Kenneth Arrow

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Kenneth Arrow
Kenneth Arrow, Stanford University.jpg
National Medal of Science award ceremony, 2004
Born
Kenneth Joseph Arrow

(1921-08-23)23 August 1921
New York City, New York, U.S.
Died21 February 2017(2017-02-21) (aged 95)
Palo Alto, California, U.S.
NationalityAmerican
Institution Stanford University
Field Microeconomics
General equilibrium theory
Social choice theory
School or
tradition		 Neoclassical economics
Alma mater City College of New York
Columbia University
Doctoral
advisor		 Harold Hotelling
Doctoral
students
Influences
Contributions General equilibrium theory
Fundamental theorems of welfare economics
Arrow's impossibility theorem
Endogenous growth theory
Awards
Information at IDEAS / RePEc
Website healthpolicy.fsi.stanford.edu/people/kenneth_j_arrow

Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972.

Economist professional in the social science discipline of economics

An economist is a practitioner in the social science discipline of economics.

Mathematician person with an extensive knowledge of mathematics

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

The Nobel Memorial Prize in Economic Sciences, commonly referred to as the Nobel Prize in Economics, is an award for outstanding contributions to the field of economics, and generally regarded as the most prestigious award for that field. The award's official name is The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.

Contents

In economics, he was a major figure in post-World War II neo-classical economic theory. Many of his former graduate students have gone on to win the Nobel Memorial Prize themselves. His most significant works are his contributions to social choice theory, notably "Arrow's impossibility theorem", and his work on general equilibrium analysis. He has also provided foundational work in many other areas of economics, including endogenous growth theory and the economics of information.

Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Social choice theory dates from Condorcet's formulation of the voting paradox. Kenneth Arrow's Social Choice and Individual Values (1951) and Arrow's impossibility theorem in it are generally acknowledged as the basis of the modern social choice theory. In addition to Arrow's theorem and the voting paradox, the Gibbard–Satterthwaite theorem, the Condorcet jury theorem, the median voter theorem, and May's theorem are among the more well known results from social choice theory.

In social choice theory, Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem stating that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a specified set of criteria: unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book Social Choice and Individual Values. The original paper was titled "A Difficulty in the Concept of Social Welfare".

Endogenous growth theory economic theory

Endogenous growth theory holds that economic growth is primarily the result of endogenous and not external forces. Endogenous growth theory holds that investment in human capital, innovation, and knowledge are significant contributors to economic growth. The theory also focuses on positive externalities and spillover effects of a knowledge-based economy which will lead to economic development. The endogenous growth theory primarily holds that the long run growth rate of an economy depends on policy measures. For example, subsidies for research and development or education increase the growth rate in some endogenous growth models by increasing the incentive for innovation.

Education and early career

Arrow was born on 23 August 1921, in New York City. Arrow's mother, Lilian (Greenberg), was from Iași, Romania, and his father, Harry Arrow, was from nearby Podu Iloaiei. [5] [6] The Arrow family were Romanian Jews. [7] [8] His family was very supportive of his education. [9] Growing up during the Great Depression, he embraced socialism in his youth. He would later move away from socialism, but his views retained a left-leaning philosophy. [10]

New York City Largest city in the United States

The City of New York, usually called either New York City (NYC) or simply New York (NY), is the most populous city in the United States. With an estimated 2018 population of 8,398,748 distributed over a land area of about 302.6 square miles (784 km2), New York is also the most densely populated major city in the United States. Located at the southern tip of the state of New York, the city is the center of the New York metropolitan area, the largest metropolitan area in the world by urban landmass and one of the world's most populous megacities, with an estimated 19,979,477 people in its 2018 Metropolitan Statistical Area and 22,679,948 residents in its Combined Statistical Area. A global power city, New York City has been described as the cultural, financial, and media capital of the world, and exerts a significant impact upon commerce, entertainment, research, technology, education, politics, tourism, art, fashion, and sports. The city's fast pace has inspired the term New York minute. Home to the headquarters of the United Nations, New York is an important center for international diplomacy.

Iași County Seat in Romania

Iași, also referred to as Jassy or Iassy, is the second largest city in Romania, and the seat of Iași County. Located in the historical region of Moldavia, Iași has traditionally been one of the leading centres of Romanian social, cultural, academic and artistic life. The city was the capital of the Principality of Moldavia from 1564 to 1859, then of the United Principalities from 1859 to 1862, and the capital of Romania from 1916 to 1918.

Podu Iloaiei Town in Iași County, Romania

Podu Iloaiei is a town in Iași County, Romania. It has 9,573 inhabitants as of 2011, and was declared a town in 2005. Four villages are administered by the town: Budăi, Cosițeni, Holm and Scobâlțeni.

He graduated from Townsend Harris High School and then earned a Bachelor's degree from the City College of New York in 1940 in mathematics, where he was a member of Sigma Phi Epsilon. He attended Columbia University, for his graduate studies. While there, he studied under Harold Hotelling, and was greatly influenced by him. [10] He received a Master's degree in 1941. [11] He served as a weather officer in the United States Army Air Forces from 1942 to 1946. [12]

Townsend Harris High School

Townsend Harris High School (THHS) is a public magnet high school for the humanities in the borough of Queens in New York City. Students and alumni often refer to themselves as "Harrisites." Townsend Harris consistently ranks as among the top 100 High Schools in the United States. Its most recent U.S. News and World Report ranking in 2019 puts THHS at #1 in New York City, #1 in New York State and #11 in the nation.

A bachelor's degree or baccalaureate is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to seven years. In some institutions and educational systems, some bachelor's degrees can only be taken as graduate or postgraduate degrees after a first degree has been completed. In countries with qualifications frameworks, bachelor's degrees are normally one of the major levels in the framework, although some qualifications titled bachelor's degrees may be at other levels and some qualifications with non-bachelor's titles may be classified as bachelor's degrees.

City College of New York senior college of the City University of New York (CUNY) in New York City

The City College of the City University of New York is a public senior college of the City University of New York (CUNY) in New York City. Founded in 1847, City College was the first free public institution of higher education in the United States. It is the oldest of CUNY's 24 institutions of higher learning, and is considered its flagship college.

Academic career

From 1946 to 1949 Arrow spent his time partly as a graduate student at Columbia and partly as a research associate at the Cowles Commission for Research in Economics at the University of Chicago. During that time he also held the rank of Assistant Professor in Economics at the University of Chicago and worked at the RAND Corporation in California. He left Chicago to take up the post of Acting Assistant Professor of Economics and Statistics at Stanford University. In 1951, he earned his Ph.D. from Columbia. [11] He served in the government on the staff of the Council of Economic Advisers in the 1960s with Robert Solow. [13] In 1968, he left Stanford for the position of Professor of Economics at Harvard University. It was during his tenure there that he received the Nobel Prize in Economics. [11] [14]

University of Chicago Private research university in Chicago, Illinois, United States

The University of Chicago is a private research university in Chicago, Illinois. Founded in 1890, the school is located on a 217-acre campus in Chicago's Hyde Park neighborhood, near Lake Michigan. The University of Chicago holds top-ten positions in various national and international rankings.

RAND Corporation non-profit organisation in the USA

RAND Corporation is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financed by the U.S. government and private endowment, corporations, universities and private individuals. The company has grown to assist other governments, international organizations, private companies and foundations, with a host of defense and non-defense issues, including healthcare. RAND aims for interdisciplinary and quantitative problem solving by translating theoretical concepts from formal economics and the physical sciences into novel applications in other areas, using applied science and operations research.

Stanford University Private research university in Stanford, California

Leland Stanford Junior University is a private research university in Stanford, California. Stanford is known for its academic strength, wealth, selectivity, proximity to Silicon Valley, and ranking as one of the world's top universities.

Arrow returned to Stanford in 1979 and became the Joan Kenney Professor of Economics and Professor of Operations Research. He retired in 1991. As a Fulbright Distinguished Chair, in 1995 he taught Economics at the University of Siena. He was also a founding member of the Pontifical Academy of Social Sciences and a member of the Science Board of Santa Fe Institute. At various stages in his career he was a Fellow of Churchill College, Cambridge. [11]

The U.S.- Italy Fulbright Commission is a bi-national, non-profit organization promoting the opportunities for study, research, and teaching in Italy and the United States. The commission acts as executor of the Fulbright Program to and from Italy. Since 1948, the commission has fostered mutual cultural understanding through educational exchange of persons, knowledge, and skills. The commission offers competitive, merit-based grants for students, scholars, teachers, professionals, scientists and artists.

University of Siena Italian university

The University of Siena in Siena, Tuscany is one of the oldest and first publicly funded universities in Italy. Originally called Studium Senese, the institution was founded in 1240. It had around 20,000 students in 2006, nearly half of Siena's total population of around 54,000. Today, the University of Siena is best known for its Schools of Law, Medicine, and Economics and Management.

Pontifical Academy of Social Sciences

The Pontifical Academy of Social Sciences was established on 1 January 1994 by Pope John Paul II and is headquartered in the Casina Pio IV in Vatican City. It operates much like other learned societies worldwide, but has the special task of entering into dialogue with the Church. Its scientific activities are organised and focused to promote this dialogue.

Five of his former students have gone on to become Nobel Prize winners. These include Eric Maskin, John Harsanyi, Michael Spence and Roger Myerson. [15] A collection of Arrow's papers is housed at the Rubenstein Library at Duke University. [16]

Arrow's impossibility theorem

Arrow's monograph Social Choice and Individual Values derives from his 1951 Ph.D. thesis.

If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial. [17]

In what he named the General Impossibility Theorem, he theorized that it was impossible to formulate a social preference ordering that satisfies all of the following conditions: [18]

  1. Nondictatorship: The preferences of an individual should not become the group ranking without considering the preferences of others.
  2. Individual Sovereignty: each individual should be able to order the choices in any way and indicate ties
  3. Unanimity: If every individual prefers one choice to another, then the group ranking should do the same
  4. Freedom From Irrelevant Alternatives: If a choice is removed, then the others' order should not change
  5. Uniqueness of Group Rank: The method should yield the same result whenever applied to a set of preferences. The group ranking should be transitive.

The theorem has implications for welfare economics and theories of justice. It was extended by Amartya Sen to the liberal paradox which argued that given a status of "Minimal Liberty" there was no way to obtain Pareto optimality, nor to avoid the problem of social choice of neutral but unequal results. [18]

General equilibrium theory

Work by Arrow and Gérard Debreu and simultaneous work by Lionel McKenzie offered the first rigorous proofs of the existence of a market clearing equilibrium. [19] For this work and his other contributions, Debreu won the 1983 Nobel Prize in Economics. [20] Arrow went on to extend the model and its analysis to include uncertainty, the stability. His contributions to the general equilibrium theory were strongly influenced by Adam Smith's Wealth of Nations .[ citation needed ] Written in 1776, The Wealth of Nations is an examination of economic growth brought forward by the division of labor, by ensuring interdependence of individuals within society. [21]

In 1974, The American Economic Association published the paper written by Kenneth Arrow, General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice, where he states:

From the time of Adam Smith's Wealth of Nations in 1776, one recurrent theme of economic analysis has been the remarkable degree of coherence among the vast numbers of individual and seemingly separate decisions about the buying and selling of commodities. In everyday, normal experience, there is something of a balance between the amounts of goods and services that some individuals want to supply and the amounts that other, different individuals want to sell. Would-be buyers ordinarily count correctly on being able to carry out their intentions, and would-be sellers do not ordinarily find themselves producing great amounts of goods that they cannot sell. This experience of balance indeed so widespread that it raises no intellectual disquiet among laymen; they take it so much for granted that they are not supposed to understand the mechanism by which it occurs. [22]

Fundamental theorems of welfare economics

In 1951, Arrow presented the first and second fundamental theorems of welfare economics and their proofs without requiring differentiability of utility, consumption, or technology, and including corner solutions. [23]

Endogenous-growth theory

Arrow was one of the precursors of endogenous growth theory, which seeks to explain the source of technical change, which is a key driver of economic growth. Until this theory came to prominence, technical change was assumed to occur exogenously – that is, it was assumed to occur outside economic activities, and was outside (exogenous) to common economic models. At the same time there was no economic explanation for why it occurred. Endogenous-growth theory provided standard economic reasons for why firms innovate, leading economists to think of innovation and technical change as determined by economic actors, that is endogenously to economic activities, and thus belong inside the model. Endogenous growth theory started with Paul Romer's 1986 paper, [24] borrowing from Arrow's 1962 "learning-by-doing" model which introduced a mechanism to eliminate diminishing returns in aggregate output. [25] A literature on this theory has developed subsequently to Arrow's work. [26]

Information economics

In other pioneering research, Arrow investigated the problems caused by asymmetric information in markets. In many transactions, one party (usually the seller) has more information about the product being sold than the other party. Asymmetric information creates incentives for the party with more information to cheat the party with less information; as a result, a number of market structures have developed, including warranties and third party authentication, which enable markets with asymmetric information to function. Arrow analysed this issue for medical care (a 1963 paper entitled "Uncertainty and the Welfare Economics of Medical Care", in the American Economic Review); [27] later researchers investigated many other markets, particularly second-hand assets, online auctions and insurance.

Awards and honors

Arrow was awarded the John Bates Clark Medal in 1957 [28] and was elected a Fellow of the American Academy of Arts and Sciences in 1959. [29] He was the joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972 and the 1986 recipient of the von Neumann Theory Prize. [11] He was one of the recipients of the 2004 National Medal of Science, the nation's highest scientific honor, presented by President George W. Bush for his contributions to research on the problem of making decisions using imperfect information and his research on bearing risk. [4]

He has received honorary doctorates from the University of Chicago (1967), the University of Vienna (1971) the City University of New York (1972). [11] On 2 June 1995 he received an honorary doctorate from the Faculty of Social Sciences at Uppsala University, Sweden. [30] He was elected a Foreign Member of the Royal Society (ForMemRS) in 2006. [31] [4]

Personal life and death

Arrow was a brother to the economist Anita Summers, uncle to economist and former Treasury Secretary and Harvard President Larry Summers, and brother-in-law of the late economists Robert Summers and Paul Samuelson. [32] In 1947, he married Selma Schweitzer, graduate in economics at the University of Chicago [33] and psychotherapist, who died in 2015; they had two children: David Michael (b. 1962), an actor, [34] and Andrew Seth (b. 1964). [11]

Arrow was well known for being a polymath, possessing prodigious knowledge of subjects far removed from economics. On one occasion (recounted by Eric Maskin), in an attempt to artificially best Arrow's knowledge, the junior faculty agreed to closely study the breeding habits of gray whales – a suitably obscure topic – and discuss it in his presence. To their surprise, Arrow actually joined into the conversation. [32] [35]

Arrow died in his Palo Alto, California home on 21 February 2017 at the age of 95. [32]

Publications

Reprinted as: Arrow, Kenneth J. (1963). Social Choice and Individual Values (2nd ed.). New Haven: Yale University Press. ISBN   9780300013641.
Also available as: Arrow, Kenneth J.; Hurwicz, Leonid (1977). "Appendix: An optimality criterion for decision-making under ignorance". (online Book). Cambridge Books Online: 461–72. doi:10.1017/CBO9780511752940.015. ISBN   9780511752940.
and as: Arrow, Kenneth J.; Hurwicz, Leonid (1977), "Appendix: An optimality criterion for decision-making under ignorance", in Arrow, Kenneth J.; Hurwicz, Leonid (eds.), Studies in resource allocation processes, Cambridge New York: Cambridge University Press, pp. 461–72, ISBN   9780521215220.
Including: Arrow, Kenneth J. Price-quantity adjustments in multiple markets with rising demands, pp. 3–15.
Reprinted as: Arrow, Kenneth J. (1983b), "The organization of economic activity: issues pertinent to the choice of market versus non-market allocations", in Arrow, Kenneth J. (ed.), Collected papers of Kenneth J. Arrow, volume 2: general equilibrium, Cambridge, Massachusetts: Belknap Press, pp. 133–55, ISBN   9780674137615.
Also reprinted as a pdf.
Reprinted as: Arrow, Kenneth J. (1983a), "Extended sympathy and the possibility of social choice", in Arrow, Kenneth J. (ed.), Collected papers of Kenneth J. Arrow, volume 1: social Choice and justice, Cambridge, Massachusetts: Belknap Press, ISBN   9780674137608.
Arrow, Kenneth J. (1983a). Collected papers of Kenneth J. Arrow, volume 1: social Choice and justice. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137608.
Arrow, Kenneth J. (1983b). Collected papers of Kenneth J. Arrow, volume 2: general equilibrium. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137615.
Arrow, Kenneth J. (1984a). Collected papers of Kenneth J. Arrow, volume 3: individual choice under certainty and uncertainty. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137622.
Arrow, Kenneth J. (1984b). Collected papers of Kenneth J. Arrow, volume 4: the economics of information. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137639.
Arrow, Kenneth J. (1985a). Collected papers of Kenneth J. Arrow, volume 5: production and capital. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137776.
Arrow, Kenneth J. (1985b). Collected papers of Kenneth J. Arrow, volume 6: applied economics. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137783.
Also available online as: Arrow, Kenneth J. (2008). "Arrow's theorem". The new Palgrave dictionary of economics online, (2nd ed.) . Palgrave Macmillan: 241–245. doi:10.1057/9780230226203.0061. ISBN   978-0-333-78676-5.
Also available online as: Arrow, Kenneth J. (2008). "Hotelling, Harold (1895–1973)". The new Palgrave dictionary of economics online, (2nd ed.) . Palgrave Macmillan: 73–75. doi:10.1057/9780230226203.0747. ISBN   978-0-333-78676-5.

Further reading

See also

Related Research Articles

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References

  1. ↑ Andrea Prat's CV
  2. ↑ PROFILE: Nancy Stokey.(Accessed September 2016)
  3. ↑ Kenneth Joseph Arrow (2017). On Ethics and Economics: Conversations with Kenneth J. Arrow. Routledge. pp. 12, 33. ISBN   978-1-138-67606-0.
  4. 1 2 3 "Professor Kenneth Arrow ForMemRS, elected 2006". London: Royal Society. Archived from the original on 17 November 2015.
  5. ↑ "Premiat Nobel cu origini românești, Doctor Honoris Causa al Universității "Al. I. Cuza" din Iași". Jurnalul.ro. Retrieved 1 November 2014.
  6. ↑ Arrow and the Foundations of the Theory of Economic Policy
  7. ↑ Abu N.M. Wahid (2002). Frontiers of Economics: Nobel Laureates of the Twentieth Century. Greenwood Publishing. p. 5. ISBN   0-313-32073-X.
  8. ↑ Steven Pressman (1999). Fifty major economists: Business & Economics. Routledge Publishing. p. 177. ISBN   0-415-13480-3.
  9. ↑ "American Jewish Recipients of the Nobel Prize". Fau.edu. Retrieved 1 November 2014.
  10. 1 2 "Econ Journal Watch – Ideological Profiles of the Economics Laureates". Econjwatch.org. Retrieved 1 November 2014.
  11. 1 2 3 4 5 6 7 "Kenneth J. Arrow – Biographical". Nobelprize.org. Retrieved 1 November 2014.
  12. ↑ "Kenneth J. Arrow, MA, PhD". Stanford University. Retrieved 1 November 2014.
  13. ↑ "American President". Millercenter.org. Archived from the original on 2 November 2014. Retrieved 1 November 2014.
  14. ↑ Velupillai, K. Vela (1 July 2019). "Kenneth Joseph Arrow. 23 August 1921—21 February 2017". Biographical Memoirs of Fellows of the Royal Society. 0 (0): 20190002. doi:10.1098/rsbm.2019.0002.
  15. ↑ John B. Shoven. "Kenneth Arrow Contributions to Economics" (PDF). Siepr.stanford.edu. Retrieved 1 November 2014.
  16. ↑ "Kenneth J. Arrow Papers, 1939–2009". Rubenstein Library, Duke University.
  17. ↑ Kenneth Arrow, "A Difficulty in the Concept of Social Welfare" (1950).
  18. 1 2 Morreau, Michael (1 January 2016). "Arrow's Theorem". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 25 February 2017.
  19. ↑ Mas-Colell, Andreu; Whinston, Michael D.; Green, Jerry R. (1995). Microeconomic Theory. New York: Oxford University Press. pp. 691–93. ISBN   0-19-507340-1.
  20. ↑ "Gerard Debreu – Biographical". www.nobelprize.org. Retrieved 25 February 2017.
  21. ↑ Smith, Adam, and Andrew S. Skinner. The wealth of nations. London: Penguin Books, 1999. Print.
  22. ↑ Arrow, Kenneth (1974). "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice". American Economic Review . 64 (3): 253–72. JSTOR   1808881.
  23. ↑ "Kenneth Arrow (1921– )". Concise Encyclopedia of Economics. Liberty Fund. 2008. Retrieved 18 June 2017.
  24. ↑ Romer, Paul M. (1986). "Increasing Returns and Long-Run Growth". Journal of Political Economy . 94 (5): 1002–37. doi:10.1086/261420. JSTOR   1833190.
  25. ↑ Arrow, Kenneth J. (1962). "The Economic Implications of Learning by Doing". Review of Economic Studies . 29 (3): 155–73. doi:10.2307/2295952. JSTOR   2295952.
  26. ↑ Barro, Robert J.; Sala-i-Martin, Xavier (2004). Economic Growth (2nd ed.). Cambridge: MIT Press. pp. 212–20. ISBN   0-262-02553-1.
  27. ↑ "Uncertainty and the Welfare Economics of Medical Care" (PDF).Cite journal requires |journal= (help)
  28. ↑ "John Bates Clark Medal". American Economic Association. Retrieved 25 February 2017.
  29. ↑ "Book of Members, 1780–2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 25 April 2011.
  30. ↑ Honorary Doctors of the Faculty of Social Sciences
  31. ↑ Velupillai, K. Vela (2019). "Kenneth Joseph Arrow. 23 August 1921—21 February 2017". Biographical Memoirs of Fellows of the Royal Society. 67: 20190002. doi:10.1098/rsbm.2019.0002.
  32. 1 2 3 Weinstein, Michael M. (21 February 2017). "Kenneth Arrow, Nobel-Winning Economist Whose Influence Spanned Decades, Dies at 95". New York Times . Retrieved 21 February 2017.
  33. ↑ Heller, Walter P.; Starr, Ross M.; Starrett, David A., eds. (1986). "Kenneth J. Arrow". Social Choice and Public Decision Making: Essays in Honor of Kenneth J. Arrow, Volume I. Cambridge University Press. p. xiv. ISBN   0-521-30454-7.
  34. ↑ David Arrow on IMDb
  35. ↑ Arrow, Kenneth Joseph (2012). Social choice and individual values. Yale University Press. ISBN   9780300179316. OCLC   837682848.
Awards
Preceded by
Simon Kuznets 		Laureate of the Nobel Memorial Prize in Economics
1972
Served alongside: John R. Hicks 		Succeeded by
Wassily Leontief
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