Atlantic Economic Journal

, Volume 12, Issue 3, pp 30–44 | Cite as

The millions of equations debate: Seventy years after Barone

  • M. H. I. Dore
  • M. C. Kaser


The general study of allocation mechanisms began with Barone's work, which established the theoretical feasibility of an alternative allocation mechanism. There were a number of aspects of the problem that Barone did not explicitly take into account, and it seemed that the central planner would have to solve millions of equations for feasibility and optimality of the allocation. Lange and Taylor were among the first to claim that if the parametric role of prices is kept, the problem of millions of equations would not arise. Socially desirable outcomes could be achieved in a decentralized manner, even without private property. The modern research has established rigorously the conditions under which this can be done.

The 70-year-old debate on the feasibility of socialist planning identified at least three problem areas: the lack of an acceptable, all embracing and complete social criterion function, the problem of incentives, and the magnitude of the informational load. This review attempts to show that these issues continue to dominate modern research in the theory of allocation mechanisms.


International Economic Public Finance Private Property General Study Criterion Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Mahmoud Abdel-Fadil,La Planification des prix en économie socialiste, Paris: Presses universitaires de France, 1975.Google Scholar
  2. Edward Ames,Soviet Economic Processes, Homewood, Illinois: Irwin, 1965.Google Scholar
  3. _____, “The Theory of Planning-Discussion,”American Economic Review, Vol. 61, No. 2, May 1971, pp. 436–7.Google Scholar
  4. _____, “Théorie de la planification économique,”Revue d'économie politique, Vol. 84, 1974, pp. 364–98.Google Scholar
  5. Kenneth J. Arrow and Leonid Hurwicz, “Decentralization and computation in resource allocation” in R. Pfouts (ed.),Essays in Economics and Econometrics in Honour of Harold Hotelling, Chapel Hill, North Carolina: University of North Carolina Press, 1960.Google Scholar
  6. _____, “Reduction of constrained maxima to saddle-point problems” in J. Neyman (ed.),Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles: University of California Press, 1956, Vol. V, pp. 1–20.Google Scholar
  7. Kenneth J. Arrow, Leonid Hurwicz, and Hirofumi Uzawa (eds.),Studies in Linear and Non-linear Programming, Stanford, California: Stanford University Press, 1958.Google Scholar
  8. Kenneth Arrow, Samuel Karlin, and Patrick Suppes, (eds.),Mathematical Methods in the Social Sciences, Stanford, California: Stanford University Press, 1960.Google Scholar
  9. Enrico Barone, “The minstry of production in a collectivist state” in F. A. von Hayek, (ed.),Collectivist Economic Planning, London: Routledge, 1935.Google Scholar
  10. Abram Bergson, “Socialist economics” in H. S. Ellis, (ed.),A Survey of Contemporary Economics, Philadelphia: Blakiston Co., 1948.Google Scholar
  11. Joseph S. Berliner,Factory and Manger in the USSR, Cambridge, Massachusetts: Harvard University Press, 1957.Google Scholar
  12. _____,The Innovation Decision in Soviety Industry, Cambridge, Massachusetts: The MIT Press, 1976.Google Scholar
  13. L. V. Bortkiewiez, “On the correction of Marx's fundamental theoretical construction in the third volume of Capital” in P. M. Sweezy (ed.),Karl Marx and the Close of His System, New York: Augustus M. Kelley, 1949, pp. 197–221.Google Scholar
  14. X. Calsamiglia, “Decentralized resource allocation and increasing returns,”Journal of Economic Theory, Vol. 14, 1977, pp. 263–83.CrossRefGoogle Scholar
  15. George B. Dantzig and P. Wolfe, “The decomposition algorithm for linear programs,”Econometrica, Vol. 29, 1961, pp. 767–78.Google Scholar
  16. H. D. Dickinson, “Price formation in a socialist community,”Economic Journal, June 1933.Google Scholar
  17. _____, “The economic basis of socialism,”Political Quarterly, September–December 1930.Google Scholar
  18. Maurice Dobb, “Economic theory and the problem of a socialist economy,”Economic Journal, December 1933.Google Scholar
  19. Jacques Drèze and D. de la Vallée Poussin, “A tâtonnement process for public goods,”Review of Economic Studies, Vol. 38, 1971, pp. 133–50.Google Scholar
  20. Michael Ellman,Soviet Planning Today, Cambridge: Cambridge University Press, 1971.Google Scholar
  21. _____,Planning Problems in the USSR, Cambridge: Cambridge University Press, 1973.Google Scholar
  22. _____, “Bonus formulae and Soviet managerial performance: A further comment,”Southern Economic Journal, Vol. 39, April 1973, pp. 652–3.Google Scholar
  23. L. S. Fan, “On the reward system,”The American Economic Review, Vol. 65, No. 1, March 1975, pp. 226–9.Google Scholar
  24. David Granick,Management of the Industrial Firm in the USSR, New York, Columbia University Press, 1953.Google Scholar
  25. _____, “Management incentives in the USSR and in Western firms,”Journal of Comparative Administration, Vol. 2, August 1973, pp. 169–99.Google Scholar
  26. _____,Enterprise Guidance in Eastern Europe, Princeton, New Jersey: Princeton University Press, 1975.Google Scholar
  27. Jerry Green and Jean-Jacques Laffont, “Characterization of satisfactory mechanisms for the revelation of preferences for public goods,”Econometrica, Vol. 45, No. 2, March 1977.Google Scholar
  28. P. R. Gregory and R. C. Stuart,Soviet Economic Structure and Performance, New York: Harper and Row, 1974, pp. 301–27.Google Scholar
  29. Theodore Groves, “Information, incentives and the internalization of production externalities” in S. A. Lin (ed.),Theory and Measurement of Economic Externalities, New York: Academic Press, 1976.Google Scholar
  30. _____, “Incentives in teams,”Econometrica, Vol. 41, 1973, pp. 617–63.Google Scholar
  31. _____ and John Ledyard, “Optimal allocation of public goods: A solution to the ‘free rider’ problem,”Econometrica, Vol. 45, No. 4, May 1977, pp. 783–809.Google Scholar
  32. _____, “An incentive mechanism for efficient resource allocation in general equilibrium with public goods,” Discussion Paper No. 119, The Center for Mathematical Studies in Economics and Management Science, Northwestern University, Evanston, Illinois, 1974.Google Scholar
  33. _____ and Martin Loeb, “Incentives and public inputs,”Journal of Public Economics, Vol. 4, 1975, pp. 211–26.CrossRefGoogle Scholar
  34. Geoffrey M. Heal,The Theory of Planning, Amsterdam: North-Holland, 1973.Google Scholar
  35. _____, “Planning, prices and increasing returns,”Review of Economic Studies, Vol. XXVIII(3), No. 115, July 1971.Google Scholar
  36. _____, “Planning without prices,”Review of Economic Studies, Vol. XXXVI(3), No. 107, July 1969.Google Scholar
  37. H. Hori, “The structure of the equilibrium points of Heal's process,”Review of Economic Studies, 1975, pp. 457–67.Google Scholar
  38. Leonid Hurwicz, “The design of mechanisms for resource allocation,”American Economic Review, Vol. 63, 1973, pp. 1–30.Google Scholar
  39. _____, “On informationally decentralized systems,” in C. B. McGuire and R. Radner (eds.),Decision and Organization, Amsterdam: North-Holland, 1972.Google Scholar
  40. _____, “Centralization and decentralization in economic processes” in A. Eckstein (ed.),Comparison of Economic Systems, Berkeley: University of California Press, 1971.Google Scholar
  41. _____, “On the concept and possibility of informational decentralization,”American Economic Review, Vol. 59, No. 2, 1969.Google Scholar
  42. _____, “Optimality and information efficiency in resource allocation processes” in K. J. Arrow, S. Karlin, and P. Suppes (eds.),Mathematical Methods in the Social Sciences, Stanford University Press, 1960.Google Scholar
  43. Leonid Hurwica, “Conditions for economic efficiency of centralized and decentralized structures” in G. Grossman (ed.),Value and Plan, Berkeley: University of California Press, 1960.Google Scholar
  44. _____, Roy Radner, and Stanley Reiter, “A stochastic decentralized resource allocation process, Part I,”Econometrica, Vol. 43, 1975, pp. 187–221; “Part II,” pp. 363–93.Google Scholar
  45. H. Kanemitsu, “On the stability of an adjustment process in non-convex environments—A case of the commodity space (strong) inertia-greed process” presented at the Second World Congress of the Econometric Society, Cambridge, 1970.Google Scholar
  46. Michael Kaser,Soviet Economics, New York: McGraw-Hill, 1970.Google Scholar
  47. Tjalling Koopmans (ed.),Activity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, New York: Wiley, 1951.Google Scholar
  48. _____,Three Essays on the State of Economic Science, New York: McGraw-Hill, 1957.Google Scholar
  49. _____ and John M. Montias, “On the description and comparison of economic systems” in A. Eckstein (ed.),Comparison of Economic Systems: Theoretical and Methodological Approaches, Berkeley: University of California Press, 1971.Google Scholar
  50. János Kornai and Tamas Lipták, “Two-level planning,”Econometrica, Vol. 33, 1965, pp. 141–69.Google Scholar
  51. Tadeusz Kowalik, “Economics and praxeology, Oskar Lange'sPolitical Economy,”Organon, Vol. II, 1975, pp. 303–24.Google Scholar
  52. Oskar Lange, “On the economic theory of socialism,”Review of Economic Studies, Vol. IV, Nos. 1 and 2, 1936–7; also in B. Lippincott (ed.),On the Economic Theory of Socialism, Minnesota: University of Minnesota Press, 1938.Google Scholar
  53. _____,Optymalne decyzje, Zasady programowania, Warsaw: PWN, 1971.Google Scholar
  54. _____,O socjalismie i gospodacre socjalistycznej, Warsaw: PWN, 1966.Google Scholar
  55. W. A. Leeman, “Bonus formulae and Soviet managerial performance,”Southern Economic Journal, Vol. 36, April 1970, pp. 434–45.Google Scholar
  56. Abba P. Lerner,The Economics of Control, New York: Macmillan, 1944.Google Scholar
  57. Martin Loeb and Wesley A. Magat, “Success Indicators in the Soviet Unoin: The Problem of Incentives and Efficient Allocations,”American Economic Review, March 1978, 68, pp. 173–81.Google Scholar
  58. Edmond Malinvaud, “Decentralized procedures for planning” in E. Malinvaud and M.O.L. Bacharach (eds.),Activity Analysis in the Theory of Growth and Planning, London: Macmillan, 1967.Google Scholar
  59. Stephen A. Marglin, “Information in price and command systems” in J. Margolis and H. Guitton (eds.),Public Economics, London: Macmillan, 1969.Google Scholar
  60. Thomas Marshak, “Centralization and decentralization in economic organizations,”Econometrica, Vol. 27, 1959, pp. 399–430.Google Scholar
  61. Jacob Marschak, “Wirtschaftsrechnung and Gemeinwirtschaft,”Archiv fuer Sozialwissenschaft und Sozialpolitik, Tuebingen, 1924, 51, pp. 501–20.Google Scholar
  62. _____ and Roy Radner,Economic Theory of Teams, New Haven: Yale University Press, 1972.Google Scholar
  63. James A. Mirrlees, “The optimal structure of incentives and authority within an organization,”The Bell Journal of Economics, Vol. 7, No. 1, Spring 1976, pp. 105–31.Google Scholar
  64. John-Michael Montias,The Structure of Economic Systems, New Have and London: Yale University Press, 1976.Google Scholar
  65. _____, “On the consistency and efficiency of central plans,”Review of Economic Studies, Vol. 29, 1961–62, pp. 280–90.Google Scholar
  66. _____, “Planning with material balances in Soviet-type economics,”The American Economic Review, Vol. 49, 1959, pp. 963–85.Google Scholar
  67. Kenneth Mount and Stanely Reiter, “Economic environments for which there are Pareto satisfactory mechanisms,”Econometrica, Vol. 45, No. 4, May 1977, pp. 821–42.Google Scholar
  68. _____ and Stanley Reiter, “The informational size of message spaces,”Journal of Economic Theory, Vol. 8, 1974, pp. 161–92.CrossRefGoogle Scholar
  69. Alec Nove, “The problem of ‘success-indicators’ in Soviet Industry,”Economica, Vol. 25, February 1958, pp. 1–13.Google Scholar
  70. _____ and Domenico Nuti (eds.),Socialist Economics, Harmondsworth: Penguin, 1972.Google Scholar
  71. A. A. Pervozvansky, “A dynamic model of management system and its approximate optimization,”Avtomatika i Telemekhanika, No. 8, 1971.Google Scholar
  72. Arthur C. Pigou,Socialism versus Capitalism, London: Macmillan & Co., 1937.Google Scholar
  73. Richard Portes, “Decentralized Planning Procedures and Centrally Planned Economies,”American Economic Review, Vol. 71, No. 2, May 1971, pp. 422–9.Google Scholar
  74. V. F. Pugachev, G. V. Martynov, V. G. Myednitsky, and A. K. Pitelin, “Multi-level optimization with a local criterion of a general form,”Ekonomika i matematicheskie methody, No. 5, 1972.Google Scholar
  75. Stanley Reiter, “Information and performance in the (New)2 Welfare Economics,”The American Economic Review, Papers and Proceedings, Vol. 67, No. 1, February 1977, pp. 226–34.Google Scholar
  76. Lionel Robbins,The Great Depression, London: Macmillan, 1934.Google Scholar
  77. W. C. Roper,The Problem of Pricing in a Socialist State, Cambridge, Massachusetts, 1929.Google Scholar
  78. Amrtya K. Sen, “Concept of efficiency” in M. Parkin and A. R. Nobay (eds.),Essays in Modern Economics: AUTE Proceedings, New York: Barnes and Noble, 1973.Google Scholar
  79. _____,Collective Choice and Social Welfare, London: Oliver and Boyd, 1970.Google Scholar
  80. V. Snowberger, “The new Soviet incentive model: Comment,”The Bell Journal of Economics, Vol. 8, No. 2, Autumn 1977.Google Scholar
  81. Nicholas Spulber, “On some issues in the theory of the ‘socialist economy,’”Kyklos, Vol. 25, No. 4, 1972, pp. 715–35.Google Scholar
  82. Frederick M. Taylor, “The guidance of production in the socialist state,”American Economic Review, Vol. 19, No. 1, 1929. Also in B. Lippincott,On the Economics Theory of Socialism, Minnesota: University of Minnesota Press, 1938.Google Scholar
  83. R. K. Turner and C. Collis,The Economics of Planning, London: Macmillan, 1977.Google Scholar
  84. Fredrich A. von Hayek,The Road to Serfdom, London: Routledge, 1944.Google Scholar
  85. _____, (ed.),Collectivist Economic Planning, London: Routledge, 1935.Google Scholar
  86. Ludwig von Mises, “Economic calculation in the socialist commonwealth,” in F. A. von Hayek (ed.),Collectivist Economic Planning, London: Routledge, 1935.Google Scholar
  87. Martin L. Weitzman, “The new Soviet incentive model,”The Bell Journal of Economics, Vol. 7, Spring 1976, pp. 251–7.Google Scholar
  88. _____, “Iterative multi-level planning with production targets,”Econometrica, 38, No. 1, 1970.Google Scholar
  89. Alfred Zauberman,Aspects fo Planometrics, London: Athlone Press, 1967.Google Scholar
  90. _____,The Mathematical Revolution in Soviet Economics, London: Oxford University Press, 1975.Google Scholar
  91. _____,Mathematical Theory in Soviet Planning, London: Oxford University Press, 1976.Google Scholar

Copyright information

© Atlantic Economic Society 1984

Authors and Affiliations

  • M. H. I. Dore
    • 1
  • M. C. Kaser
    • 2
  1. 1.Brock UniversityUK
  2. 2.University of OxfordUK

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