Some envelope theorems for integer and
discrete choice variables
Raaj Sah and Jingang Zhao
International Economic Review, Volume 39, Number 3, August 1998, pages 623-634.
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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. Our 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 owner-ship, and migration.
Previous working versions include:
“Some envelope theorems for integer and discrete choice variables.” Yale University, Department of Economics. Economic Growth Center, Center discussion paper number 598. March 1990.