Choice of technique
As regards the first problem, with several alternative ways to produce a given commodity we get as many reduction equations as there are technical alternatives. Obviously, and flukes apart, different methods of production do not support the same rate of profits r, given the real wage rate.
Bortkiewicz corroborated Ricardo’s finding that in competitive conditions the method will be chosen that minimizes unit costs. If the method that does so is at the same time a method employed directly or indirectly in the production of wage goods, its adoption will entail an increase in the general rate of profits. Otherwise, in the case of “luxuries”, it will only lead to a reduction in the price of the commodity in the production of which the new method is used (and in the prices of commodities in whose production the commodity enters as a means of production).This argument anticipates already why Bortkiewicz refuted Marx’s attempt at explaining a falling tendency of the rate of profits in terms of technical progress. Technical progress implies that new methods of production become available, and for a given real wage rate they will be adopted by cost-minimizing producers if and only if they allow to reduce costs of production, which however means that the general rate of profits will either rise or stay constant. This result became known later as the “Okishio theorem”.