Consider a variant of the model of the golden rule capital stock. For each date 1 2 1, N, young agents are born who are endowed with y> 0 goods when young and zero goods when old. The population grows according to N, = N, Young agents (and the planner) have access to a technology, capital, that converts k. goods at time / into (k,) goods when old. The marginal product of capital, f'(k,), is always positive and is decreasing in k. After capital produces goods at time +1, dk, units of capital are lost to depreciation. Thus, d is the depreciation rate of capital where 0