The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd


  • Charles Blackorby
  • Daniel Primont
  • R. Robert Russell
Reference work entry


Given a smooth increasing function, two variables are separable from a third if the marginal rate of substitution between the first two variables is independent of the third. In this case it is possible to construct an aggregator function over the first two variables that is independent of the third. This is much weaker than additive separability or additivity. We show that separability is equivalent to decentralization and that additive separability is closely related to two-stage budgeting.


Additivity Conditional indirect utility function Consumer expenditure Decentralization Demand theory Gorman, W. M. Gorman’s overlapping th Indirect utility function Leontief, W. Marginal rates of substitution Optimal income allocation Price aggregation Separability Social welfare function Two-stage budgeting Sono independence Strotz, R. 

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  1. Blackorby, C., and R.R. Russell. 1997. Two-stage budgeting: An extension of Gorman’s th. Economic Theory 9: 185–193.CrossRefGoogle Scholar
  2. Blackorby, C., D. Primont, and R.R. Russell. 1978. Duality, separability, and functional structure: Theory and economic applications. New York: North-Holland.Google Scholar
  3. Blackorby, C., D. Primont, and R.R. Russell. 1998. Separability: A survey. In Handbook of utility theory, ed. S. Barbara, P.J. Hammond, and C. Seidl. Dordrecht: Kluwer.Google Scholar
  4. Debreu, G. 1959. Topological methods in cardinal utility theory. In Mathematical methods in the social sciences, ed. K. Arrow, S. Karlin, and P. Suppes. Stanford: Stanford University Press.Google Scholar
  5. Gorman, W.M. 1959. Separability and aggregation. Econometrica 27: 469–481.CrossRefGoogle Scholar
  6. Gorman, W.M. 1968. The structure of utility functions. Review of Economic Studies 32: 369–390.Google Scholar
  7. Leontief, W.W. 1947a. A note on the interrelation of subsets of independent variables of a continuous function with continuous first derivatives. Bulletin of the American Mathematical Society 53: 343–350.CrossRefGoogle Scholar
  8. Leontief, W.W. 1947b. Introduction to a theory of the internal structure of functional relationships. Econometrica 15: 361–373.CrossRefGoogle Scholar
  9. Sono, M. 1945. The effect of price changes on the demand and supply of separable goods [in Japanese]. Kokumin Keisai Zasshi 74: 1–51.Google Scholar
  10. Sono, M. 1961. The effect of price changes on the demand and supply of separable goods. International Economic Review 2: 239–271.CrossRefGoogle Scholar
  11. Strotz, R.H. 1957. The empirical implications of a utility tree. Econometrica 25: 269–280.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Charles Blackorby
    • 1
  • Daniel Primont
    • 1
  • R. Robert Russell
    • 1
  1. 1.