The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan


  • Lawrence E. Blume
Living reference work entry

Latest version View entry history



This article surveys duality in producer theory, consumer theory and welfare economics. As opposed to the usual analysis through first-order conditions for optimization, the various dualities are derived here from convex duality theory, using Fenchel transforms and subdifferentials.


Antonelli, G.B. Bergson–Samuelson social welfare function Convex programming Convexity Cost functions Cyclic monotonicity Duality Envelope th Fenchel transform Firm, theory of the Hicksian-compensated demand Hotelling, H. Hotelling’s lemma Hyperplanes Indirect utility function Lagrange multipliers Marginal revolution Monotonicity Profit functions Quasi-equilibrium Saddlepoints Separation th Shephard, R.W. Shephard’s lemma 

JEL Classifications

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


  1. Arrow, K.J. 1952. An extension of the basic theorems of classical welfare economics. In Proceedings of the second berkeley symposium on mathematical statistics and probability, ed. J. Neyman. Berkeley: University of California Press.Google Scholar
  2. Debreu, G. 1951. The coefficient of resource utilization. Econometrica 19: 273–292.CrossRefGoogle Scholar
  3. Diewert, W.E. 1981. The measurement of deadweight loss revisited. Econometrica 49: 1225–1244.CrossRefGoogle Scholar
  4. Hotelling, H. 1932. Edgeworth’s taxation paradox and the nature of demand and supply. Journal of Political Economy 40: 577–616.CrossRefGoogle Scholar
  5. Rockafellar, R.T. 1970. Convex analysis. Princeton: Princeton University Press.CrossRefGoogle Scholar
  6. Rockafellar, R.T. 1974. Conjugate duality and optimization. Philadelphia: SIAM.CrossRefGoogle Scholar
  7. Shephard, R.W. 1953. Cost and production functions. Princeton: Princeton University Press.Google Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Lawrence E. Blume
    • 1
  1. 1.