The transformation problem under positive rank one input matrices: on a new approach by Schefold

Recently, Schefold proposed a new approach to the transformation problem consisting of two contentions. One is that input matrices of large-scale economies can be approximated by positive rank one matrices. The second is that additional original assumptions about the relationship among input coefficients, labor coefficients, gross outputs, and surplus outputs can establish the equality of the total profits and total surplus value under a numéraire equalizing the total production prices and total value. The purpose of this study is to critically examine the second part of Schefold’s argument. First, we will confirm that it is an attempt to give plausible grounds to a condition that has been known as sufficient for the successful solution of the transformation problem but considered to hold only by chance. Next, we will indicate that, except for a supposition about the rank of input matrices, his key assumptions depend on the measurement units of each product. Because this dependence implies that these assumptions hold only when measurement units fill particular conditions, it naturally casts a serious doubt on the generality of the analysis based on them. While it is possible to combine these assumptions into a unit-independent form, such a reformulation deprives them of the meaning attached to their original form. Thus, in spite of its unique viewpoint, Schefold’s new approach does not succeed in bringing the value system closer to the production price system.