Heterodox
We compare the conditions of two isolated market systems A and B. Both are equal in size and population figures, the state of technological knowledge, and in natural resources. They differ from one another only in the supply of capital goods, this supply being larger in A than in B. This enjoins that in A many processes of production are employed with which the output is greater per unit of input than with those employed in B. In B one cannot consider the adoption of these processes on account of the comparative scarcity of capital goods. Their adoption wouId require a restriction of consumption. In B many manipulations are performed by manual labor which in A are performed by labor-saving machines. In A goods are produced with a longer durability; in B one must abstain from producing
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Robert Vienneau considers the following as important: Austrian School Of Economics, Example in Mathematical Economics
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We compare the conditions of two isolated market systems A and B. Both are equal in size and population figures, the state of technological knowledge, and in natural resources. They differ from one another only in the supply of capital goods, this supply being larger in A than in B. This enjoins that in A many processes of production are employed with which the output is greater per unit of input than with those employed in B. In B one cannot consider the adoption of these processes on account of the comparative scarcity of capital goods. Their adoption wouId require a restriction of consumption. In B many manipulations are performed by manual labor which in A are performed by labor-saving machines. In A goods are produced with a longer durability; in B one must abstain from producing them although the lengthening of durability is obtained by a less than proportionate increase in input. In A the productivity of labor and consequently wage rates and the standard of living of the wage earners are higher than in B. -- Ludwig Von Mises Human Action, Chapter XVIII, Section 4
The above seems to be simply wrong, insofar as any sense can be made of it. What does it mean to say the supply of capital goods is larger on one island than another? These are heterogeneous quantities. Presumably some capital goods would be only made on one island, and other capital goods might be made only on the other. Von Mises even almost recognizes this in his remark about "labor-saving machines". Even if the same types of capital goods were made on both islands, it need not be the case that the quantities are uniformly larger on one island. In adapting production to final output, some quantities of some capital goods might be larger on one island while quantities of other capital goods might be smaller.
But put these objections aside. Remarks about "output is greater per unit of input" and a "higher standard of living of the wage earners" might give us a tautological definition of "the supply of capita1 goods". To simplify and to consider, for the sake of argument, a case in which some of these terms have a sharp meaning, suppose both islands A and B are in a stationary equilibrium, what Von Mises considers an evenly rotating economy. Suppose all labor is homogeneous and net output is in the same proportions.
Is the adoption of labor-saving machines, as compared to manual labor, associated with a greater output per unit of labor input? Is the use of capital goods for a longer period of time also associated with a greater output per unit of labor input? We know from numerical examples, the answer to the second question is otherwise.
Von Mises is not operating with a tautological definition of more or less capital goods, in which a greater supply results in a greater standard of living. He also makes assertions about physical properties of these capital goods. And, as a simple matter of logic - that praxeology he goes on about - he is wrong about these entailments.