Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems

Abstract
This paper considers a class of discrete-time, infinite-horizon optimization problems arising in economics. Necessary optimality conditions for such problems consist of an Euler equation and a transversality condition at infinity. Our concern here is with the latter condition. Previous results for this type of problem have required such restrictions as concavity and boundedness of the utility functions whose sum is being maximized. Here we derive a transversality condition that remains valid under considerably more general hypotheses. In doing so, we introduce methods that may also be applicable to other situations, such as optimization in continuous time.

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