A Revised Proof of the Labor Theory of Value Based on Marginalist Principle

The labor theory of value is the very base to prove labor exploitation because only by its base we can compare capitalist exploitation with other types of exploitation in serfdom and slavery and claim that all exploitation have the same character as a labor exploitation. However, the labor theory of value was not proved mathematically. This is our remaining task, and the reason why this paper aims to modernize the labor theory of value by showing its reality mathematically in the machine-based production system after the industrial revolution.
However, what is the meaning of the labor theory of value mathematically? This paper defines it as the proportionality between input labor and physical output. For example, if we input twice as large amounts of labor into a production process, we can produce twice as large amounts of products. Under this condition, we assume the linear production function, which is usually adopted by Marxian economics, including Okishio’s Fundamental Marxian Theorem to prove labor exploitation.
Because this challenge was carried out first by Onishi (2019), this paper also follows it but also modifies it in the following two points: 1)correct technical misspecification, 2) transform “capital” from a flow variable to a stock. First, his paper explains the original set-up in Onishi (2019) and then modifies the two points above. Finally, we subtract some implications from this research.