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A Sweeping New Non-substitution Theorem: Kaldor’s Discovery of the von Neumann Input-Output Model

  • P. A. Samuelson

Abstract

Nicholas Kaldor is rightly famous for his many theoretical and empirical researches in the fields of microeconomics and macroeconomics. Among many other accomplishments, he independently discovered the von Neumann time-phased system, in which there are no primary (non-producible) factors of production and in which goods as outputs are produced out of themselves as inputs. This remarkable 1937 contribution is little known,1 much less known for example than Kaldor’s 1940 intuitive derivation of a unique limit cycle of determinate amplitude and period, that is asymptotically approached from any perturbed initial business-cycle position.

Keywords

Interest Rate Joint Product Price Ratio Unit Production Cost Equilibrium Interest Rate 
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References

  1. Dorfman, R., P. A. Samuelson and R. M. Solow (1958), Linear Programming and Economic Analysis (New York: McGraw-Hill; reprinted (1986) New York: Dover).Google Scholar
  2. von Hayek, F. A. (1931) Prices and Production (London: Routledge).Google Scholar
  3. Kaldor, N. (1937) ‘Annual survey of economic theory: the recent controversy on the theory of capital’, Econometrica, 5, July, 201–33. Reproduced in N. Kaldor (1960) Essays on Value and Distribution (The Free Press: Glencoe, Illinois).Google Scholar
  4. —— (1938) ‘On the theory of capital: a rejoinder to Professor Knight’, Econometrica, 6, April, 163–76.CrossRefGoogle Scholar
  5. Reproduced in N. Kaldor (1960) Essays on Value and Distribution (The Free Press: Glencoe, Illinois).Google Scholar
  6. —— (1940) ‘A model of the trade cycle’, Economic Journal, 50, March, 78–92.CrossRefGoogle Scholar
  7. Knight, F. (1921) Risk, Uncertainty and Profit (Boston: Houghton-Mifflin).Google Scholar
  8. Lange, O. (1937) ‘Professor Knight’s note on interest theory’, Review of Economic Studies, 4, June, 231–3.CrossRefGoogle Scholar
  9. McKenzie, L. W. (1987), ‘Turnpike theory’, in J. Eatwell, The New Palgrave: A Dictionary of Economics, Vol. 4. (London, New York: Macmillan), pp. 712–20.Google Scholar
  10. Malinvaud, E. (1953) ‘Capital accumulation and efficient allocation of resources’, Econometrica, 21, April, 233–68.CrossRefGoogle Scholar
  11. Marcuzzo, M. C. (ed.) (1986) N. Kaldor: Ricordi di un Economista (Italia: Garzanti).Google Scholar
  12. Punzo, L. F. (1984) Essays on Formalism and Empiricism in Economics: Origins, Theory, Methods (Siena: Institute of Economics, University of Siena, Italy).Google Scholar
  13. Radner, R. (1961) ‘Prices and the turnpike, III. Paths of economic growth that are optimal with regard only to final states: a turnpike theorem’, Review of Economic Studies, 28, February, 98–104.CrossRefGoogle Scholar
  14. Samuelson, P. A. (1949) Market Mechanisms and Maximization, Part HI. Dynamics and Linear Programming, Research Memorandum, RAND Corporation, 29 June 1949.Google Scholar
  15. Reproduced as ch. 33 in J. E. Stiglitz (ed.) The Collected Scientific Papers of Paul A. Samuelson I, (Cambridge, MA.: MIT Press, 1965), pp. 471–92.Google Scholar
  16. —— (1951), ‘Abstract of a theorem concerning substitutability in open Leontief models’, in T. C. Koopmans (ed.) Activity Analysis of Production and Allocation (New York: Wiley), pp. 142–6. Reproduced as ch. 36 in The Collected Scientific Papers of Paul A. Samuelson I, (op. cit.), pp. 515–9.Google Scholar
  17. —— (1987) ‘Sraffian economies’, in J. Eatwell, M. Milgate and P. Newman, The New Palgrave: A Dictionary of Economics, Vol. 4. (London, New York: Macmillan) pp. 452–61.Google Scholar
  18. Sraffa, P. (1960) Production of Commodities by Means of Commodities (Cambridge: Cambridge University Press).Google Scholar
  19. Thirlwall, A. P. (1987) Nicholas Kaldor (Brighton: Wheatsheaf Books).Google Scholar
  20. von Neumann, J. (1932, 1937, 1945) ‘Uber ein okonomisches Gleichungs-System und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes’, in K. Menger (ed.), Ergebnisse eines Mathematischen Kolloquiums, no. 8, 1937. Speech presented at Princeton (1932) and Vienna (1936), translated by G. Morgenstern as ‘A model of general economic equilibrium’, Review of Economic Studies, 13, 1, 1–9 (1945).Google Scholar
  21. Wood, A. (1987) ‘Nicholas Kaldor (1908–1986)’, in J. Eatwell, M. Milgate and P. Newman, The New Palgrave: A Dictionary of Economics, Vol. 3, (London, New York: Macmillan) pp. 3–8.Google Scholar

Copyright information

© Edward J. Nell and Willi Semmler 1991

Authors and Affiliations

  • P. A. Samuelson

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