Some Envelope Theorems for Integer and Discrete Choice Variables

International Economic Review, Vol. 39, No. 3, 1998

Yale University Economic Growth Center Discussion Paper No. 598

16 Pages Posted: 27 Jun 2012

See all articles by Raaj Kumar Sah

Raaj Kumar Sah

University of Chicago

Jingang Zhao

affiliation not provided to SSRN

Date Written: March 1990

Abstract

Though the envelope theorem is a widely used tool of applied economic analysis, the standard version of the theorem can only be used if all of the choice variables are assumed to be continuous. This limitation is significant because the natural description of many economic choice variables is as integers (e.g., the number of projects or children, as well as variables that represent various yes-no choices and choices that entail fixed costs). A continuous representation of such variables is not only unsatisfactory and a source of potential error, but it can also make certain kinds of economic analyses intractable or unproductive.

This paper shows that modified but intuitive versions of the envelope theorem can be used with integer or discrete choice variables, provided the optimization problem satisfies the usual conditions. Thus, the results presented here make it possible to use the envelope theorem in a variety of economic problems.

Suggested Citation

Sah, Raaj Kumar and Zhao, Jingang, Some Envelope Theorems for Integer and Discrete Choice Variables (March 1990). International Economic Review, Vol. 39, No. 3, 1998; Yale University Economic Growth Center Discussion Paper No. 598. Available at SSRN: https://ssrn.com/abstract=2085879

Raaj Kumar Sah (Contact Author)

University of Chicago ( email )

Chicago, IL 60637
United States
+1 773 288 1117 (Phone)

Jingang Zhao

affiliation not provided to SSRN ( email )

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