Advertisement

Economics and Thermodynamics: von Neumann’s Problematic Conjecture

  • Paul A. Samuelson
Chapter

Abstract

Of the attempts to find analogies between thermodynamics and economies there is alas no end. But the mathematical genius John von Neumann has earned the right to command our investigation when he suggests that his growth model (1945; earlier 1932 and 1937) defines a function Value of Inputst/Value of Outputst+1
$$ = \sum\limits_i^n {\sum\limits_j^m {{P_i}} } {A_{ij}}{X_j}/\sum\limits_i^n {\sum\limits_j^m {{P_i}} } {B_{ij}}{X_j}$$
$$ = \phi \left( {P,X} \right)$$
whose “role seems to be similar to that of thermodynamic potentials in phenomenological thermodynamics.” (1945, p.1)

Keywords

Classical Thermodynamic Indicator Diagram Full Duality Conjugate Vector Concave Programming 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brody, A. 1989. “Economics and Thermodynamics,” in M. Dore, S. Chakravarty, and R. Goodwin, eds., John von Neumann and Modern Economics. Oxford: Clarendon Press.Google Scholar
  2. Champernowne, D. 1953. “Commentaries on J. Robinson on Capital,” Review of Economic Studies 21, 107–35.Google Scholar
  3. Court, L. 1941. “Invariable Classical Stability of Entrepreneurial Demand and Supply Functions,” Ouarterly Journal of Economics 55, 134–44.Google Scholar
  4. Georgescu-Roegen, N. 1971. The Entropy Law and the Economic Process. Cambridge, Massachusetts: Harvard University Press.Google Scholar
  5. Gibbs, J.W. 1873, 1873, 1876–78. Thermodynamics papers in The Collected Works of J. Willard Gibbs, Volume I. New Haven, Conn.: Yale University Press.Google Scholar
  6. Hotelling, H. 1932. “Edgeworth’s Taxation Pardox and the Nature of Demand and Supply Functions,” Journal of Political Economy 40, 577616.Google Scholar
  7. von Neumann, J. 1928. “Zur Theorie der Gesellschaftsspiele”, Math. Annalen 100, 295–320.Google Scholar
  8. von Neumann, J. 1945. “A Model of General Equilibrium,” Review of Economic Studies 13, 1–9.Google Scholar
  9. Roy, R. 1942. “De l’Utilité, Contribution à la Theorie des Choix.” Paris: Hermann.Google Scholar
  10. Samuelson, P. 1947 and 1983. Foundations of Economic Analysis. Cambridge, Mass.: Harvard University Press.Google Scholar
  11. Samuelson, P. 1938. “A Note on the Pure Theory of Consumer’s Behavior,” Economica N.S. 5, 61–71.Google Scholar
  12. Samuelson, P. 1953. “Prices of Factors and Goods in General Equilibrium,” Review of Economic Studies 21, 1–20.Google Scholar
  13. Samuelson, P. 1960. “Structure of a Minimum System,” in R. Pfouts, ed., Essays in Honor of Harold Hotelling. Chapel Hill: University of North Carolina Press.Google Scholar
  14. Samuelson, P. 1962. “Parable and Realism in Capital Theory,” Review of Economic Studies 29, 193–206, particularly Appendix.Google Scholar
  15. Samuelson, P. 1965. “Using Full Duality to Show That Simultaneously Additive Direct and Indirect Utilities Implies Unitary Price Elasticity of Demand”, Econometrica 33, 781–96.Google Scholar
  16. Samuelson, P. 1972. “Unification Theorem for the Two Basic Dualities of Homothetic Demand Theory,” Proceedings of the National Academy of Science, USA 69, 2673–74.Google Scholar
  17. Samuelson, P. 1990. “Gibbs in Economics” in D. G. Caldi and G. D. Mostow, eds., Proceedings of the Gibbs Symposium, Yale University 1989. Providence, Rhode Island: American Mathematical Society ani American Institute of Physics, 255–68.Google Scholar
  18. Shephard, R. 1953. Cost and Production Functions. Princeton, N.J.: Princeton University Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Paul A. Samuelson
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations