Selected Topics in Economics Involving Mathematical Reasoning

Abstract

Next article Selected Topics in Economics Involving Mathematical ReasoningTjalling C. Koopmans and Augustus F. BauschTjalling C. Koopmans and Augustus F. Bauschhttps://doi.org/10.1137/1001021PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Kenneth J. Arrow, An extension of the basic theorems of classical welfare economics, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 507–532 MR0044815 0044.34608 Kenneth J. Arrow, An extension of the basic theorems of classical welfare economics, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 507–532 MR0044815 0044.34608 Robert Dorfman, Mathematical, or “linear,” programming: a nonmathematical exposition, American Economic Review, (1953), 797–825, December T. C. Koopmans, Allocation of Resources and the Price System, 1957, (especially section 4), see reference under topic 1 Robert Dorfman, , Paul A. Samuelson and , Robert M. Solow, Linear programming and economic analysis, A Rand Corporation Research Study, McGraw-Hill Book Co., Inc., New York, 1958ix+525, Chapter 12 MR0128543 0123.37102 Frank D. Graham, The Theory of International Values, Princeton, 1948 Kenneth J. Arrow and , Gerard Debreu, Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265–290, July MR0077069 0055.38007 Kenneth J. Arrow, Alternative approaches to the theory of choice in risk-taking situtations, Econometrica, 19 (1951), 404–437, Oct. MR0046020 0044.15304 G. Dantzig, , R. Fulkerson and , S. Johnson, Solution of a large-scale traveling-salesman problem, J. Operations Res. Soc. Amer., 2 (1954), 393–410, Nov. MR0070932 R. G. D. Allen, Mathematical Economics, London, 1956, Sec. 1.2 R. G. D. Allen, Mathematical Economics, Sections 1.7, 1.8, 1.9, 2.5, 2.6, 2.7 R. G. D. Allen, Mathematical Economics, London, 1956, Sections 3.1, 3.2, 3.7, 7.1, 7.2, 7.3, 7.4 T. W. Anderson, On estimation of parameters in latent structure analysis, Psychometrika, 19 (1954), 1–10 10.1007/BF02288989 MR0075492 0059.12802 CrossrefISIGoogle Scholar[2] Gerard Debreu, Valuation equilibrium and Pareto optimum, Proc. Nat. Acad. Sci. U. S. A., 40 (1954), 588–592 MR0065896 0055.38006 N. Bourbaki, Eléments de mathématique. Livre V: Espaces vectoriels topologiques. Chapitre II: Ensembles convexes et espaces localement convexes, Actualités Sci. Ind., no. 1189, Herman & Cie, Paris, 1953ii+124+iv MR0054161 0050.10703 T. C. Koopmans, Allocation of Resources and the Price System, 1957, (especially section 3), see reference under topic 1 Edmond Malinvaud, Capital accumulation and efficient allocation of resources, Econometrica, 21 (1953), 233–268, April MR0056267 0052.16001 David Gale, The closed linear model of productionLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N. J., 1956, 285–303, Paper 18 in Kuhn and Tucker, ed. MR0085961 0072.37903 Shizuo Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J., 8 (1941), 457–459 10.1215/S0012-7094-41-00838-4 MR0004776 0061.40304 Gerard Debreu, A social equilibrium existence theorem, Proc. Nat. Acad. Sci. U. S. A., 38 (1952), 886–893, Oct. MR0050251 0047.38804 I. N. Herstein and , John Milnor, An axiomatic approach to measurable utility, Econometrica, 21 (1953), 291–297, April MR0061356 0050.36705 Tjalling C. Koopmans and , Martin Beckmann, Assignment problems and the location of economic activities, Econometrica, 25 (1957), 53–76, Jan. MR0089106 0098.12203 J. B. D. Derksen, Long cycles in residential building, Econometrica, (1940), 97–116 Richard Ruggles and , Nancy D. Ruggles, National Income Accounts and Income Analysis, New York, 1956 W. Baumol, Economic Dynamics, New York, 1959 T. W. Anderson and , Herman Rubin, Statistical inference in factor analysis, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. V, University of California Press, Berkeley and Los Angeles, 1956, 111–150 MR0084943 0070.14703 CrossrefISIGoogle Scholar[3] Gerard Debreu, Thrall, , Coombs and , Davis, Representation of a Preference Ordering by a Numerical Function, Decision Processes, Wiley, 1954, 159–165 0058.13803 Debreu, The coefficient of resource utilization, Econometrica, 19 (1951), 273–292 0045.41404 H. W. Kuhn and , A. W. Tucker, Linear Inequalities and Related Systems, Princeton Univ. Press, 1956 0072.37502 J. Von Neumann, A model of general equilibrium, Rev. of Ec. Studies, 13 (1945-46), 1–9, (translated from German original of 1936) Lionel McKenzie, On equilibrium in Graham's model of world trade and other competitive systems, Econometrica, (1954), 147–161, April 0055.13702 Gerard Debreu, Market equilibrium, Proc. Nat. Acad. Sci. U.S.A., 42 (1956), 876–878, Nov. MR0081811 0072.37405 R. Duncan Luce and , Howard Raiffa, Games and decisions: introduction and critical survey, John Wiley & Sons Inc., New York, N. Y., 1957xix+509 MR0087572 0084.15704 John von Neumann, Kuhn and , Tucker, A certain zero-sum two-person game equivalent to the optimal assignment problemContributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, Princeton University Press, Princeton, N. J., 1953, 5–12 MR0054920 0050.14105 Mordecai Ezekiel, The cobweb theorem, Quart. Journal of Economics, (1938), 255–280, Feb. reprinted in Readings in Business Cycle Theory, Philadelphia 1951 T. Schelling, National Income Behavior, New York, 1951, especially part I J. R. Hicks, Contribution to the Theory of the Trade Cycle, Oxford, 1950 Hood and , Koopmans, Studies in econometric method, Cowles Commission Monograph No. 14, John Wiley & Sons Inc., New York, 1953xix+323, Chapters I by J. Marschak, (C, I, E), II by T. C. Koopmans (I), III by H. A. Simon (C, I), IV–IX by various authors (E). Extensive references to other literature are found in this book MR0061358 0053.27905 CrossrefISIGoogle Scholar[4] Gerard Debreu, Notes on value theory, 1957, (multilithed) Cowles Foundation for Research in Economics at Yale University Gerard Debreu, Valuation equilibrium and Pareto optimum, Proc. Nat. Acad. Sci. U. S. A., 40 (1954), 588–592 MR0065896 0055.38006 George B. Dantzig, T. C. Koopmans, Maximization of a linear function of variables subject to linear inequalitiesActivity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons Inc., New York, N. Y., 1951, 339–347, Chapter XXI MR0056260 0045.09802 John G. Kemeny, , J. Laurie Snell and , Gerald L. Thompson, Introduction to finite mathematics, Prentice-Hall Inc., Englewood Cliffs, N. J., 1957xi+372, Chapter VII, Sections 9, 10 MR0084454 0077.01603 Gerard Debreu, Notes on Value Theory, 1957, multilithed by the Cowles Foundation, 1957, especially Chapter 5 John Milnor, Thrall, , Coombs and , David, Games against Nature, Decision Processes, New York, 1954, 49–60 0058.13702 T. Koopmans, Distributed lags in Dynamic economics, Econometrica, (1941), 128–134 P. A. Samuelson, Interaction between the multiplier analysis and the principle of acceleration, Review of Economic Statistics, 1939, 75–78, May, reprinted in Readings in Business Cycle Theory, Blakiston, 1951 T. C. Koopmans and , O. Reiersøl, The identification of structural characteristics, Ann. Math. Statistics, 21 (1950), 165–181 MR0039967 0038.29303 CrossrefISIGoogle Scholar[5] J. R. Hicks, Value and Capital, Oxford, 1946 V. L. Klee, Jr., Convex sets in linear spaces, Duke Math. J., 18 (1951), 443–466 10.1215/S0012-7094-51-01835-2 MR0044014 0042.36201 C. Hildreth and , S. Reiter, T. C. Koopmans, On the choice of a crop rotation plan, Activity Analysis of Production and Allocation, Wiley, 1951, 177–188, Chapter XI 0045.09701 David Gale, The law of supply and demand, Math. Scand., 3 (1955), 155–169 MR0077070 0064.39401 Leonard J. Savage, The foundations of statistics, John Wiley & Sons Inc., New York, 1954xv+294 MR0063582 0055.12604 J. Tinbergen, Ein Schiffbauzyklus?, Weltwirtschaftliches Archiv, (1931), 152–164 Richard B. McHugh, Efficient estimation and local identification in latent class analysis, Psychometrika, 21 (1956), 331–347 10.1007/BF02296300 MR0082427 0074.13802 CrossrefISIGoogle Scholar[6] J. R. Hicks and , R. G. D. Allen, A reconsideration of the theory of value, I, Economica, (1934), 52–176 and 196–219 V. L. Klee, Jr., Convex sets in linear spaces. II, Duke Math. J., 18 (1951), 875–883 10.1215/S0012-7094-51-01882-0 MR0047251 0044.11201 T. C. Koopmans, Introduction, Activity Analysis of Production and Allocation, Wiley, 1951a, 1–12 Lawrence M. Graves, The Theory of Functions of Real Variables, McGraw-Hill Book Company, Inc., New York, 1946x+300 MR0018708 0063.01720 Abraham Wald, Statistical Decision Functions, John Wiley & Sons Inc., New York, N. Y., 1950ix+179 MR0036976 0040.36402 Olav Reiersøl, Identifiability of a linear relation between variables which are subject to error, Econometrica, 18 (1950), 375–389 MR0038054 0040.22502 CrossrefISIGoogle Scholar[7] Tjalling C. Koopmans, Efficient allocation of resources, Econometrica, (1951), 455–465, Oct. V. L. Klee, Jr., Convex sets in linear spaces. III, Duke Math. J., 20 (1953), 105–111 10.1215/S0012-7094-53-02010-9 MR0056190 0050.10901 Tjalling C. Koopmans, Analysis of production as an efficient combination of activitiesActivity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons Inc., New York, N. Y., 1951, 33–97, Chapter III MR0046017 0045.09506 Shizuo Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J., 8 (1941), 457–459 10.1215/S0012-7094-41-00838-4 MR0004776 0061.40304 George B. Dantzig, Linear programming under uncertainty, Management Sci., 1 (1955), 197–206, April–July MR0075511 0995.90589 Olav Reiersøl, On the identifiability of parameters in Thurstone's multiple factor analysis, Psychometrika, 15 (1950), 121–149 MR0035966 0037.36901 CrossrefISIGoogle Scholar[8] Tjalling C. Koopmans, Allocation of Resources and the Price System, 1957, (especially Sections 1 and 2), see reference under Topic 1 T. C. Koopmans, Activity Analysis of Production and Allocation, J. Wiley, 1951, In particular Chapter 3 and Part 3 0045.09503 Tjalling C. Koopmans and , Stanley Reiter, A model of transportationActivity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons Inc., New York, N. Y., 1951, 222–259, Chapter XIV MR0052757 0045.09704 H. W. Kuhn, On a theorem of WaldLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N. J., 1956, 265–273, Paper 16 in Kuhn and Tucker, ed. MR0082913 0072.37901 Rudolf J. Freund, The introduction of risk into a programming model, Econometrica, 24 (1956), 253–263, July MR0081204 0073.15507 CrossrefISIGoogle Scholar[9] Alfred Marshall, Principles of Economics, London, 1920, especially Book IV, Ch. XIII and Book V, Ch. XIII P. T. Bateman, , Hans Radstrom, , Olaf Hanner, , A. M. Macbeath, , C. A. Rogers and , V. L. Klee, Seminar on convex sets, The Institute for Advanced Study, Princeton, N.J., 1949–1950. Reprinted November, 1955, 88– MR0080938 Lionel W. McKenzie, Competitive equilibrium with dependent consumer preferences, Proceedings of the Second Symposium in Linear Programming, Washington, D. C., 1955, National Bureau of Standards, Washington, D. C., 1955, 277–294 MR0073922 H. Markowitz, Portfolio selection, Journal of Finance, (1952), 77–91, March ISIGoogle Scholar[10] Vilfredo Pareto, Manuel d'Economic Politique, Paris, 1927, especially Chap. VI, par. 32–64 Edmond Malinvaud, Capital accumulation and efficient allocation of resources, Econometrica, 21 (1953), 233–268 MR0056267 0052.16001 A. Wald, Über die eindeutige positive Lösbarbeit der neuen Produktionsgleichungen, Ergebnisse eines Mathematischen Kolloquiums, 6 (1933–4), 12–20 0010.40706 Harry M. Markowitz, Portfolio selection: Efficient diversification of investments, Cowles Foundation for Research in Economics at Yale University, Monograph 16, John Wiley & Sons Inc., New York, 1959x+344 MR0103768 CrossrefISIGoogle Scholar[11] A. C. Pigou, The Economics of Welfare, London, 1932, especially Chapters IX, X, XI Fenchel, Convex Cones, Sets, and Functions, Princeton University, 1953 0053.12203 A. Wald, Über die Produktionsgleichungen der ökonomischen Wertlehre, Ergebrlisse eines Mathematischen Kolloquiums, 7 (1934–5), 1–6 0014.22306 Google Scholar[12] Knut Wicksell, Lectures on Political Economy, Vol. I, second printing, London, 1935, translated from Swedish original of 1901, 1935 Abraham Wald, On some systems of equations of mathematical economics, Econometrica, 19 (1951), 368–403, Oct. translated from German original of 1936 MR0044097 0043.35004 CrossrefISIGoogle Scholar Next article FiguresRelatedReferencesCited byDetails Utility Matters18 July 2020 | History of Political Economy, Vol. 52, No. 5 Cross Ref Utility Matters: Edmond Malinvaud and Growth Theory in the 1950s and 1960sSSRN Electronic Journal Cross Ref Non-causal understanding with economic models: the case of general equilibrium7 June 2017 | Journal of Economic Methodology, Vol. 24, No. 3 Cross Ref The Limits of Inference with Theory: A Review of Wolpin (2013)Journal of Economic Literature, Vol. 52, No. 3 Cross Ref OPTIMUM SAVINGS AND OPTIMAL GROWTH: THE CASS–MALINVAUD–KOOPMANS NEXUS25 July 2013 | Macroeconomic Dynamics, Vol. 18, No. 1 Cross Ref The Fed, IMF and Disregarded Warnings7 February 2012 Cross Ref Alan Greenspan, the Quants and Stochastic Optimal ControlSSRN Electronic Journal Cross Ref Alan Greenspan, the Quants and Stochastic Optimal ControlSSRN Electronic Journal Cross Ref Monetary Policy, Inflation and the Level of Economic Activity in Brazil after the Real Plan: Stylized Facts from Svar ModelsSSRN Electronic Journal Cross Ref The Lucas Critique in Practice Cross Ref Empirical analysis of macroeconomic time series: VAR and structural modelsEuropean Economic Review, Vol. 35, No. 4 Cross Ref Vector autoregressions for causal inference?Carnegie-Rochester Conference Series on Public Policy, Vol. 22 Cross Ref A Functional Description of ANALYZE: A Computer-Assisted Analysis System for Linear Programming ModelsACM Transactions on Mathematical Software, Vol. 9, No. 1 Cross Ref Chapter 15 Existence of competitive equilibrium Cross Ref IMPLEMENTATION ASPECTS OF MODEL MANAGEMENT: A FOCUS ON COMPUTER-ASSISTED ANALYSIS Cross Ref Implementation Aspects of Model Management: A Focus on Computer-Assisted Analysis Cross Ref Value Cores for Finite AgentsEconomic Record, Vol. 55, No. 1 Cross Ref The uses of mathematics in the social sciencesMathematics and Computers in Simulation, Vol. 20, No. 3 Cross Ref Relative Cores at Planned PricesEconomic Analysis and Policy, Vol. 7, No. 2 Cross Ref Concepts of optimality and their usesMathematical Programming, Vol. 11, No. 1 Cross Ref Spatial Equilibrium in U.S. Agriculture: A Quadratic Programming Analysis18 July 2006 | SIAM Review, Vol. 17, No. 2AbstractPDF (1634 KB)Lancaster's version of the Walras-Wald modelJournal of Economic Theory, Vol. 6, No. 5 Cross Ref References Cross Ref REFERENCES AND BIBLIOGRAPHY Cross Ref Economic Growth at a Maximal Rate Cross Ref A GENERAL DUALITY THEOREM OF CONVEX PROGRAMMING *Metroeconomica, Vol. 17, No. 2-3 Cross Ref Dynamic risk programming with learning adjustmentUnternehmensforschung Operations Research - Recherche Opérationnelle, Vol. 7, No. 4 Cross Ref Recent Developments in Linear Programming Cross Ref Volume 1, Issue 2| 1959SIAM Review History Submitted:19 January 1959Published online:18 July 2006 InformationCopyright © 1959 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1001021Article page range:pp. 79-148ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 87 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.