1. This paper elaborates the problem of optimum saving first discussed by Frank Ramsey in 1928 [4]. For this purpose a centralized, closed economy is postulated; it is assumed to be adequately described by the aggregative model first closely analyzed by Solow [51. 2 The social welfare to be maximized is then represented by the total of the discounted utility of consumption per capita, where a general concave utility index is employed. Within this framework it is demonstrated that there is a unique optimum growth path, and the qualitative nature of this path as well as its relation to the golden rule growth path are discussed.

2. The basic premises of our model can be described as follows: A single homogeneous output, Y (t), is produced with the use of two homogeneous factors, labor, L (t), and capital goods, K (t), under the direction of a central planning board. The technically efficient possibilities for production, which are unchanging over time, are known to the planning board and are summarized in an aggregate production function. This relation exhibits constant returns to scale, positive marginal productivities, and a diminishing marginal rate of substitution. In addition, it is known that roundaboutness in production is extremely productive when capital is relatively very scarce, while capital saturation only occurs when capital is relatively very abundant. If we denote by lower case letters quantities measured in terms of labor, these assumptions about production can be represented by