The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Vickrey, William Spencer (1914–1996)

  • Richard Arnott
Reference work entry


William Spencer Vickrey was awarded the 1996 Nobel Prize in Economics ‘for his fundamental contributions to the economic theory of incentives under asymmetric information’. While best known as the father of auction theory, he made important contributions on a broad range of topics including social choice, marginal cost pricing, the design of tax systems, transportation economics, urban economics, and macroeconomics.


Asymmetric information Auctions (theory) Congestion pricing Cumulative averaging taxation Efficient allocation Estate taxes Gibbard–Satterthwaite theorem Groves–Clark–Vickrey mechanisms Land use Land value taxation Marginal cost pricing Mirrlees, J. A. Natural rate of unemployment Optimal income tax Philanthropy Philosophy and economics Ramsey pricing Responsive pricing Revelation of preferences Second best Shoup, C. S. Site value taxation Social choice Strategic misrepresentation Transport economics Urban economics User fees Veil of ignorance Vickrey second-price auction Vickrey, W. S. 

William Spencer Vickrey was awarded the 1996 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, jointly with James A. Mirrlees, ‘for [his] fundamental contributions to the economic theory of incentives under asymmetric information’ (Royal Swedish Academy of Sciences, 1996). His most influential papers, as well as a comprehensive bibliography, are contained in Public Economics: Selected Papers by William Vickrey (Arnott et al., 1994). Articles that pay tribute to his contributions include Arnott (1998), Drèze (1995), Harriss (2000), and Laffont (2003).

Vickrey was born in Victoria, Canada, where his maternal grandfather had built a group of department stores. Towards the end of the First World War, his father, a Congregational minister, became actively involved in the relief of Armenian and Greek refugees from the Ottoman Empire. In conjunction with this work, the family moved to New York and later Switzerland. Vickrey attended high school in Scarsdale, NY, and Phillips Andover Academy. He received his bachelor’s degree in engineering and mathematics from Yale University in 1935. He then moved to Columbia University for graduate studies in economics. After two years of course work, he went to Washington, DC, to work for the National Resources Committee, in a group pioneering studies on the structure of the US economy. During the Second World War, as a conscientious objector, he served in the Division of Tax Research of the Department of the Treasury, working on broad macroeconomic issues related to war finance and more specific issues of tax structure. In 1946 he returned to Columbia to teach and to complete his doctoral dissertation, published as An Agenda for Progressive Taxation (1947). Apart from sabbaticals and missions abroad, he remained at Columbia until his death.

Throughout his career, Vickrey had considerable practical policy experience. As part of Carl Shoup’s team, he helped design several countries’ tax systems, including Japan’s after the Second World War. He also advised many public utilities, and even introduced skip-stop scheduling to the Indian rail service. But he was never a major player on the policy front. His legacy is his body of publications. He published eight longer works, including graduate textbooks in microeconomics and macroeconomics, three technical monographs, and two co-authored country tax system studies, as well as his thesis. Apart from his thesis, however, he is best known for his some 200 papers.

Though covering an unusually broad range of topics, his papers are consistent in theme and style. While his choice of topics stemmed from social and moral concerns, his treatments of them stressed improvements in resource allocation. ‘Greater efficiency for the common good’ would be an appropriate slogan for his work. His style of writing and reasoning is idiosyncratic and paradoxical. Most of his papers advocate specific policy innovations. To reach a broader audience, he developed his ideas primarily verbally, and with literary flair, but the precision and sophistication of his economic reasoning largely defeated this purpose. He also tended to emphasize practical issues of policy implementation, while presenting in an offhand manner the novel theoretical and conceptual insights for which the papers have been remembered. Many of his policy recommendations, though derived with impeccable logic, were impractical at the time he proposed them. (Technological advances have since rendered some, such as auto congestion pricing and land value taxation, more practical.) These smaller paradoxes can be resolved by understanding Vickrey as a social crusader with a theorist’s cast of mind. The larger paradox is that the tension between crusader and theorist was the source first of his creativity, and then of the neglect for many years of much of his work, and ultimately of the distinction of his intellectual legacy. Many of his ideas were overlooked until they were independently discovered many years later, while others lay dormant until their time had come.

Vickrey’s major contributions lie in four areas: social choice and resource allocation mechanisms, taxation, marginal cost pricing, and urban transportation.

Vickrey is best known as the father of auction theory, due to his seminal paper, ‘Counterspeculation, Auctions, and Competitive Sealed Tenders’ (1961). The question posed by Vickrey in that paper is how to achieve efficiency in resource allocation with a small number of buyers or sellers under asymmetric information. He presented and analysed two classes of mechanisms that circumvent the strategic misrepresentation of costs and preferences. The first is auctions. Consider the simplest auction in which there is a single item for sale, for which bidders have different private valuations. Efficiency entails the item being sold to the bidder with the highest valuation. If the item is sold to the highest bidder at his bid, then each bidder has an incentive to bid less than his valuation, since if he bids his valuation he gains no surplus from purchase of the item. In deciding on his bid, each bidder must guess others’ valuations, and there is no guarantee that the item will be sold to the bidder with the highest valuation. Suppose instead that the item is sold to the highest bidder but at the second highest bid (the Vickrey second-price auction). Whatever other bidders do, if a particular bidder bids more than his valuation he will win more often but only when the second-highest bid, and therefore the price he pays, exceeds his valuation, while if he bids less than his valuation he will win less often and only when the winning bid falls short of his valuation. Since bidding one’s private valuation is the dominant strategy, the item should go to the bidder with the highest valuation, achieving efficiency. Auction theory has developed from this insight. Auctions are now extensively used in the allocation of goods with a small number of buyers; timber and drilling rights, bandwidth, Treasury bills and sealed bid tenders are well-known examples. Vickrey’s paper also investigated a class of demand-revealing mechanisms – now known as Groves–Clark–Vickrey mechanisms – that elicit truthful revelation of preferences, for pure public goods for example.

Vickrey made several other contributions to the literature on social choice and resource allocation mechanisms. In ‘Measuring Marginal Utility by Reactions to Risk’ (1945), he provided the first statement of social choice based on the maximization of expected utility behind the veil of ignorance, which was independently stated by Harsanyi (1955) a decade later, and also the first formulation of the optimal income tax problem, which was not solved until a quarter-century later by James Mirrlees (1971). ‘Utility, Strategy, and Social Decision Rules’ (1960) provides a masterful survey of social choice theory as of that date and conjectures what is now known as the Gibbard–Satterthwaite theorem.

The efficiency of marginal cost pricing in general and of short-run marginal-cost pricing in particular were well understood when Vickrey was a graduate student. Vickrey’s contributions were in communicating the breadth of application of the principles and in conceiving ingenious technological schemes for their implementation. From the early 1950s he was a strong advocate of responsive marginal cost pricing, whereby the current price reflects the current realization of stochastic demand and supply; for instance, he proposed varying the parking meter rate on a city block according to the meters’ realized occupancy rate (1959) and dealing with airline overbooking via responsive pricing (1972). His crusading for congestion pricing in transportation, for site value taxation (1970), and for the extended application of user fees to finance local public services (1963) are examples of his advocacy of marginal cost pricing in novel contexts.

His major contributions to the theory of taxation derived from his experience in the Department of the Treasury during the Second World War. All are contained in his thesis, which was a tour de force. The goal of the thesis was the comprehensive design of a practical, coherent, fair, and efficient tax system. At the time, a steeply progressive income tax was the primary source of federal tax revenue. Rates had been increased sharply to generate the revenue needed to finance the war effort. The combination of steep progression and high rates encouraged taxpayers to devote considerable effort to altering the timing of expenditures and receipts in order to average income. To eliminate this waste, Vickrey proposed cumulative averaging, a method of taxing individuals on their discounted lifetime incomes, with a minimum of accounting. A steeply progressive estate tax was also in place, which wealthy individuals avoided through generation-skipping trusts. Vickrey proposed an integrated successions tax, which retained the progressivity of the tax while reducing the incentives for complex tax avoidance schemes. Since then, income and estate tax rates have been lowered and made less progressive, mitigating the problems that Vickrey’s proposed reforms addressed. His contributions lie not so much in his specific proposals, however, as in his conception of redesigning the tax system from basic principles. How much influence his book had on the Carter Commission in Canada, the Meade Committee in the UK, or the Reagan tax reforms is hard to say, but they are in the same spirit.

While best known for his auctions paper, Vickrey was also the pre-eminent transport economic theorist of his generation. As a transport economist, he is famous for his 50-year-long advocacy of auto congestion pricing (of charging drivers for the externality cost each imposes on other drivers by slowing them down), and in North America at least is known as the father of congestion pricing. After many years of political resistance, urban auto congestion pricing is slowly being adopted, first in Singapore and more recently in London and Stockholm. His first work on the subject (1955) was a proposed fare structure for New York City’s subway system, based on marginal cost pricing principles. His empirical research on the project entailed travelling the subway system, stopwatch in hand, while his discussion of deviations from first-best marginal cost pricing to take into account equity concerns and the transit authority’s budgetary constraints anticipates the theory of the second best. His second work (1959) detailed an automobile congestion-pricing scheme for downtown Washington, DC. A schedule gives the prices of traversing major intersections by time of day. Each car is equipped with a transponder. When the car enters an intersection, its transponder sends a signal to a roadside receptor and is conveyed to a central computer, which adds the appropriate charge to the car’s bill. The theoretical work on the project included an independent derivation of Ramsey pricing with a marginal cost of public funds. His later work in urban transport economics is noteworthy in two respects. He, more than any other urban transport economist, grappled with the complex physics of auto congestion. He also introduced the bottleneck model of traffic congestion (1969), the first analytically tractable model of equilibrium rush-hour traffic dynamics. Each commuter decides when to leave home in the morning, trading off schedule inconvenience against congestion delay. Congestion takes the form of a queue behind a bottleneck of fixed flow capacity, with the queue length (and hence the departure time distribution) evolving to achieve equilibrium.

His other work spans a diversity of topics. Viewing unemployment as a tragic waste of human resources, he wrote many macroeconomic papers arguing against a natural rate of unemployment and for Keynesian macroeconomic stabilization. He also made important contributions to urban economics, most noteworthy of which are pioneering papers on traffic congestion and land use (Solow and Vickrey, 1971) and on the Henry George theorem (1977) – which states that efficient spatial economies can be decentralized via marginal cost pricing, with land rents being used to cover the deficits deriving from the economies of scale underlying agglomeration. His miscellaneous papers cover such topics as game theory, student loans, gerrymandering, international dispute resolution, cost-of-living indices, equivalence scales and sorting theory. One paper on the economics of traffic accidents (1968), another on the economics of philanthropy (1962), and another on economics and philosophy (1950) have been influential. The last of these papers provides insight into the moral purpose underlying Vickrey’s work.

Prior to his receipt of the Nobel Prize, Vickrey’s work, apart from his justly celebrated auctions paper, was not well known to most economists. But Vickrey is much more than just a ‘one-paper economist’. The same intellectual qualities that spawned the auctions paper are evident in the rest of his work. Perhaps the whole of the rest of his work is greater than the sum of the individual papers, demonstrating the wealth of ideas that are generated when a brilliant economic theorist applies his creativity to devising solutions to practical public policy problems.

See Also

Selected Works

  • 1945. Measuring marginal utility by reactions to risk. Econometrica 13: 319–333.

  • 1947. An agenda for progressive taxation. New York: Ronald Press.

  • 1950. Ethics and economics: An exchange of questions between economics and philosophy. In Goals of economic life, ed. A.D. Ward. New York: National Council of Churches.

  • 1955. A proposal for revising New York’s subway fare structure. Journal of Operations Research Society of America 3: 38–68.

  • 1959. Statement on the pricing of urban street use. Hearings: US Congress, Joint Committee on Metropolitan Washington Problems 11(November): 466–477.

  • 1960. Utility, strategy, and social decision rules. Quarterly Journal of Economics 74: 507–535.

  • 1961. Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance 16: 8–37.

  • 1962. One economist’s view of philanthropy. In Philanthropy and public policy, ed. F.G. Dickinson. New York: NBER.

  • 1963. General and specific financing of urban services. In Public expenditure decisions in the Urban community, ed. H.G. Schaller. Washington, DC: Resources for the Future.

  • 1968. Automobile accidents, tort law, externalities, and insurance: an economist’s critique. Safety: Law and Contemporary Problems 33: 464–487.

  • 1969. Congestion theory and transport investment. American Economic Review 59: 251–260.

  • 1970. Defining land value for taxation purposes. In The assessment of land value, ed. D.H. Holland. Madison: University of Wisconsin Press.

  • 1971. (With R.M. Solow.) Land use in a long, narrow city. Journal of Economic Theory 3: 403–447.

  • 1972. Airline overbooking: some further solutions. Journal of Transport Economics and Policy 6: 257–270.

  • 1977. The city as a firm. In The economics of public services, ed. M.S. Feldstein and R.F. Inman. New York: Wiley.


  1. Arnott, R. 1998. William Vickrey: Contributions to public policy. International Tax and Public Finance 5: 93–113.CrossRefGoogle Scholar
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  3. Drèze, J.H. 1995. Forty years of public economics: A personal perspective. Journal of Economic Perspectives 9 (2): 111–130.CrossRefGoogle Scholar
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  5. Harsanyi, J. 1955. Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Journal of Political Economy 63: 309–321.CrossRefGoogle Scholar
  6. Laffont, J.-J. 2003. William Vickrey: A pioneer in the economics of incentives. In Nobel lectures, economics, 1996–2000, ed. T. Persson. Singapore: World Scientific Publishing Co.Google Scholar
  7. Mirrlees, J.A. 1971. An exploration in the theory of optimum income taxation. Review of Economic Studies 38: 175–208.CrossRefGoogle Scholar
  8. Royal Swedish Academy of Sciences. 1996. Press release, 8 Oct Online. Available at Accessed 18 Jan 2007.

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Richard Arnott
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  1. 1.