1 Introduction

As the most important critique of the Marxian labor theory of value, the transformation problem has long been discussed. It is century-long controversy and has not perfectly been settled. Why has not it been settled? We consider that behind the Marxian labor theory of value, an important problem currently exists in our understanding of numeration of value, which is the process that underlies all economic activities. The purpose of this study is to explore this problem as the theoretical standpoint of economics.
Numeration of value is the process of converting commodity values into prices. We assume that a price has relation with value. Many people suppose, like neo-classical economists do, that a price is determined by supply and demand at a market. However, the marginal utility theory cannot move back before the determination at a market to explain the mechanism how a price is generated. Therefore, the theory of supply and demand cannot argue value before markets.
This theoretical limitation is linked with the fact that in economics the theory of supply and demand and the labor theory of value have not been united. In economics after the marginal revolution neo-classical economics became to be a mainstream school, it does not mean the two theories united. Theoretically, there is a significant gap between the theory of supply and demand and the labor theory of value.
There is the gap within the Marxian theory too, and it became an issue of the transformation problem. In the disputation of the transformation problem, the labor theory of value was difficult to be reconciled to a price, and arguments have been entangled. The reason is that the mechanism of numeration of value is not understood.
Marx explained this process through the concept of transformation. He presumed that value and prices naturally coincide and therefore ‘equivalents are exchanged’ (Marx 2014 [1867]: 117). The concept of numeration of value is similar to Marx’s transformation as both are processes of conversion. However, the two concepts differ in their underlying mechanisms and assumptions. The term ‘transformation’ is not used to explain our theme because we regard Marx’s transformation concept as being erroneous.
The transformation problem has long been discussed primarily as an instance of internal inconsistency within Marxian theory. This study, however, seeks to reconsider the domain of numeration of value separate from Marx to reframe the concept. When or how is value numerated? We define prenumerated value as ideas. The labor theory of value is one of the ideas and the expectation of supply-side and demand-side is too. This is a different definition with Marx’s.
Many problems are entangled in a complex way, and we discuss two types of approaches to disentangle them. The first step is examining the numeration of value and the measurement problem. The disputation in economics what point of time numerical value is determined has not been settled. The reason is a confusion of causal recognition. After resolving it, we reveal a deeper issue: a fundamental confusion over the mechanism of numeration of value. Although the transformation problem delves into an extremely mathematical argument, a mechanism of numeration of value cannot be represented as equations. In the process of explaining our proposed conception, we highlight the crucial error in the Marxian labor theory of value and, thus, settle the long dispute plaguing the transformation problem.
Second, we use a structuralist approach11Structuralism has developed under the influence of the Marx’s historical materialism. We appreciate the contribution of Marx to structuralism.. Numeration of value includes currently unknown dynamics. Marx was interested in the mystery of value to argue the fetishism of commodities (Marx 2014 [1867]: 46). We seek another path from Marx to determine this mystery by structurally exploring the process by which value turns into prices. We refer to the point where prestructural value turns into a price within a structure as a singular point . The problem surrounding the singular point is related to the theoretical change that occurs at the point where economic thought shifts from the classical to neoclassical school. It marks a change in the theoretical standpoint of economics. By the structuralist approach, it is clarified that the standpoint of all economics has a fundamental problem.