A sensitivity analysis on optimal economic growth

A model of capital accumulation is considered and the relation between the optimal path and the initial capital stock is analyzed. Mathematically speaking, the model is a convex model of infinite horizon in continuous time. The existence of optimal paths of capital accumulation is proved. By using the continuity of the value function, it is proved that the optimal path of capital accumulation is a continuous function of the initial capital stock. The analysis is so general that neither the smoothness of the model nor the interiority of the optimal path are made.