This paper presents first a general theory of a capitalistic optimum and a model illustrating its essential features, and, secondly, the empirical justification of this model, and its principal applications. Under very general conditions it is possible to show that we cannot expect, from an indefinite increase of available real capital, an indefinite increase of real national income consumed per inhabitant, and that there is an optimum amount of capital for which the real income per inhabitant is maximum. The conditions under which this maximum is attained are given. The general model, which is presented, and, in particular, its exponential variety, appear quit remarkably confirmed by all presently available empirical data, with respect to both the hypotheses and the results. A $very$ $simple$ expression of consumed real income is given in terms of the rate of interest i and the rate of growth $\varrho$.