Abstract
This paper deals with the existence problem of optimal growth with recursive utility in a continuous-time model without convexity assumptions. We consider a general reduced model of capital accumulation and provide an existence result allowing the production technology to be nonconvex and the objective functional to be nonconcave and recursive. The program space under investigation is a weighted Sobolev space with discounting built in, as introduced by Chichilnisky. The compactness of the feasible set and the continuity of the objective are proven by the effective use of ℒ2-convergence. Existence follows from the classical Weierstrass theorem.
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SAGARA, N. Optimal Growth with Recursive Utility: An Existence Result without Convexity Assumptions. Journal of Optimization Theory and Applications 109, 371–383 (2001). https://doi.org/10.1023/A:1017518523055
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DOI: https://doi.org/10.1023/A:1017518523055