The purpose of this paper is to examine the critical arguments made by Burmeis ter, Samuelson, and others, with respect to Sraffa (1960). Sraffa did not address these arguments, but they are relevant from the viewpoint of modern economic theories. In his arguments about the standard commodity, Sraffa assumed that a change in in- come distribution has no effect on the output level and choice of techniques. However, modern economic theories allow interdependence among changes in income distribution, output level, and choice of techniques. Therefore, it is interesting to consider the existence of an invariable measure of value and linearity of income distribution in a model where such interdependence is discussed. We assume general convex economies with non-increasing returns to scale. In this model, we obtain the conditions under which the existence of an invariable measure of value and the validity of the linearity of income distribution are assured.