On a Class of Variational Problems Arising in Mathematical Economics
نویسنده
چکیده
This paper studies a class of variational problems that arise in the analysis of resource allocation over an infinite horizon. Such problems are characterised by an underlying technology that generates the basic set of feasible programs and by a preference ordering that selects from among these programs an optimal one. The problem of establishing the existence of an optimal program differs from the standard variational problems on a closed finite interval in that certain inequalities on parameters characterising the asymptotic properties of the underlying technology and preferences play a crucial role in the basic existence condition. This paper generalises the earlier results of Koopmans [7] and is closely related to the abstract approach developed by Bewley [2]. The basic existence result is applied in Section 4 to the model of an expanding economy introduced by von Neumann. The definition of impatience adopted in Section 5 is motivated by the results of Brown and Lewis [3].
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