The classic integrability problem asks (i) what conditions guarantee that demand functions can be rationalized by a well-behaved utility function and (ii) if such a utility exists, how can it be recovered. Hurwicz and Uzawa (1971) provided answers to both questions. However for the popular case of changing tastes, as represented by a sequence of non-nested utilities, the Hurwicz and Uzawa conditions fail to hold in general. Following Strotz (1956), an individual can determine her dynamic demands via a naive or sophisticated solution technique. For given dynamic demands, we provide necessary and sufficient conditions such that the demands are rationalized by a set of utilities using the sophisticated solution process. Moreover we provide a means for recovering the generating sequence of utilities, although this sequence of utilities is not unique. We also give sufficient conditions for demands to be rationalized by a sequence of utilities using the naive solution process and for recovering the complete set of generating utilities for two special cases.
Kannai, Yakar, Larry Selden, and Xiao Wei. "On Integrability and Changing Tastes." Columbia Business School, November 2015.
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