The Concavity Assumption on Felicities and Asymptotic Dynamics in the RSS Model |
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Authors: | M Ali Khan Adriana Piazza |
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Institution: | 1.Department of Economics,The Johns Hopkins University,Baltimore,USA;2.Departamento de Matemática,Universidad Técnica Federico Santa María,Valparaíso,Chile |
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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. |
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