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Wassily Leontief

From Wikipedia, the free encyclopedia

Wassily Wassilyevich Leontief (Russian: Василий Васильевич Леонтьев; August 5, 1905 – February 5, 1999), was a Russian-American economist known for his research on input-output analysis and how changes in one economic sector may affect other sectors.[5]

Leontief won the Nobel Committee's Nobel Memorial Prize in Economic Sciences in 1973, and four of his doctoral students have also been awarded the prize (Paul Samuelson 1970, Robert Solow 1987, Vernon L. Smith 2002, Thomas Schelling 2005).

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We are going to look at an application of homogeneous systems of equations Called Leontief Input-Output analysis A little bit of history on this topic, Leontief was an economist who wrote a paper In 1951 where he described this way to analyze an economy And later on in 1972 he was awarded The Nobel Prize in economics for this work The example he will look at today begins as follows Suppose that an economy consists of Coal, Electric and Steel sectors The output for each sector is distributed among the various sectors As shown in the table below where the entries in a column Represent the fractional parts of a sector's total output The basic idea here is that each one of these sectors this dependent upon Other sectors and when we look at the table we can see That the distribution of output is divided up Columns of the table where the rows Represent what is needed by each one of the sectors The third column of the table says that the total output Is divided as follows 60% of it is going to coal 20% of it is going to electricity And 20% of it remains in the steel sector. The idea is That the steel sector will need coal in order to produce steel It will need electricity in order to produce steel and it will Will need steel in order to produce steel. You can see that columns of this table add up to 1 that's because that's 100% Of the output from that sector This can also be shown in the diagram where we can see Where the output from each one of the sectors is going to go So when I look at the electricity sector I can see That 10% of the electricity sector is staying in the electricity sector While 40% of it is moving to Coal and 50% of it is moving to steel. If you look at this diagram you can see That all of the arrows pointing out of each particular sector Will have to add up to 1. I have 10% going out Electricity going to electricity 40% of electricity going out of Electricity to coal 50% of electricity going to steel The arrows going out of a sector have to add up to 1 The arrows going into a sector do not necessarily need to add up to one For example, the third row of the table says That still needs 40% of Coal's output 50% of the electric output and 20% Of the steel output. If we p_C, p_E p_s represent the total output of each sector This steel is going to need .4p_C Of coal, its going to need 0.5 p_E of electricity And .2 p_S of steel We can now say that in order for steel to produce Enough to meet the needs of all of the other sectors p_S is the amount of steel that is produced That amount is going to have to equal The amount that is needed by these other sectors Similarly I can say that the amount That coal produces will need to be 40% of what Electricity produces and 60% of what steel produces Electricity will need to be 60% of what coal produces 10% of what electricity produces and 20% of what steel produces And then as we decided the equation for steel You will notice that the right side of the equations Match exactly the coefficients that we find in this table We have a system of equations You will recognize that this does not fit into the standard form Of a system of equations because we have variables on both the left side And the right side. In order to have a standard form we want All of the variables on the same side so if I do a little bit of algebra to this To the system of equations I can rewrite it like this which was just Subtracting the left side from the right side And you will see that this is now become a homogeneous system of equations We know how to solve a system of homogeneous equations I took the system of equations and put it into a matrix This is an augmented matrix and I'm going to take that and And put it into reduced row echelon form which comes out looking like this. and these are the fractions -31/33 And -28/33 probably best to round those to decimals so a decimal representation 31/33 is approximately 94% and And we have -85% I can write this in terms of Variables I will write the solution and I will get p_S is a free variable and p_E is .85p_S and p_C is .94p_s. This allows us to draw the conclusion That the equilibrium production level is That coal must produce 94% of what steel produces And electricity must produce 85% of what steel produces So the basic idea here is that We want each sector of the economy to produce enough To satisfy all the other sectors of the economy When Leontief originally wrote his paper he had divided and economy into 500 sectors you can see that an economy with 500 sectors Would be a lot more complicated but it really wouldn't be much more difficult Because we would have an incredibly large matrix which we could still Which we could reduce and then find these equilibrium production levels In a similar way



Early life

Wassily Leontief was born on August 5, 1906, in Munich, Germany, the son of Wassily W. Leontief (professor of Economics) and Zlata (German spelling Slata; later Evgenia) Leontief (née Becker).[6][7] W. Leontief, Sr., belonged to a family of old-believer merchants living in St. Petersburg since 1741.[8] Genya Becker belonged to a wealthy Jewish family from Odessa.[9] At 15 in 1921, Wassily, Jr., entered University of Leningrad in present-day St. Petersburg. He earned his Learned Economist degree (equivalent to Master of Arts) in 1925 at the age of 19.

Opposition in USSR

Leontief sided with campaigners for academic autonomy, freedom of speech and in support of Pitirim Sorokin. As a consequence, he was detained several times by the Cheka. In 1925, he was allowed to leave the USSR, mostly because the Cheka believed that he was mortally ill with a sarcoma, a diagnosis that later proved false.[8] He continued his studies at the Frederick William University and, in 1928 earned a Ph.D. degree in economics under the direction of Werner Sombart, writing his dissertation on The Economy as Circular Flow (original German title: Die Wirtschaft als Kreislauf).

Early professional life

From 1927 to 1930, he worked at the Institute for the World Economy of the University of Kiel. There he researched the derivation of statistical demand and supply curves. In 1929, he traveled to China to assist its ministry of railroads as an advisor.

In 1931, he went to the United States and was employed by the National Bureau of Economic Research.

During World War II, Leontief served as consultant at the U. S. Office of Strategic Services.

Affiliation with Harvard

Leontief joined Harvard University's department of economics in 1932 and in 1946 became professor of economics there.

In 1949, Leontief used an early computer at Harvard and data from the U.S. Bureau of Labor Statistics to divide the U.S. economy into 500 sectors. Leontief modeled each sector with a linear equation based on the data and used the computer, the Harvard Mark II, to solve the system, one of the first significant uses of computers for mathematical modeling,[10][11][12][13] along with George W. Snedecor's usage of the Atanasoff–Berry computer.

Leontief set up the Harvard Economic Research Project in 1948 and remained its director until 1973. Starting in 1965, he chaired the Harvard Society of Fellows.

Affiliation with New York University

In 1975, Leontief joined New York University and founded and directed the Institute for Economic Analysis. He taught graduate and undergraduate classes.


In 1932, Leontief married poet Estelle Marks. Their only child, Svetlana Leontief Alpers, was born in 1936. Leontief's wife Estelle wrote a memoir, Genia and Wassily,[9] of their relations with his parents after they came to the US as emigres.

As hobbies Leontief enjoyed fly fishing, ballet, and fine wines. He vacationed for years at his farm in West Burke, Vermont, but after moving to New York in the 1970s moved his summer residence to Lakeville, Connecticut.

Leontief died in New York City on Friday, February 5, 1999 at the age of 93. His wife died in 2005.

Major contributions

Leontief is credited with developing early contributions to input-output analysis and earned the Nobel Prize in Economics for his development of its associated theory. He has also made contributions in other areas of economics, such as international trade where he documented the Leontief paradox. He was also one of the first to establish the composite commodity theorem.

Leontief earned the Nobel Prize in economics for his work on input-output tables. Input-output tables analyze the process by which inputs from one industry produce outputs for consumption or for inputs for another industry. With the input-output table, one can estimate the change in demand for inputs resulting from a change in production of the final good. The analysis assumes that input proportions are fixed; thus the use of input-output analysis is limited to rough approximations rather than prediction. Input-output was novel and inspired large-scale empirical work; in 2010 its iterative method was recognized as an early intellectual precursor to Google's PageRank.[14][15][16]

Leontief used input-output analysis to study the characteristics of trade flow between the U.S. and other countries, and found what has been named Leontief's paradox; "this country resorts to foreign trade in order to economize its capital and dispose of its surplus labor, rather than vice versa", i.e., U.S. exports were relatively labor-intensive when compared to U.S. imports. This is the opposite of what one would expect, considering the fact that the U.S.'s comparative advantage was in capital-intensive goods. According to some economists, this paradox has since been explained as due to the fact that when a country produces "more than two goods, the abundance of capital relative to labor does not imply that the capital intensity of its exports should exceed that of imports."[17]

Leontief was also a very strong proponent of the use of quantitative data in the study of economics. Throughout his life Leontief campaigned against "theoretical assumptions and non-observed facts".[17] According to Leontief, too many economists were reluctant to "get their hands dirty" by working with raw empirical facts. To that end, Wassily Leontief did much to make quantitative data more accessible, and more indispensable, to the study of economics.


  • 1925: Баланс народного хозяйства СССР. ("Balans narodnogo khozyaystva SSSR") in Planovoe Khozyaystvo [ru]; translated into Italian in Spulber N.(Ed.) as "Il Bilancio dell'economia nazionale dell'URSS." in La Strategia Sovietica per Sviluppo Economico 1924–1930, Giulio Einaudi ed., Torino [discussing the Soviet "Balance of the National Economy", 1923–4]
  • 1928: Die Wirtschaft als Kreislauf, Tübingen: Mohr: re-published as The economy as a circular flow, pp. 181–212 in: Structural Change and Economic Dynamics, Volume 2, Issue 1, June 1991; this translation is abridged to avoid controversial statements.
  • Wassily W. Leontief (Aug 1936). "Quantitative Input and Output Relations in the Economic System of the United States". Review of Economics and Statistics. 18 (3): 105–125. JSTOR 1927837.
  • Wassily W. Leontief (Aug 1937). "Interrelation of Prices, Output, Savings and Investment: A Study in Empirical Application of Economic Theory of General Interdependence". Review of Economics and Statistics. 19 (3): 109–132. JSTOR 1927343.
  • 1941: Structure of the American Economy, 1919–1929
  • 1953: Studies in the Structure of the American Economy
  • 1966: Input-Output Economics[18]
  • 1966: Essays in Economics
  • Wassily W. Leontief (Aug 1967). "An Alternative to Aggregation in Input-Output Analysis and National Accounts". Review of Economics and Statistics. 49 (3): 412–419. JSTOR 1926651.
  • Wassily W. Leontief (Aug 1970). "Environmental repercussions and the economic structure: an input-output approach". Review of Economics and Statistics. 52: 262–271. JSTOR 1926294.
  • Wassily W. Leontief (1970). "The Dynamic Inverse". In A.P. Carter and A. Brody (ed.). Contributions to Input-Output Analysis: Proc. 4th Int. Conf. on Input-Output Techniques (1). North-Holland Publishing Company. pp. 17–46.
  • 1977: Essays in Economics, II
  • 1977: The Future of the World Economy
  • 1983: Military Spending: Facts and Figures, Worldwide Implications and Future Outlook co-authed with F. Duchin.
  • 1983: The Future of Non-Fuel Minerals in the U. S. And World Economy co-authed with J. Koo, S. Nasar and I. Sohn
  • 1986: The Future Impact of Automation on Workers co-authored with F. Duchin
  • Wassily W. Leontief (1986). Input-Output Economics (2nd ed.). New York: Oxford University Press. ISBN 9780195035278.


In honor

The Global Development and Environment Institute at Tufts University awards the Leontief Prize in Economics each year in his honor.

Leontief is listed in the Russian-American Chamber of Fame of Congress of Russian Americans, which is dedicated to Russian immigrants who made outstanding contributions to American science or culture.[19][20][21]



Much of current academic teaching and research has been critizied for its lack of relevance, that is, of immediate practical impact. ... The trouble is caused, however, not by an inadequate selection of targets, but rather by our inability to hit squarely on them, ... by the palpable inadequacy of the scientific means with which they try to solve them. ... The weak and all too slowly growing empirical foundations clearly cannot support the proliferating superstructure of pure, or should I say, speculative economic theory.... By the time it comes to interpretations of the substantive conclusions, the assumptions on which the model has been based are easily forgotten. But it is precisely the empirical validity of these assumptions on which the usefulness of the entire exercise depends. ... A natural Darwinian feedback operating through selection of academic personnel contributes greatly to the perpetuation of this state of affairs.[22]

The role of humans as the most important factor of production is bound to diminish in the same way that the role of horses in agricultural production was first diminished and then eliminated by the introduction of tractors.[23]

See also

References and sources

  1. ^ "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1973".
  2. ^ Wassily Leontief Birth Certificate. U.S. Library of Congress
  3. ^ Harvard IOHP | Khodadad Farmanfarmaian Transcripts. Retrieved on 2017-09-06.
  4. ^ Jorgenson, Dale W. (1998) Growth, Vol. 1: Econometric General Equilibrium Modeling. Cambridge, Massachusetts: MIT Press. ISBN 026226322X
  5. ^ Dalyell, Tam (11 February 1999). "Obituary: Wassily Leontief". The Independent. Retrieved 18 May 2019.
  6. ^ See birth data, provided October 4, 2005 Archived January 14, 2007, at the Wayback Machine. In his Nobel Prize website biographical information it states that recent information sets his year of birth to 1905.
  7. ^ Bjerkholt, Olav, and Heinz D. Kurz (2006). "Introduction: the History of Input–Output Analysis, Leontief's Path and Alternative Tracks". Economic Systems Research. 18 (18.4): 331–33. doi:10.1080/09535310601020850.CS1 maint: Multiple names: authors list (link)
  8. ^ a b Kaliadina, Svetlana A.; Pavlova, Natal'ia Iu.; Wittich, Claus (2006). "The Family of W. W. Leontief in Russia". Economic Systems Research. 18 (4): 335. doi:10.1080/09535310601020876.
  9. ^ a b Estelle Leontief (1987). Genia & Wassily: a Russian-American memoir. Zephyr Press. ISBN 978-0-939010-11-0.
  10. ^ Lay, David C. (2003). Linear Algebra and Its Applications (Third ed.). Addison Wesley. p. 1. ISBN 0-201-70970-8.
  11. ^ Polenske, Karen R. (2004). "Leontief's 'magnificent machine' and other contributions to applied economics". Wassily Leontief and Input-Output Economics. Cambridge University Press. p. 12.
  12. ^ See also, Leontief, Input-Output Economics (Scientific American, 1951) reprinted in Input-Output Economics (1966).
  13. ^ Iverson, Kenneth E. (1954). Machine Solutions of Linear Differential Equations Applications to a Dynamic Economic Model, Ph.D. Thesis. Harvard University.
  14. ^ PageRank-Type Algorithm From the 1940s Discovered – Slashdot. (2010-02-17). Retrieved on 2017-09-06.
  15. ^ Scientist Finds PageRank-Type Algorithm from the 1940s – MIT Technology Review. (2010-02-17). Retrieved on 2017-09-06.
  16. ^ Massimo Franceschet (2010). "PageRank: Standing on the shoulders of giants". arXiv:1002.2858 [cs.IR].
  17. ^ a b "Wassily Leontief (1906–1999)". Econlib. Library of Economics and Liberty. 5 May 2014. Retrieved 5 May 2014.
  18. ^ Wassily Leontief (1986). Input-output Economics. Oxford University Press. ISBN 978-0-19-503527-8.
  19. ^ European Russians: The place of Russian Emigration in US Science and technology. Retrieved on 2017-09-06.
  20. ^ Anatoly Bezkorovainy (2008). All Was Not Lost: Journey of a Russian Immigrant from Riga to Chicagoland. AuthorHouse. p. 457. ISBN 9781434364586. Retrieved August 15, 2017.
  21. ^ CRA Hall of Fame.
  22. ^ Leontief, W., Theoretical Assumptions and nonobserved Facts, American Economic Review, Vol. 61, No. 1 (March 1971), pp. 1–7; Presidential address to the American Economic Association 1970.
  23. ^ Hallak, Jacques; Caillods, Françoise (1995). "Educational Planning: The International Dimension". ISBN 9780815320241.

External links

Preceded by
John R. Hicks
Kenneth J. Arrow
Laureate of the Nobel Memorial Prize in Economics
Succeeded by
Gunnar Myrdal
Friedrich August von Hayek
This page was last edited on 18 May 2019, at 19:52
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