Set-Valued and Variational Analysis

, Volume 19, Issue 1, pp 135–156 | Cite as

The Concavity Assumption on Felicities and Asymptotic Dynamics in the RSS Model

Article

Abstract

An analysis of the RSS model in mathematical economics involves the study of an infinite-horizon variational problem in discrete time. Under the assumption that the felicity function is upper semicontinuous and “supported” at the value of the maximally-sustainable level of a production good, we report a generalization of results on the equivalence, existence and asymptotic convergence of optimal trajectories in this model. We consider two parametric specifications, and under the second, identify a “symmetry” condition on the zeroes of a “discrepancy function” underlying the objective function that proves to be necessary and sufficient for the asymptotic convergence of good programs. With a concave objective function, as is standard in the antecedent literature, we show that the symmetry condition reduces to an equivalent “non-interiority” condition.

Keywords

Good program Maximal program Optimal program Value-loss Non-differentiability Discrepancy function Non-interiority Existence of optimal programs Asymptotic convergence 

JEL Classification

C62 D90 

Mathematics Subject Classifications (2010)

52A41 91B55 49J45 37B25 39A06 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of EconomicsThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile

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