Nobuo Okishio (置塩 信雄; January 2, 1927 – November 13, 2003) was a Japanese Marxian economist and emeritus professor of Kobe University. In 1979, he was elected President of the Japan Association of Economics and Econometrics, which is now called Japanese Economic Association. Okishio studied mathematical economics under Kazuo Mizutani. In 1950 he graduated from Kobe University and later taught there. He soon began to doubt the premises and results of modern economics, and decided to search for alternatives by studying Marxian economics. Okishio worked to clarify the logic of Karl Marx’s economic system, offering formal and mathematical proofs for many Marxian theorems. For example, in 1955, he gave the world's first proof of the “Marxian fundamental theorem”, as it was later named by Michio Morishima, which is the theory that the exploitation of surplus labor is the necessary condition for the existence of positive profit. Concerning Marx’s Falling Rate of Profit, Okishio considered that his famous theorem would not deny it. Okishio wrote many papers covering various important fields in modern and Marxian economics, for example value and price, accumulation theory, critical analysis of Keynesian economics, trade cycle theory and on the long run tendency of capitalistic economy. They were published in over twenty books and two hundred papers, almost all in Japanese. About thirty of his published papers have been translated in English, and much of these materials are collected in the book (Nobuo Okishio, Michael Kruger and Peter Flaschel, 1993).
Value and exploitation theory
Formulation of labor embodied value Okishio showed how Marxian value is determined quantitatively. The value equation presented by Okishio determines the amount of labor directly and indirectly needed to produce one unit of a commodity as follows:
t i = ∑ j a i j + τ i , i = 1 , … , n {\displaystyle t_{i}=\sum _{j}a_{ij}+\tau _{i},\quad i=1,\ldots ,n}
where a i j {\displaystyle a_{ij}} is the amount of j {\displaystyle j} -th goods and τ i {\displaystyle \tau _{i}} is the direct labor input needed to produce one unit of i {\displaystyle i} -th goods. He first got this idea when he was writing “On Exchange Theory” in 1954 in Japanese, and in 1955 published a revised version in English as “Monopoly and the Rates of Profits” in Kobe University Economic Review.
Fundamental Marxian theorem Using this equation, Okishio proved Marx's fundamental proposition that the exploitation of surplus labor is the necessary condition for the existence of positive profit, later called the Fundamental Marxian Theorem by Michio Morishima. This proof is notable in that it does not rely on Marx's theory of value. Instead, the existence of surplus value can be deduced as a logical consequence of the existence of profit expressed in terms of price. This is the opposite of the approach taken by Marx, who started with a theory of value and used it to explain price and profit. After its publication, Okishio's proof persuaded many non-Marxian economists of the validity of Marx's theory of exploitation.
Measurement The value equation given above can be used to make quantitative measurements using input–output tables, a technique developed after World War II. Okishio first performed these measurements in 1958, using data from the Japanese economy. Subsequent analyses have been performed on other countries as well. Measurements from 1955 to 1985 in the Japanese economy show that values and prices appear to have low correlation across short time scales, but are very highly correlated across longer time scales. Thus, Okishio argues that prices tend to gravitate toward values in the long run.
Some propositions of Marxian economics
Transformation problem Okishio's work is related to clarifying the logic of Marx's theory. First, there is the transformation problem. Marx argued in Das Kapital Book Three about the transformation from values to prices. There he discussed that output prices also enter input prices in various sectors. And he warned us that we could make a mistake if we ignore this fact because there exists some discrepancy between prices and values. Here, of course, prices mean output prices and values mean input prices at the first stage. So Marx suggested the need to proceed this iterative transformation process to the end. Marx showed the transformation formula although he left others to do it. Okishio executed the iteration process to the end using mathematical tools and proved that it converges to production price equilibrium with positive profits, i.e. equal to Bortkiewicz equation. One important finding relating this work is that the equilibrium rate of profit and the production prices are determined depending on real wage rate and technologies in basic sectors only. This result was accepted with surprise, because many economists considered that non-basic sectors also have some relations with the equilibrium rate of profit. As far as Japan is concerned, some heated arguments are held between Okishio and some other Marxian economists.
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