The Concavity Assumption on Felicities and Asymptotic Dynamics in the RSS Model
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- Khan, M.A. & Piazza, A. Set-Valued Anal (2011) 19: 135. doi:10.1007/s11228-010-0168-2
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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.