On the minimum rate of impatience for complicated optimal growth paths (Q1183701)

The paper deals with a class of discounted optimal growth models in reduced form. A new type of necessary optimality condition is developed: If the growth path \(x\) is optimal in any standard optimal growth problem with discount rate \(\rho\), then there is no representation of the initial state \(x_ 0\) as a weighted average of all future capital stocks along this path with the weights decreasing at a rate greater than or equal to \(\rho\). This condition can be used to derive a lower bound on the rate of impatience under which a given path can be optimal. Both the discrete time case and the continuous case are treated.