Solution existence theorems for finite horizon optimal economic growth problems

Abstract

The solution existence of finite horizon optimal economic growth problems is studied by invoking Filippov's Existence Theorem for optimal control problems from the monograph of Cesari L. [Optimization theory and applications. New York: Springer-Verlag; 1983]. Our results are obtained not only for general problems but also for typical ones, where the production function is given by either the AK function or the Cobb–Douglas one, while the utility function can be in a linear or power form. Some open questions and conjectures about the regularity of global solutions of finite horizon optimal economic growth problems are formulated in this paper.