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Concepts of optimality and their uses

Nobel Memorial Lecture — 11 December 1975

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References

  • I. Adelman and E. Thorbecke, eds. [1966],The Theory and Design of Economic Development. Baltimore, Johns Hopkins Press.

    Google Scholar 

  • K.J. Arrow, and M. Kurz [1970],Public Investment, The Rate of Return, and Optimal Fiscal Policy. Baltimore, Johns Hopkins Press.

    Google Scholar 

  • E. Barone [1908], “Il Ministro della Produzione nello Stato Collettivista”,Giorn. degli Econ.; English Translation in F.A. Hayek, ed.,Collectivist Economic Planning, London, 1935.

  • R. Beals and T.C. Koopmans [1969], “Maximizing Stationary Utility in a Constant Technology”,SIAM Journal of Applied Mathematics 17, 5, pp. 1001–1015.

    Google Scholar 

  • C.R. Blitzer, P.C. Clark and L. Taylor, eds. [1975],Economy-Wide Models and Development Planning. Oxford U. Press.

  • D. Cass [1966], “Optimum Growth in an Aggregate Model of Capital Accumulation: A Turnpike Theorem”,Econometrica 34, 4, pp. 833–850.

    Google Scholar 

  • Gustav Cassel [1918],The Theory of Social Economy. London, 1923. Originally published in German, 1918.

  • S. Chakravarty [1969],Capital and Development Planning. Cambridge, Mass., M.I.T. Press.

    Google Scholar 

  • H.B. Chenery [1952], “Overcapacity and the Acceleration Principle”,Econometrica 20, 1, pp. 1–28.

    Google Scholar 

  • H.B. Chenery and K. Kretschmer [1956], “Resource Allocation for Economic Development”,Econometrica 24, 4, pp. 365–399.

    Google Scholar 

  • H.B. Chenery and H. Uzawa [1958], “Non-Linear Programming in Economic Development” in K.J. Arrow, L. Hurwicz and H. Uzawa, eds.,Studies in Linear and Non-Linear Programming. Stanford U. Press.

  • H.B. Chenery, ed. [1971],Studies in Development Planning. Cambridge, Mass., Harvard U. Press.

    Google Scholar 

  • J.S. Chipman [1965], “A Survey of the Theory of International Trade: Part I, The Classical Theory”,Econometrica, 33, 3, pp. 477–519.

    Google Scholar 

  • G.B. Dantzig [1951], “Application of the Simplex Method to a Transportation Problem” in T.C. Koopmans, ed.,Activity Analysis⋯ (see below), pp. 359–373.

  • G.B. Dantzig and P. Wolfe [1960], “The Decomposition Principle for Linear Programming”,Operations Research 8, 1, pp. 101–111.

    Google Scholar 

  • G.B. Dantzig and P. Wolfe [1961], “The Decomposition Algorithm for Linear Programs”,Econometrica 29, 4, pp. 767–778.

    Google Scholar 

  • G.B. Dantzig [1963],Linear Programming and Extensions. Princeton U. Press.

  • P.S. Dasgupta [1969], “On the Concept of Optimum Population”,Review of Econ. Studies, 36, 1, pp. 295–318.

    Google Scholar 

  • P.S. Dasgupta and G. Heal [1974], “The Optimal Depletion of Exhaustible Resources”,Review of Econ. Studies, Symposium, pp. 3–28.

  • D. Gale [1956], “The Closed Linear Model of Production”, Paper 18, H. Kuhn and A.W. Tucker, eds.,Linear Inequalities and Related Systems. Princeton U. Press.

  • D. Gale, H.W. Kuhn and A.W. Tucker [1951], “Linear Programming and the Theory of Games”, Ch. XIX of T.C. Koopmans, ed.,Activity Analysis⋯ (see below), pp. 317–329.

  • L.M. Goreux, A.S. Manne and coauthors [1973],Multi-Level Planning: Case Studies in Mexico. Amsterdam, North-Holland Publ.

    Google Scholar 

  • F.A. Hayek [1945], “The Use of Knowledge in Society”,Am. Econ. Rev., 35, 4, pp. 519–30.

    Google Scholar 

  • F.L. Hitchcock [1941], “The Distribution of a Product from Several Sources to Numerous Localities”,Journal of Mathematics and Physics, 20, pp. 224–230.

    Google Scholar 

  • L.V. Kantorovich [1939],Mathematicheskie Metody Organizatsii i Planirovania Proizvodstva, Leningrad State University Publishers, translated as “Mathematical Methods in the Organization and Planning of Production” [1960] inManagement Science, 6, 4, pp. 366–422.

  • L.V. Kantorovich and M.K. Gavurin [first version 1940, publ. 1949], “Primenenie matematicheskikh metodov v voprosakh analiza gruzopotokov”, inProblemy povysheniia effektivnosti raboty transporta (The Use of Mathematical Methods in Analyzing Problems of Goods Transport, inProblems of Increasing the Efficiency in the Transport Industry, pp. 110–138). Academy of Sciences, U.S.S.R.

  • L.V. Kantorovich [1942], “On the Translocation of Masses”,Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS, 37, nos. 7–8. Reprinted [1958] inManagement Science, 5, 1, pp. 1–4.

  • L.V. Kantorovich [1959], Ekonomicheskii raschët nailichshego ispolzovania resursov, Acad. of Sc., USSR (translated [1965],The Best Use of Economic Resources. Cambridge, Mass., Harvard U. Press.)

    Google Scholar 

  • T.C. Koopmans [memo dated 1942, publ. 1970], “Exchange Ratios between Cargoes on Various Routes”, inScientific Papers of Tjalling C. Koopmans. Berlin, Springer Verlag.

    Google Scholar 

  • T.C. Koopmans [1949] (conference paper, publ. 1951), “Optimum Utilization of the Transportation System”, inProceedings of the International Statistical Conferences, 5, pp. 136–145.

  • T.C. Koopmans, ed. [1951],Activity Analysis of Production and Allocation. New York, Wiley.

    Google Scholar 

  • T.C. Koopmans [1951], “Analysis of Production as an Efficient Combination of Activities”, in T.C. Koopmans, ed.,Activity Analysis⋯, op. cit.

  • T.C. Koopmans and S. Reiter [1951], “A Model of Transportation”, in T.C. Koopmans, ed.,Activity Analysis⋯, op. cit., pp. 222–259.

  • T.C. Koopmans [1957],Three Essays on the State of Economic Science. New York, McGraw-Hill.

    Google Scholar 

  • T.C. Koopmans and A.F. Bausch [1959], “Selected Topics in Economics Involving Mathematical Reasoning”,SIAM Review, 1, 2, pp. 79–148.

    Google Scholar 

  • T.C. Koopmans [1960], “Stationary Ordinal Utility and Impatience”,Econometrica, 28, 2, pp. 287–309.

    Google Scholar 

  • T.C. Koopmans, P.A. Diamond and R.E. Williamson [1964], “Stationary Utility and Time Perspective”,Econometrica, 32, 1–2, pp. 82–100.

    Google Scholar 

  • T.C. Koopmans [1965], “On the Concept of Optimal Economic Growth”, inThe Econometric Approach to Development Planning, Pontif. Acad. Sc. Scripta Varia. 28, pp. 225–300; reissued North-Holland Publ. [1966].

  • T.C. Koopmans [1967], “Intertemporal Distribution and ‘Optimal’ Aggregate Economic Growth”, in Fellneret al., Ten Economic Studies in the Tradition of Irving Fisher, pp. 95–126. New York, Wiley.

    Google Scholar 

  • T.C. Koopmans [1973], “Economic Growth and Exhaustible Resources”, in H.C. Bos, H. Linneman and P. de Wolff, eds.,Economic Structure and Development, Essays in Honour of Jan Tinbergen, pp. 239–255. Amsterdam, North Holland Publ.

    Google Scholar 

  • J. Kornai and Th. Liptak [1962, 1965], “Two-Level Planning”, ‘duplicated’, in Hungarian;Econometrica, 33, 1, pp. 141–169.

    Google Scholar 

  • J. Kornai [1967],Mathematical Planning of Structural Decisions. Budapest, Hungarian Academy of Sciences.

    Google Scholar 

  • H.W. Kuhn and A.W. Tucker [1950], “Nonlinear Programming”, in J. Neyman, ed.,Proc. Second Berkeley Symposium on Math. Stat. and Probability, Berkeley, pp. 481–492.

  • O. Lange [1936], “On the Economic Theory of Socialism”,Review of Econ. Studies, 4, 1 and 2, pp. 53–71, 123–142. Repr. in B. Lippincott, ed.,On the Economic Theory of Socialism [1938]. Minneapolis, U. of Minnesota Press.

    Google Scholar 

  • W.W. Leontief [1936], “Quantitative Input and Output Relations in the Economic System of the United States”,Review of Econ. Statistics, 18, 3, pp. 105–125.

    Google Scholar 

  • W.W. Leontief [1941],The Structure of American Economy, 1919–1939. Oxford U. Press.

  • A.P. Lerner [1937], “Statics and Dynamics in Socialist Economics”,Economic Journal, 47, 2, pp. 253–270.

    Google Scholar 

  • A.P. Lerner [1938], “Theory and Practice in Socialist Economics”,Review of Econ. Studies, 6, 1, pp. 71–75.

    Google Scholar 

  • E. Malinvaud [1965], “Croissances optimales dans un modèle macroéconomique”, inThe Econometric Approach⋯., see Koopmans [1965].

  • E. Malinvaud [1967], “Decentralized Procedures for Planning”, in E. Malinvaud and M.O.L. Bacharach, eds.,Activity Analysis in the Theory of Growth and Planning. London, Macmillan; New York, St. Martin's Press.

    Google Scholar 

  • A.S. Manne and H. Markowitz, eds. [1963],Studies in Process Analysis. New York, Wiley.

    Google Scholar 

  • A.S. Manne and coauthors [1967],Investments for Capacity Expansion: Size, Location, and Time-Phasing. Cambridge, Mass., M.I.T. Press.

    Google Scholar 

  • A.S. Manne [1970], “Sufficient Conditions for Optimality in an Infinite Horizon Development Plan”,Econometrica 38, 1, pp. 18–38.

    Google Scholar 

  • P. Massé and R. Gibrat [1957], “Application of Linear Programming to Investments in the Electric Power Industry”,Management Science 3, 2, pp. 149–166.

    Google Scholar 

  • J.E. Meade [1955],Trade and Welfare. Oxford U. Press.

  • J. von Neumann [1936], “Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes”, in K. Menger, ed.,Ergebnisse eines mathematischen Kolloquiums, no. 8. Translated as “A Model of General Equilibrium”,Review of Econ. Studies 13, 1, pp. 1–9 [1945].

    Google Scholar 

  • V.V. Novozhilov [1939], “Metody soizmerenia narodnokhaziaistvennoi effektivnosti planovikh i proiektnikh variantov” (“Methods of Comparison of the National Economic Efficiency of Plan- and Project-Variants”),Transactions of the Leningrad Industrial Institute, 4.

  • J.D. Pitchford [1974],Population in Economic Growth. Amsterdam, North-Holland Publ.

    Google Scholar 

  • J.D. Pitchford [1975], “Population and Economic Growth: Macroeconomics”, paper presented at the Econometric Society, Third World Congress, Toronto, Canada.

  • F.P. Ramsey [1928] “A Mathematical Theory of Saving”,Economic Journal, 38, 4, pp. 543–559.

    Google Scholar 

  • P.A. Samuelson [1949, 1966], “Market Mechanisms and Maximization”, Rand Corporation, 1949. Reprinted inThe Collected Scientific Papers of Paul A. Samuelson. Cambridge, Mass., M.I.T. Press, pp. 425–493.

    Google Scholar 

  • Adam Smith [1776],The Wealth of Nations.

  • A.W. Tucker [1957], “Linear and Nonlinear Programming”,Operations Research, 5, 2, pp. 244–257.

    Google Scholar 

  • L. Walras [1874],Eléments d'économie politique pure, Lausanne; translated [1954] by W. Jaffé asElements of Pure Economics, London.

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Koopmans, T.C. Concepts of optimality and their uses. Mathematical Programming 11, 212–228 (1976). https://doi.org/10.1007/BF01580392

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