The semi-log portfolio balance schedule is tenuous

A well-known procedure in the context of the semi-log portfolio balance schedule is to impose an arbitrary terminal condition that rules out the occurrence of runaway inflations in the absence of runaway growth in the money supply. Notwithstanding the fact that a formal justification for this procedure is sometimes available in the context of equations that emerge from optimum problems, this paper finds that no such justification is available in the context of several leading optimizing models of money that either conceivably or actually deliver the Cagan schedule. A byproduct of the analysis is a demonstration that the semi-log, double-log, and Box-Cox schedules are integrable (can be generated by at least one optimizing framework).