Set-Valued Anal (2011) 19:135–156 DOI 10.1007/s11228-010-0168-2 The Concavity Assumption on Felicities and Asymptotic Dynamics in the RSS Model M. Ali Khan · Adriana Piazza Received: 30 November 2009 / Accepted: 18 October 2010 / Published online: 30 October 2010 © Springer Science+Business Media B.V. 2010 Abstract An analysis of the RSS model in mathematical economics involves the study of an infinite-horizon variational problem in discrete time. Under the assump- tion 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 M. A. Khan (B ) Department of Economics, The Johns Hopkins University, Baltimore, MD 21218, USA e-mail: akhan@jhu.edu A. Piazza Departamento de Matemática, Universidad Técnica Federico Santa María, Avda. España 1680, Casilla 110-V, Valparaíso, Chile e-mail: adriana.piazza@usm.cl