Optimal growth with recursive utility: An existence result without convexity assumptions

This paper deals with the existence problem of optimal growth with recursiv e utility in a continuous-time model without convexity assumptions. We cons ider a general reduced model of capital accumulation and provide an existen ce result allowing the production technology to be nonconvex and the object ive functional to be nonconcave and recursive. The program space under inve stigation is a weighted Sobolev space with discounting built in, as introdu ced by Chichilnisky. The compactness of the feasible set and the continuity of the objective are proven by the effective use of F-2-convergence. Exist ence follows from the classical Weierstrass theorem.