Some Envelope Theorems for Integer and Discrete Choice Variables.

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.