial, as it leaves out altogether Vickrey's interest in macroeconomic stabilization, which became his major concern from the mid-eighties on. It also leaves out most of his writings about ethics and justice and sundry contributions on such topics as "The Prevention of Gerrymandering" (1961), "Application of Demand Revealing Procedures to International Disputes" (1978), and many more.

The momentous research output of William Vickrey has some distinctive features that give him a very special place among contemporary economists.

• First, it should be clear from the foregoing that his work combine depth and breadth--depth, by grounding specific research firmly in the theory of economic efficiency (leading, for instance, to a correct definition of SRMSC), as well as in a modern approach to equity and social choice; and breadth in the treatment of a wide range of topics covering the revenue as well as the real side of public economics.
• Second, the starting point of Vickrey's investigations is always rooted in real world problems. His interest was to solve the problem at hand. To that end, he brings in general principles, and his proficiency as a theorist pays off. Often he is led to extend the principles into new theory, but he is hardly interested in theory for its own sake--only to the extent that it carries policy implications.
• Third, and related, Vickrey was unique among his contemporaries for his determination to carry out theoretical contributions all the way to practical application. This is illustrated already in his work on cumulative averaging, which led him to develop concrete proposals for legislation. Further examples are found in his work on subway fares and road pricing, and there are many more.
• Fourth, and again related, there is "a certain characteristic style of understatement and specificity of application in Vickrey's work, which has in some ways helped, in perhaps more ways hindered, the full understanding of his originality." Vickrey's papers contain little or no mathematics. Where they do, he is apologetic. Intricate reasoning is typically encapsulated in a sentence or two, as exemplified in the four original quotations used above. Important statements like these repeatedly appear as side remarks in the discussion of a specific application. The generality is hardly stressed except through reference to further applications. The modern economic style of proceeding from numbered assumptions to numbered theorems was quite foreign to Vickrey, in spite of his familiarity with, and thorough understanding of, the relevant literature--a refreshing exception, given the richness of content.

There is no doubt that William Vickrey was a powerful theorist, capable of abstraction and conscious of generality. It is also clear that he was eager to communicate. He was not writing for himself, but to be read. He was particularly eager to be understood by policy makers. Relying on the simplicity of basic reasoning and expressing it verbally was for him a natural vehicle of broad communication. Mostly, he was himself. His relative neglect of systematic theoretical construction probably reflected the little need he felt for it, being able to understand quickly principles and their main implications. He could himself dispense with spelling out details, unless directly relevant to his immediate purpose.

Given Vickrey's talent and analytical ability, some of us regret that he did not put more systematic theoretical effort into his favored topics. Given his bend of mind, it is hard to tell how successful that different orientation would have been. Indeed, creative theoretical work is often produced by researchers primarily interested in real-world problems; and imaginative practical solutions often come from gifted theorists. Vickrey's bend of mind was indispensable to bridge the gap between theory and application. And it was probably an efficient division of labor that he would let others refine the theory, while he himself stayed on the development frontier, demonstrating the fruitfulness of an approach that too few among us are capable of pursuing with excellence.

Ultimately, William Vickrey's forte was originality and creativity, reaching out of the boundaries of standard frameworks to develop a different viewpoint. In so doing, he was saved from esoterism by his uncompromising logic. His style of writing partook of his originality, and may have interacted with the originality of the ideas to explain late recognition, a feature stressed in the citation presenting him as a distinguished fellow of the American Economic Association in 1978:

Many of us have had the experience of thinking we were the first to show the neutrality of a particular tax scheme, to prove the incentive characteristics of a particular bidding institution, to deduce the redistributive implications of the expected utility hypothesis, to invent a demand revealing process, and so on, only to find that William S. Vickrey had done it earlier--sometimes much earlier--and whereas our "original contribution" may have contained minor or even a substantive error, Vickrey had done it correctly. Some great scholars receive recognition from the beginning, but inscrutably, with others it takes a little longer. His numerous works, appearing in all the leading journals in economics, law, operations research, finance and taxation, contain many seminal contributions, and many more that would have been seminal but for the fact that the profession was not yet ready for his ideas.

² Vickrey's presidential address to the Atlantic Economic Association in October 1992, entitled "My Innovative Failures in Economics," begins as follows: "You are looking at an economist who has repeatedly failed in achieving his objective, even though achieving considerable esteem among his fellows."

³ I have often heard a younger colleague report: "I went to give a talk at Columbia. There sat that tall white-haired man, asleep with his head against the wall. All of a sudden, without raising an eyelid, he mumbled the most penetrating question, and I wondered for a while whether I still had a paper . . . ."

⁴ Strahan and Cadell, Glasgow.

⁵ F. Y. Edgeworth. The pure theory of taxation, III. Econ. J. 7(1897):550-71.

⁶ See D. Bernoulli. Specimen theoriae novae de mensura sortis. Comment. Acad. Sci. Imp. Petropol. 5(1738):175-92.

⁷ Princeton University Press, Princeton.

⁸ Harvard University Press, Cambridge, Mass., 1971.

⁹ Cf. Scand. J. Econ. 99(1997):175.

¹⁰ Cf. Scan. J. Econ. 99(1997):177.

¹¹ Cf. J. Macmillan. Selling spectrum rights. J. Econ. Perspect. 8(1994):145-62.

¹² Quoted by D. O'Flaherty. William Vickrey, 1914-1996. The Independent. London, October 13, 1996.

¹³ See also J. Drèze. Forty years of public economics. J. Econ. Perspect. 9(1995):111-30.

¹⁴ Wiley and Sons, 1951.

¹⁵ Quoted from W. Vickrey. Public Econ., op. cit., p. 101.

¹⁶ F. P. Ramsey. A contribution to the theory of taxation. Econ. J. 37(1927):47-61.

¹⁷ Public Economics, op. cit., p. 274.

¹⁸ Quoted from K. Arrow in Public Econ., op. cit., p. 13.

¹⁹ Quoted from J. H. Drèze. Research and development in public economics: William Vickrey's inventive quest of efficiency. Scand. J. Econ. 99(1997):194.

1939 Averaging of income for income tax purposes. J. Polit. Econ. 47:379-97.

1944 The rationalization of succession taxation. Econometrica 12:215-36.

1945 Measuring marginal utility by reactions to risks. Econometrica 13:319-33.

A reasonable undistributed profits tax. Taxes, pp. 122-27.

1947 Agenda for Progressive Taxation . New York: Ronald Press.

1948 Some objections to marginal cost pricing. J. Polit. Econ. 56:218-38.

1949 Resource distribution patterns and the classification of families. Stud. Inc. Wealth 10:266-97, 324-29.

1950 Ethics and economics: An exchange of questions between economics and philosophy. In Goals of Economic Life, ed. A. D. Ward, pp. 148-77.

1952 The Revision of the Rapid Transit Fare Structure of the City of New York. Technical monograph no. 3, finance project, Mayor's Committee for Management Survey.

1955 A proposal for revising New York's subway fare structure. J. Oper. Res. Soc. Am. 3:38-68.

1957 Expenditure, capital gains, and the basis of progressive taxation. The Manchester School, pp. 1-25.

1959 The optimum trend of prices. South. Econ. J. 25:315-26.

Statement on the pricing of urban street use. Hearings: U.S. Congress, Joint Committee on Metropolitan Washington Problems, pp. 466-77.

1960 Utility, strategy and social decision rules. Q. J. Econ. 74:507-35.

1961 On the prevention of gerrymandering. Polit. Sci. Q. 76:105-10.

Counterspeculation, auctions, and competitive sealed tenders. J. Finan. 16:8-37.

1962 One economist's view of philanthropy. In Philanthropy and Public Policy, ed. F. G. Dickinson, pp. 31-56. New York: NBER.

Auctions and bidding games. In Recent Advances in Game Theory. Princeton University Conference, pp. 15-27.

1963 Pricing in urban and suburban transport. Am. Econ. Rev. 52(2):452-65.

General and specific financing of urban services. In Public Expenditure Decisions in the Urban Community, ed. H. G. Shaller, pp. 62-90. Resources for the Future.

1969 Congestion theory and transport investment. Am. Econ. Rev. 59:251-60.

1970 Defining land values for taxation purposes. In The Assessment of Land Value, ed. D. M. Holland, pp. 25-36. Madison: University of Wisconsin Press.

Responsive pricing of public utilities services. In Economics of the Regulated Communications Industry in the Age of Innovation. New England Telephone Company, mimeo, pp. 61-68.

1972 Cumulative averaging after 30 years. In Modern Fiscal Issues: Essays in Honor of Carl S. Shoup, eds. R. M. Bird and J. G. Head. Toronto: University of Toronto Press.

Airline overbooking: Some further solutions. J. Transp. Econ. Policy 6(3):257-70.

1977 The city as a firm. In The Economics of Public Services, eds. M. S. Feldstein and R. F. Inman.

1978 Application of demand revealing procedures to international disputes. Peace Sci. Soc. 28:97-104.

1992 Today's task for economists. Am. Econ. Rev. 82:1-10.

1993 My innovative failures in economics. Atl. Econ. J., pp. 1-9.

1994 Public Economics, Selected Papers by William Vickrey . Cambridge, U.K.: Cambridge University Press.