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Some Envelope Theorems for Integer and Discrete Choice Variables

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  • Sah, Raaj
  • Zhao, Jingang

Abstract

The envelope theorem is a genuine workhorse of economic analysis. Typically, this theorem requires that the choice variables be continuous. This paper derives envelope theorems, previously unavailable in the literature, for use with integer and discrete choice variables. The authors' results, which are intuitive, thus make it possible to use the envelope theorem in a variety of analyses in which the natural description of choice variables is not continuous. Among such choice variables are the number of projects, plants, and a couple's children, as well as binary (yes-no) choices such as labor-force participation, home ownership, and migration. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Sah, Raaj & Zhao, Jingang, 1998. "Some Envelope Theorems for Integer and Discrete Choice Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 623-634, August.
  • Handle: RePEc:ier:iecrev:v:39:y:1998:i:3:p:623-34
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    Cited by:

    1. Matthew Potts & Jeffrey Vincent, 2008. "Spatial distribution of species populations, relative economic values, and the optimal size and number of reserves," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 39(2), pages 91-112, February.
    2. Park, Timothy A. & Florkowski, Wojciech J., 2003. "Selection of Peach Varieties and the Role of Quality Attributes," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 28(01), April.
    3. O'Callaghan, Patrick, 2016. "Parametric continuity from preferences when the topology is weak and actions are discrete," MPRA Paper 72356, University Library of Munich, Germany.
    4. Guo, Christopher & Costello, Christopher, 2013. "The value of adaption: Climate change and timberland management," Journal of Environmental Economics and Management, Elsevier, vol. 65(3), pages 452-468.
    5. Yuntong Wang, 2014. "Envelope Theorem without Differentiability," Working Papers 1404, University of Windsor, Department of Economics.
    6. O'Callaghan, Patrick, 2016. "Minimal conditions for parametric continuity and stable policy in extreme settings," MPRA Paper 70989, University Library of Munich, Germany.

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