The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Envelope Theorem

  • Eugene Silberberg
Reference work entry


The envelope theorem appeared in economics following the 1931 Viner–Wong diagram (incorrectly drawn in the original paper). This famous paper indicated that, starting at some minimum cost input combination, the change of average cost when output changed was the same whether or not other inputs were allowed to vary or were held fixed. This puzzling result remained mostly a curiosity until the 1970s when, with the use of a generalization of this diagram, the modern theory of duality was developed. This new approach to comparative statics provided a clearer explanation for the appearance of refutable implications in maximization models.


Comparative statics Constrained optimization models Cost functions Envelope theorem Lagrange multipliers Primal-dual model Shadow pricing 

JEL Classifications

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  1. Samuelson, P.A. 1947. Foundations of economic analysis. Cambridge, MA: Harvard University Press.Google Scholar
  2. Silberberg, E., and W. Suen. 2000. The structure of economics. 3rd ed. New York: McGraw-Hill.Google Scholar
  3. Viner, J. 1931. Cost curves and supply curves. Zeitschrift für Nationalökonomie 3, 23–46. Repr. in American Economic Association. 1952. Readings in price theory. Homewood: Irwin.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Eugene Silberberg
    • 1
  1. 1.