Skip to main content

Theories of General Economic Equilibrium and Maximum Efficiency

  • Chapter
Equilibrium and Disequilibrium in Economic Theory

Part of the book series: Theory and Decision Library ((TDLU,volume 13))

Abstract

1. Marie Esprit Léon Walras (1834-1910) is celebrated today among economists throughout the world as the first to have formulated the equations of general economic equilibrium4. His work was without doubt a turning point in the history of economic thought and the transformation of economics into a true science. For the first time, an over-all synthesis of economic equilibrium was presented in the framework of a general model, in which all prices and quantities were determined simultaneously by a system of equations. By putting Walras’ work back into its historical context, we can assert that, whatever its weaknesses or defects, by its influence, it marked the beginning of modern economic science.

Glory is the inventor’s alone. Those who come after are only his disciples. NEWTON 1

The name of Léon Walras will remain alive in science, and his fame will grow… It was Walras who first discovered one of these systems of equations, that relating to the case of free competition. This was a discovery of capital importance, and this scientist’s merit cannot be too highly lauded. Of course our science has developed, and will develop still further, but this will not diminish the importance of Walras’ discovery in any way, any more than the progress of celestial mechanics could diminish the importance of Newton’s Principia -just the reverse… His work puts him at the top and secures his imperishable fame. VILFREDO PARETO 2

… it is essential to make the foundations of pure political economy very solid before erecting on them the mathematical constructions they will have to support. LÉON WALRAS 3

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Allais, M., A la Recherche dune Discipline Economique, Première Partie, L’Economie Pure (In Quest of an Economic Discipline, Part I, Pure Economics), 1st ed., Ateliers Industria, Paris, 1943, 2 vol., 842 p. and Annexes 68 p. Second edition entitled: Traité d’Economie Pure (Treatise on Pure Economies), Imprimerie Nationale, Paris, 1952, 5 vols., 1000 p. (The second edition is identical to the first, except for a new introduction).

    Google Scholar 

  2. Allais, M., Economie Pure et Rendement Social (Pure Economies and Social Output), Sirey, Paris, 1945, 72 p.

    Google Scholar 

  3. Allais, M., Economie et Intérêt (Economy and Interest), Imprimerie Nationale and Librairie des Publications Officielles, Paris, 1947, 2 vols., 800 p.

    Google Scholar 

  4. Allais, M., La Gestion des Houillères Nationalisées et la Théorie Economique (The Management of the Nationalized Coal Industry and Economic Theory), Imprimerie Nationale, Paris, 1953, 126 p.

    Google Scholar 

  5. Allais, M., L’Extension des Théories de l’Equilibre Economique Général et du Rendement Social au cas du Risque’ (Extension of the Theories of General Economic Equilibrium and Social Output to the Case of Risk), Econometrica (April 1953), pp. 269–290.

    Google Scholar 

  6. Allais, M., ‘Le Comportement de l’Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l’Ecole Américaine’ (The Behaviour of Rational Man under Conditions of Risk: Criticism of the Postulates and Axioms of American School), Econometrica (Octobre 1953), pp. 503–546.

    Google Scholar 

  7. Allais, M., ‘Puissance et Dangers de l’Utilisation de l’Outil Mathématique en Economique’, Econometrica (January 1954), pp. 58–71, and Nouvelle Revue d’Economie Contemporaine (January 1955), pp. 1-7.

    Google Scholar 

  8. Allais, M., ‘Observations sur la Théorie des Jeux’ (Observations on the Theory of Games), Travaux du Congrès des Economistes de Langue Française, 1954, Editions Domat-Montchrestien, Paris, 1955, pp. 143–163.

    Google Scholar 

  9. Allais, M., Fondements d’une Théorie Positive des Choix comportant un Risque et Critique des Postulats et Axiomes de l’Ecole Américaine’ (The Foundations of a Positive Theory of Choice involving Risk and a Criticism of the American School), Imprimerie Nationale, Paris, 1955, and Annales des Mines, special issue, Paris, 1955, 56 p.

    Google Scholar 

  10. Allais, M., ‘L’Influence des Besoins sur la Production des Biens de Consommation’, L’Evolution et le Rôle des Besoins de Biens de Consommation dans les Divers Régimes Economiques, Centre National de la Recherche Scientifique, Paris, 1963, pp. 133–194.

    Google Scholar 

  11. Allais, M., ‘Some Analytical and Practical Aspects of the Theory of Capital’, Paper given at July 1963 Cambridge Conference of the International Economic Association; Activity Analysis in the Theory of Growth and Planning, E. Malin-vaud and M. Bacharach (eds.), New York, 1967, pp. 64–107 and 294-297.

    Google Scholar 

  12. Allais, M., ‘La Théorie Economique et la Tarification Optimum de l’Usage des Infrastructures de Transport, La Jaune et la Rouge (publication of the Société Amicale des Anciens Elèves de l’Ecole Polytechnique), special issue Les Transports, Paris, 1964, pp. 108–114.

    Google Scholar 

  13. Allais, M., ‘Walras, Pionnier de l’Economie Mathématique et Réformateur Méconnu (1834–1910)’, Centenaire de l’Association Amicale des Anciens Elèves de l’Ecole Nationale Supérieure des Mines de Paris (1864–1964), Paris, 1964, pp. 26–29.

    Google Scholar 

  14. Allais, M., Reformulation de la Théorie Quantitative de la Monnaie (A Restatement of the Quantity Theory of Money), Editions Sedeis, Paris, 1965, 186 p.

    Google Scholar 

  15. Allais, M., ‘A Restatement of the Quantity Theory of Money’, American Economic Review (December 1966), pp. 1123–1157.

    Google Scholar 

  16. Allais, M., ‘L’Economique en tant que Science’, Revue d’Economie Politique (January-February 1968), pp. 5–30. English translation: ‘Economics as a Science’, Cahiers Vilfredo Pareto (1968), pp. 5-24.

    Google Scholar 

  17. Allais, M., ‘Les Conditions de l’Efficacité dans l’Economie’ (The Conditions of Efficiency in the Economy), (Paper presented at the Fourth International Seminar organized by Centro Studi e Ricerche su Problemi Economico-Sociali, Milan, and Ecole Nationale Supérieure des Mines de Paris in 1967); summary in English ‘The Conditions for Efficiency in the Economy’, published in Italian as ‘Le Condizioni Dell’ Efficienza Nell’ Economia’ in Programmazione E Progresso Economico, Centro Studi e Ricerche su Problemi Economico-Sociali, Franco Angeli Ed., Milan, 1969, pp. 13–303.

    Google Scholar 

  18. Allais, M., Les Fondements du Calcul Economique (The Foundations of the Economic Calculus), Ecole Nationale Supérieure des Mines de Paris, Paris Vol. I, 1967, Vols. II and III, 1968, 145, 284 and 59 p.

    Google Scholar 

  19. Allais, M., ‘Faiblesses et Inconsistances des Théories Actuelles de l’Equilibre et de l’Efficacité Maximale. La Reformulation des Théories des Echanges, de l’Equilibre Economique et de l’Efficacité Maximale’, Lectures delivered at the Economic Analysis Seminar, Centre National de 1a Recherche Scientifique and Ecole Nationale Supérieure des Mines, November 28 and December 12, 1967.

    Google Scholar 

  20. Allais, M., ‘The Conditions of Efficiency in the Economy’, Economia Internazionale (August 1968), pp. 399–420.

    Google Scholar 

  21. Allais, M., ‘Pareto, Vilfredo: Contributions to Economies’, International Encyclopedia of the Social Sciences, New York, 1968, Vol. 11, pp. 399–411.

    Google Scholar 

  22. Allais, M., ‘Oubli et Intérêt’ (Forgetfulness and Interest), Centre d’Analyse Economique, Paris, 1970, 137 p.

    Google Scholar 

  23. Allais, M., Forgetfulness and Interest, Journal of Money, Credit and Banking (February 1972), pp. 40–71.

    Google Scholar 

  24. Allais, M., ‘The Psychological Rate of Interest’, Journal of Money, Credit and Banking (Août 1974), pp. 285–331.

    Google Scholar 

  25. Allais, M., ‘La Portée et les Prolongements de l’Oeuvre de Walras dans les Théories de l’Equilibre Economique Général et de l’Efficacité Maximale, 1871–1971’ (forthcoming).

    Google Scholar 

  26. Allais, M., ‘La Theorie Générale des Surplus et l’Apport Fondamental de Vilfredo Pareto’ (The General Theory of Surplus and Pareto’s Fundamental Contribution), Revue d’Economie Politique (Nov.-Dec. 1973), No. 6, 83ème année, pp. 1044–1097.

    Google Scholar 

  27. Allais, M., ‘La Théorie Générale des Surplus, les Apports Fondamentaux de Dupuit et de Pareto, et Analyse Critique de la Littérature’ (The General Theory of the Concept of Surplus, the Fundamental Contributions of Dupuit and Pareto, and a Critical Review of the Literature), Convegno Internazionale su Vilfredo Pareto, Ottobre 1973, Accademia Nazionale dei Lincei, Roma; Centre d’Analyse Economique, 357 p. To be published shortly by the Accademia Nazionale dei Lincei.

    Google Scholar 

  28. Allais, M., ‘The General Theory of Surplus and Pareto’s Fundamental Contribution’, English translation of [26]; Convegno Internazionale Vilfredo Pareto (Roma, 25–27 Ottobre 1973), Roma, Accademia Nazionale dei Lincei, 1975, pp. 109–163.

    Google Scholar 

  29. Allais, M., ‘Les implications de rendements croissants et décroissants sur les conditions de l’équilibre économique général et d’une efficacité maximale’ (Implications of increasing and decreasing yields on the conditions of general economic equilibrium and economic efficiency), Centre d’Analyse Economique, C.N.R.S., 1974. To be published in ‘Mélanges en l’honneur du professeur Francois Perroux’.

    Google Scholar 

  30. Allais, del Viscovo, Duquesne de la Vinelle, Oort, and Seidenfus, Options de la Politique Tarifaire dans les Transports, Etudes, Séries Transports, N. 1, Communauté Economique Européenne, Brussels, 1965, 206 p. English translation: Options in Transport Tariff Policy, European Economie Community, Brussels, 1965.

    Google Scholar 

  31. Arrow, Kenneth J., ‘An Extension of the Basic Theorems of Classical Welfare Economics’, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, 1951, pp. 507–532.

    Google Scholar 

  32. Arrow, Kenneth J., ‘Economic Equilibrium’, International Encyclopedia of the Social Sciences, New York, 1968, Vol. 4, pp. 376–389.

    Google Scholar 

  33. Barone (Enrico), ‘Il Ministro della Produzione nello Stato CoUettivista’, Giornale degli Economisti (July 1908), pp. 267–293 and 391-414, published in French as ‘Le Ministre de la Production dans un Etat Collectiviste’ in L’Economie Dirigée en Régime Collectiviste, F. A. Hayek, Ed., Paris, 1939, pp. 245-299; published in English as ‘The Ministry of Production in the Collectivist State’ in Collectivist Economic Planning F.A. Hayek (ed.), London, 1935, pp. 245-290.

    Google Scholar 

  34. Bergson (A.), ‘A Reformulation of Certain Aspects of Welfare Economies’, Quarterly Journal of Economics (February 1938), pp. 310–334.

    Google Scholar 

  35. Bergson (A.), ‘Socialist Economies’, A Survey of Contemporary Economics, H.S. Ellis (ed.), Philadelphia, 1948, pp. 412–448.

    Google Scholar 

  36. Bernard (Claude), Introduction a l’Etude de la Médecine Expérimentale (1865), Garnier-Flammarion, Paris, 1966, 318 p.

    Google Scholar 

  37. Blaug (Mark), Economie Theory in Retrospect, Second edition, 1970, Heinemann Educational Book, London, 710 p.

    Google Scholar 

  38. Bousquet (G.H.), ‘Critique de l’Economie Pure’, Revue d’Economie Politique (1926), pp. 1166–1199.

    Google Scholar 

  39. Bousquet (G. H.), Essai sur l’Evolution de la Pensée Economique, Giard, Paris, 1927, 314 p.

    Google Scholar 

  40. Bousquet (G.H.), ‘Le Système Mathématique de l’Equilibre Economique selon Léon Walras et ses Origines’, Revue d’Economie Politique (November-December 1963), pp. 948–976.

    Google Scholar 

  41. Boven, Les Applications Mathématiques à l’Economie Politique, Thesis presented to the Faculty of the University of Lausanne, Imprimerie Pache, Varidel et Ebron, 1912.

    Google Scholar 

  42. Chernoff (Hermann), ‘Decision Theory’, International Encyclopedia of the Social Sciences, New York, 1968, Vol. 4, pp. 62–66.

    Google Scholar 

  43. Cournot (A.), Recherches sur les Principes Mathématiques de la Théorie des Richesses, Rivière, Paris, 1938, 258 p.; published in English as Researches into the Mathematical Principles of the Theory of Wealth, New York 1929.

    Google Scholar 

  44. Debreu (Gérard), ‘Les Fins du Système Economique’, Revue d’Economie Politique (September-December 1949), pp. 600–615.

    Google Scholar 

  45. Debreu (Gérard), ‘The Coefficient of Resource Utilization’, Econometrica (July 1951), pp. 273–292.

    Google Scholar 

  46. Debreu (Gérard), ‘Valuation Equilibrium and Pareto Optimum’, Proceedings of the National Academy of Sciences (July 1954), pp. 588–592.

    Google Scholar 

  47. Debreu (Gérard), ‘A Classical Tax-Subsidy Problem’, Econometrica (January 1954), pp. 14–22.

    Google Scholar 

  48. Debreu (Gérard), Theory of Value, Wiley, New York, 1959, 114 p.

    Google Scholar 

  49. Debreu (Gérard), ‘On a Theorem of Scarf’, Review of Economic Studies (October 1963), pp. 177–180.

    Google Scholar 

  50. Debreu (Gérard), and Scarf, H., ‘A Limit Theorem on the Core of an Economy’, International Economic Review (September 1963), pp. 235–246.

    Google Scholar 

  51. Divisia (F.), Exposés d’Economique. L’Apport des Ingénieurs Français aux Sciences Economiques. Dunod, Paris, 1950, Vol. I, 157 p.

    Google Scholar 

  52. Dorfman, R., Samuelson, P.A., and Solow, R.M., Linear Programming and Economic Analysis. Mac Graw Hill, New York, 1958.

    Google Scholar 

  53. Edgeworth (Francis Y.), Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, London, 1881, and Kelley, New York, 1953, 152 p.

    Google Scholar 

  54. Edgeworth (Francis Y.), ‘The Mathematical Theory of Political Economy’, Nature (September 5, 1889), p. 435.

    Google Scholar 

  55. Edgeworth (Francis Y.), ‘On the Determinateness of Economic Equilibrium (1891)’, Papers Relating to Political Economy, Vol. II, New York, 1963, pp. 313–319.

    Google Scholar 

  56. Eggleston (H.C.), Convexity, Cambridge University Press, Cambridge, 1963, 136 p.

    Google Scholar 

  57. Farrell (M.J.), ‘The Convexity Assumption in the Theory of Competitive Markets’, Journal of Political Economy (August 1959), pp. 377–391.

    Google Scholar 

  58. Graaf (J. de V.), Theoretical Welfare Economics, Cambridge University Press, Cambridge, 1957, 178 p.

    Google Scholar 

  59. Hahn (Frank H.), ‘A Stable Adjustment Process for A Competitive Economy’, Review of Economic Studies (October 1961), pp. 62–65.

    Google Scholar 

  60. Hahn (Frank H.), and Negishi (T.), ‘A Theorem on Non-Tâtonnement Stability’, Econometrica (July 1962), pp. 463–469.

    Google Scholar 

  61. Henderson (J. M.), and Quandt (R. E.), Microeconomic Theory: A Mathematical Approach, New York 1958.

    Google Scholar 

  62. Hicks (J.R.), ‘Léon Walras’, Econometrica (October 1934), pp. 338–348.

    Google Scholar 

  63. Hicks (J.R.), ‘The Foundations of Welfare Economics’, The Economic Journal (December 1939), pp. 696–712.

    Google Scholar 

  64. Hicks (J.R.), Value and Capital. An Inquiry into Some Fundamental Principles of Economic Theory, Oxford University Press, London, 1939, 320 p.

    Google Scholar 

  65. Hotelling (Harold), ‘The General Welf in Relation to Problems of Taxation and of Railway and Utility Rates’, Econometrica (July 1938), pp. 242–269.

    Google Scholar 

  66. Hotelling (Harold), and Frisch (R.), ‘Papers on the Dupuit Taxation Theorem’, Econometrica (April 1939), pp. 145–160.

    Google Scholar 

  67. Jaffé (William), ‘Walras’ Theory of Tâtonnement: A Critique of Recent Interpretations’, Journal of Political Economy (February 1967), pp. 1–19.

    Google Scholar 

  68. Jaffé (William), ‘Walras, Léon’, International Encyclopedia qf the Social Sciences, New York, 1968, Vol. 16, pp. 447–453.

    Google Scholar 

  69. Jaffé (William), ‘Pareto translated, A Review Article’, The Journal of Economic Literature (Dec. 1972), pp. 1190–1201.

    Google Scholar 

  70. Kakutani (S.), ‘A Generalization of Brouwer’s Fixed Point Theorem’, Duke Mathematical Journal, No. 8 (1941), pp. 457–459.

    Article  Google Scholar 

  71. Koopmans (T.J.), ‘Analysis of Production as an Efficient Combination of Activities’, Activity Analysis of Production and Allocation, T.C. Koopmans (ed.), New York, 1951, pp. 33–97.

    Google Scholar 

  72. Kuenne (Robert E.), The Theory of General Economic Equilibrium, Princeton University Press, Princeton, 1963, 590 p.

    Google Scholar 

  73. Lange (Oscar), ‘The Foundations of Welfare Economies’, Econometrica (July-October 1942), pp. 215–228.

    Google Scholar 

  74. Leduc (Gaston), ‘Léon Walras et sa Correspondance’, Revue d’Economie Politique (January-February 1967), pp. 96–108.

    Google Scholar 

  75. Lerner (Abba P.), The Economics of Control, Mac Millan, New York, 1944, 428 p.

    Google Scholar 

  76. Little (I.M.D.), A Critique of Welfare Economics, Oxford, 1950, 276 p.

    Google Scholar 

  77. Marget (A.), ‘Léon Walras and the “Cash Balance Approach” to the Problem of the Value of Money’, Journal of Political Economy (October 1931), pp. 569–600.

    Google Scholar 

  78. Marget (A.), The Monetary Aspects of the Walrasian System, Journal of Political Economy (April 1935), pp. 145–186.

    Google Scholar 

  79. Marshall (Alfred), Principles of Economics (1890), Eighth edition 1920, Mac Millan, London, 1947, 871 p.

    Google Scholar 

  80. Mishan (E.J.), ‘A Survey of Welfare Economics, 1939–59’, The Economic Journal (June 1960), pp. 197–265.

    Google Scholar 

  81. Mishan (E.J.), Welfare Economics, Second edition, Random House, New York, 1964, 333 p.

    Google Scholar 

  82. Mishan (E.J.), Welfare Economics, International Encyclopedia of the Social Sciences, New York, 1968, Vol. 16, pp. 504–512.

    Google Scholar 

  83. Moret (Jacques), L’Emploi des Mathématiques en Economie Politique, Giard et Brière, Paris, 1915, 272p.

    Google Scholar 

  84. Morgenstern (Oskar), and Shubik (Martin), ‘Game Theory: Theoretical Aspects and Economic Applications’, International Encyclopedia of the Social Sciences, New York, 1968, Vol. 6, pp. 62–69.

    Google Scholar 

  85. Murray (R.A.), Leçons d’Economie Politique, translated and adapted from the Italian by P. Boven, Payot, Paris, 1920, 501 p.

    Google Scholar 

  86. Nash (J.F.), ‘Equilibrium Points in N-Persons Games’, Proceedings of the National Academy of Sciences, of the U.S.A. 36 (1950).

    Google Scholar 

  87. Negishi (Takashi), ‘Welfare Economics and Existence of an Equilibrium for a Competitive Theory’, Metroeconomica (August-December 1960), pp. 92–97.

    Google Scholar 

  88. Negishi (Takashi), ‘On the Formation of Prices’, International Economic Review (January 1961), pp. 122–126.

    Google Scholar 

  89. Neghishi (Takashi), ‘The Stability of a Competitive Economy: A Survey Article’, Econometrica (October 1962), pp. 635–669.

    Google Scholar 

  90. Neumann (von J.), ‘Zur Theorie der Gesellschaftsspiele’, Mathematische Annalen 100 (1928), pp. 295–320.

    Article  Google Scholar 

  91. Neumann (von J.), ‘Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes’, Ergebnisse eines mathematischen Kolloquiums, No. 8 (1937), pp. 73–83; published in English as A Model of General Economic Equilibrium’, Review of Economic Studies, No. 33 (1945-46), pp. 1-9.

    Google Scholar 

  92. Neumann (von J.), and Morgenstern (O.), Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1947, 641 p.

    Google Scholar 

  93. Newman (Peter), The Theory of Exchange, Prentice Hall, Englewood Cliffs, N.J., 1965,201p.

    Google Scholar 

  94. Nikaido (Hukukane), ‘On the Classical Multilateral Exchange Problem’, Merro-economica (August 1956), pp. 135–145.

    Google Scholar 

  95. Osorio (Antonio), Théorie Mathématique de l’Echange, Giard et Brière, Paris, 1913, 395 p.

    Google Scholar 

  96. Pareto (Vilfredo), Cours d’Economie Politique (1896–1897), Rougé, Lausanne, 2 vols., 430 and 426 pp.; Droz, Geneva, 1964, 1 vol. 430-426 pp.

    Google Scholar 

  97. Pareto (Vilfredo), ‘L’Economie Pure (1901)’ Metroeconomica (April 1955), pp. 1–15.

    Google Scholar 

  98. Pareto (Vilfredo), ‘Anwendungen der Mathematik auf Nationalökonomie’, Encyklopädie der Mathematischen Wissenschaften, Leipzig, 1901, Vol. I, Sect. 2, pp. 1094–1120.

    Google Scholar 

  99. Pareto (Vilfredo), Manuale d’Economia Politica, Milan, 1906; published in French as Manuel d’Economie Politique, Giard et Brière, Paris, 1909, 695 p., and Droz, Geneva, 1966, 695 p.; published in English as Manual of Political Economy, Kelley, New York, 1971, 504p.

    Google Scholar 

  100. Pareto (Vilfredo), ‘Walras’, The Economic Journal (March 1910), pp. 137–140.

    Google Scholar 

  101. Pareto (Vilfredo), ‘Economie Mathématique’, Encyclopédie des Sciences Mathématiques, Gauthier-Villars, Paris 1911, pp. 591–541; also in Statistique et Economie Mathématique, Droz, Geneva, 1966, pp. 319-376; published in English as ‘Mathematical Economica’, International Economic Papers, No. 5, New York, 1955, pp. 58-102.

    Google Scholar 

  102. Pareto (Vilfredo), Trattato di Sociologia Generale, Barbera, Firenze, 1916; published in French as Traité de Sociologie Générale, Payot, Paris, 1919, 2 vol. 1763 p.; published in English as The Mind and Society, Dover, New York, 1935, 2 vols. 2033p.

    Google Scholar 

  103. Patinkin (Don), Money, Interest, and Prices, Row Peterson, Evanston, III., 1956, 510p.

    Google Scholar 

  104. Pirou (Gaetan), Les Théories de l’Equilibre Economique, Léon Wairas et Vilfredo Pareto, Domat-Montchrestien, Paris, 1946, 463 p.

    Google Scholar 

  105. Quandt (R.E.), ‘Programming’, International Encyclopedia of the Social Sciences, New York, 1968, Vol. 12, pp. 552–561.

    Google Scholar 

  106. Rothenberg (Jérome), ‘Non-Convexity, Aggregation, and Pareto Optimality’, Journal of Political Economy (October 1960), pp. 435–468.

    Google Scholar 

  107. Samuelson (P.A.), Foundations of Economic Analysis, 2nd ed., Harvard University Press, Cambridge, Mass., 1948 (1st ed., 1947), 447p.

    Google Scholar 

  108. Samuelson (P.A.), ‘Evaluation of Real National Income’, Oxford Economic Papers (New series), (January 1950), pp. 1–29.

    Google Scholar 

  109. Samuelson (P.A.), ‘Diagrammatic Exposition of a Theory of Public Expenditure’, Review of Economics and Statistics (November 1955), pp. 350–356.

    Google Scholar 

  110. Samuelson (P.A.), ‘Social Indifference Curves’, Quarterly Journal of Economics (February 1956), pp. 1–22.

    Google Scholar 

  111. Samuelson (P.A.), Economics. An Introductory Analysis, 4th ed., Mac Graw Hill, New York, 1958.

    Google Scholar 

  112. Samuelson (P. A.), ‘The Gains from International Trade Once Again’, Economic Journal (December 1962), pp. 820–829.

    Google Scholar 

  113. Scarf (Herbert), ‘Some Examples of Global Instability of the Competitive Equilibrium’, International Economic Review (September 1960), pp. 157–172.

    Google Scholar 

  114. Scarf (Herbert), ‘An Analysis of Markets with a Large Number of Participants’, Recent Advances in Game Theory, Princeton University Conference, Philadelphia, 1962, pp. 127–155.

    Google Scholar 

  115. Schumpeter (J.), ‘Marie, Esprit, Léon Walras’ (1910), Zeitschrift für Volkswirtschaft, Sozialpolitik und Verwaltung 19, 397–402. English translation: ‘Ten Great Economists from Marx to Keynes’, Oxford University Press, New York, 1951, pp. 74-79.

    Google Scholar 

  116. Schumpeter (J.), History of Economic Analysis, Oxford University Press, New York, 1954, 1260 p.

    Google Scholar 

  117. Shapley (L.S.), and Shubik (M.), The Core of an Economy with Non-Convex Preferences, Rand Corporation, RM 3518-PR, Santa Monica, February 1963.

    Google Scholar 

  118. Shapley (L.S.), and Shubik (M.), ‘Quasi-Cores in a Monetary Economy with Non-convex Preferences’, Econometrica (October 1966), pp. 805–827.

    Google Scholar 

  119. Shubik (Martin), ‘Game Theory: Economic Applications’, International Encyclopedia of the Social Sciences, New York 1968, Vol. 6, pp. 69–74.

    Google Scholar 

  120. Shubik (Martin), ‘A Curmudgeon’s Guide to Microeconomics’, Journal of Economic Literature (June 1970), pp. 405–434.

    Google Scholar 

  121. Starr (Ross M.), ‘Quasi-Equilibria in Markets with Non-Convex Preferences’, Econometrica (January 1969), pp. 25–38.

    Google Scholar 

  122. Stigler (George J.), ‘The Development of Utility Theory’, Journal of Political Economy (August 1950), pp. 307–327, and (October 1950), pp. 373-396.

    Google Scholar 

  123. Tintner (Gerhard), ‘A Note on Welfare Economics’, Econometrica (January 1946), pp. 69–78.

    Google Scholar 

  124. Uzawa (Hirofumi), On the Stability of a Competitive Barter Process, Technical Report No. 94, Stanford 1960.

    Google Scholar 

  125. Uzawa (Hirofumi), Edgeworth’s Barter Process and Walras’ Tâtonnement Process, Technical Report No. 83, Stanford, 1960.

    Google Scholar 

  126. Uzawa (Hirofumi), ‘Walras’ Tâtonnement in the Theory of Exchange’, Review of Economic Studies (June 1960), pp. 182–194.

    Google Scholar 

  127. Voltaire, Essai sur les Moeurs et l’Esprit des Nations et sur les Principaux Faits de l’Histoire depuis Charlemagne jusqu’ à Louis XIII (1756), Garnier, Paris, 2 vols., 1963, 905 and 1013 p.

    Google Scholar 

  128. Wald (A.), ‘Über die eindeutige positive Lösbarkeit der neuen Produktionsgleichungen’, Ergebnisse eines mathematischen Kolloquiums, No. 6 (1935), pp. 12–20.

    Google Scholar 

  129. Wald (A.), Über die Produktionsgleichungen der ökonomischen Wertlehre’, Ergebnisse eines mathematischen Kolloquiums, No. 7 (1936), pp. 1–6.

    Google Scholar 

  130. Wald (A.), ‘Über einige Gleichungssysteme der Mathematischen Ökonomie’, Zeitschrift für Nationalökonomie, No. 7 (1936), pp. 637-670; published in English: ‘On Some Systems of Equations of Mathematical Economics’, Econometrica (October 1951), pp. 368–403.

    Article  Google Scholar 

  131. Walras (Léon), Eléments d’Economie Politique Pure. Théorie de la Richesse Sociale (1874–1877, 1889, 1896, 1900, 1926), Guillaumin, Paris, 408 p.; sixth ed. 1926, Pichon et Durand-Auzias, Paris, 1952, 491p. and V Pl.

    Google Scholar 

  132. Walras (Léon), Elements of Pure Economies, English translation of 6th ed. of [130], Allen and Unwin, London, 1954, 620p.

    Google Scholar 

  133. Walras (Léon), Abrégé des Eléments d’Economie Politique Pure (1895), Pichon et Durand-Auzias, Paris, 1938, 398 p.

    Google Scholar 

  134. Walras (Léon), Correspondence of Léon Walras and Related Papers William Jaffé, ed., Amsterdam, 1965, 3 vol., 1883, 1897 and 538 pp.

    Google Scholar 

  135. Zawadski (Wladyslaw), Les Mathématiques Appliquées àl’Economie Politique, Librairie des Sciences Politiques et Sociales, Paris, 1914.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1977 D. Reidel Publishing Company, Dordrecht, Holland

About this chapter

Cite this chapter

Allais, M. (1977). Theories of General Economic Equilibrium and Maximum Efficiency. In: Schwödiauer, G. (eds) Equilibrium and Disequilibrium in Economic Theory. Theory and Decision Library, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1155-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-1155-6_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1157-0

  • Online ISBN: 978-94-010-1155-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics