The paper reviews mathematical development of Marx's economics before, by, and after Okishio. Marx's economics is based on dialectics, such as quality and quantity etc., and dialectic feature is not peculiar to Marx's economics, as seen from comparison with physics. Marx's economics has mathematical nature in many fields. The value form theory is established on the distinction between assignment and comparison, for instance. Values and production prices of commodities, the fundamental Marxian Theorem (FMT), the transformation problem, depression theory, socialist planning and relationship among men, all those are mathematical topics. Propositions within linear framework are established mainly by Okishio and his followers. Marx's theory in terms of the Leontief model turned out to be fully dependent on Perron-Frobenius (PF) theorem on nonnegative matrices. Okishio's theorem on technical changes is a corollary of PF theorem. Theory of fixed capital is one of greatest merits and contributions of economic theory of Marx and Sraffa. Fixed capital is a materialistic basis of capitalist production, so that movement of capital depends on fixed capital. It has been disclosed that the renewal process of fixed capital is described as a Markov process, that is accompanied with damped oscillation and initial spikes called Ruchti-Lohmann effect. The cycle of resonance is, nonetheless, as long as twice of durability of fixed capital. Some may argue that Marx's economics lacks micro foundation, but it is not a big point at all. Mathematical theory of Marx's economics follows Marx's fundamental idea that competition in the market is a phenomenal form of the internal dynamics of capitalist production system that governs the process. The equilibrium value itself is, if it exists, determined by a system of simultaneous equations that depict rather structural aspects of economies. Marx's economics is of computational nature, and, in this sense, highly critical against neoclassical economics, that suffers from computational difficulties. Criticism against neoclassical economics is one of important tasks for Marxian economics. It is pointed out that neoclassical macro dynamics should suffer from various formal difficulties, and neoclassical theorem based on saddle path fails in explaining cyclical depression, like 2008 world depression. Future development of Marx's economics should also include topics related to revival and renewed models of socialist planned economies, and nonlinearity or complexity of economic phenomena. As for socialist planning, there is a some stock of discussions before 1990. Fundamental problems are still worth pursuing. Meanwhile, Mandelbrot and economic physics present, from large scale data analyses, serious counter examples against neoclassical economics. This type of approach and method should be digested by Marxian economics. A basic stance of Marx's economics is that relationship among men appears in the relationships among commodities, and that the latter is a projection of the former. Hence Marx's economics is of steric nature. On the contrary, most of bourgeois economics does not analyse relationship of men, so that it is planar, and gives us no deeper insight of our economy.

抄録全体を表示

Georg von Charasoff, a Russian mathematician, was one of the first researchers to recognise that the price of production is an eigenvector of the input matrix, and to determine the rate of profit using its eigenvalue. He anticipated, at this analytical level, most of the arguments that were to be proposed later in the course of the 'transformation problem', i.e. Fundamental Marxian Theorem (FMT), convergence theorem for Marxian transformation procedure and the theorem of rising rate of profit. Moreover, he developed, prior to W. Leontief, P. Sraffa and J. v. Neumann, such ideas as the power series of the Leontief inverse, the basic and non-basic products and the duality of the growth and profit rate in the balanced growth. Although Charasoff's name and his work had been forgotten in the research of economics, his ideas were rediscovered and further developed particularly by Kei Shibata, N. Okishio and M. Morishima without any reference to Charasoff's original contribution. Maurice Potron was a French mathematician whose largely unknown contributions to economic analysis should be acknowledged as pioneering achievements. First, Potron proved de facto Fundamental Marxian Theorem 48 years earlier than Morishima, Seton and Okishio by adapting the Perron-Frobenius theorem and he proved de facto FMT by considering heterogeneous labours 65 years earlier and even more generally than Bowles and Gintis. Second, in doing so, Potron was the first to apply the Perron-Frobenius theorem to economics; third, he laid the foundations of input-output table long before Leontief by calculating input coefficients for some products. And finally, Potron articulated and proved the socalled Hawkins-Simon condition. Furthermore, a comparison between Charasoff's and Potron's treatment of FMT provides us with some insights into the role of mathematics in economic thoughts. Both mathematicians devoted themselves to economic research, and at last they could reach comparable results concerning price determination and especially FMT by using the concepts of eigenvectors and eigenvalues. They had, however, quite different ideological backgrounds, and correspondingly they took quite different positions on normative issues in the face of the so-called social problems around the turn of the 19^<th> to the 20^<th> century where the impoverishment of the working class was increasingly serious. Starting from the FMT, the existence of profit and, equivalently, the execution of surplus labour was condemned by Charasoff from the Marxian or 'human' viewpoint of economizing of living labour. Based on the same FMT, Potron affirmed surplus labour and therefore profit as the condition that enabled and stabilised the compatibility of just price and just wage, i.e. those two principles of justice which were thought to incorporate the Roman Catholic position of reconciling class interests. Both mathematicians and their economic research exemplified a limit to mathematical reasoning in economics in that FMT just as mathematical propositions in general cannot justify any specific normative assertion.

抄録全体を表示

Generally speaking, mathematical modeling is more advanced in modern economics than in Marxist economics. However, why? One way to answer is to focus on the characteristics of the modern economics which ignore what mathematics is not good at. However, another way to answer is to focus on the attitude of Marxist economists who do not like optimization theory. In my understanding, this attitude is a big mistake because materialistic concept of human being is same as that of modern economics; rational economic man. Even if human beings are living not only for their interest but also for justice, justice itself is an ideology which justifies the interests. In this sense, we built two types of Marxist model based on its optimization theory: one is Lenin's model of imperialism, and the other is 'Marxist optimal growth model'. The former model expresses the mechanism of uneven development of capitalist countries that is catching-up of the developing countries to the advanced countries by means of international capital flow. Here, we replaced an assumption of diminishing return technology which Lenin assumed as that of increasing return technology which is introduced Krugman's model of uneven development. The other model has two sectors like Marx's reproduction equations, and explains why capitalism appeared after the industrial revolution, why it developed, and why it will die in the future. While prof. Okishio proved the exploitation of labor by the capitalists, we proved the historical materialism. One more important characteristic of mathematical modeling is that it makes sciences to progress incrementally, and this characteristic gives the modern economics a tendency to avoid challenging researches in referee system of their journals, and it should be the normal way of progress of sciences. However, this type of attitude becomes a obstacle to explain phenomenon which have not been seen before or not been fit for their ideologies. In this sense, mathematics has to be used by ideology-free scientists; that is Marxists. In this paper, we also referred characteristics of 'area studies' comparing with Marxist methodologies.

抄録全体を表示

The mainstream of economics is named neoclassical economics. Its success in 20th century economics is obvious and it remains dominant even in 21st century. One of the reasons why neoclassical economics so succeeded is the appropriate employment of mathematical methods. Two pillars of the neoclassical framework are optimization and equilibrium. Both permitted to transform economic problems into tractable mathematical formulations. But, the cost of this use of mathematics was not cheap. It enclosed the economics to the simple world of calculus and put aside many of important questions that economics should attack. Neoclassical way of explanation seems to be flourishing but it is an effort to make scarecrows from in one field to in another. They may be impressive for naive people, as the explanation is full of high mathematics. But, this is not the real way to develop economics. Problem setting itself is designed such that the problem thus obtained is soluble. By consequence, there are full of ridiculer explanations. To cite an example, the RBC (Real Business Cycle) theory is one. This "theory" claims that business cycle is caused by the technical shocks the economy incurs. How does it explain the present world wide depression? Is financial crisis also a technical shock? I cited many other examples in the text, but the main question is not this point. RBS is only an example, but of what? It is a symptom of the crisis of economics as discipline. Now it is the time to seek a breakthrough. We should build a new economics different from neoclassical economics. There are many schools in economics and all but few are for it. But the question is how? Most of the endeavors that schools of economics tried failed. Is it possible after all? The attempt is not an easy one, of course. It requires a firm strategy. It is not a question of changing this hypothesis to another. The trouble that neoclassical economics faces is that it is enclosed in a circle of mathematical tractability. This circle is very loose and hard to see it, but it is strong enough that it never permits to go beyond it, as far as economics continues to use mathematics as main methodology. By consequence, the new strategy must be as powerful and as omnipotent as mathematics. What I propose as such a candidate is MAS (Multi-Agent simulation). MAS may liberate us from the yoke of mathematical tractability. Process analysis becomes the major field of MAS. By mathematics, analysis of processes was difficult except for special types of time development, i.e. differential and difference equations. In MAS, varieties of people can be included. People of different income, of different taste, of different opinion, and so on. Goods can be also very different. Firms may be different too. Evolution of behaviors can be implemented. MAS may open a new stage of economics. It is time to bet for it.

抄録全体を表示

This paper attempts to synthesize the famous Okishio theorem on Marx's theory of the falling rate of profit with what we call the 'Foley-Laibman theorem.' By presenting a comprehensive list of all of the possible cases in a biased technical change, the equilibrium rate of profit will be identified in relation to the real wage and the rate of exploitation. Using an explicitly dynamic framework, a plausible path of capital accumulation will also be provided. It follows that all of the possible cases analyzed in a comparative static setting consecutively emerge at each phase of the accumulation. According to our interpretation, the capitalist accumulation process at earlier stages is specified as the Invisible Hand game, which will eventually be transformed into the Prisoner's Dilemma game at later stages due to the changes in the conditions of capital accumulation.

抄録全体を表示

This paper presents a Kaleckian model of growth in which income distribution and technological progress are endogenously determined through class conflict between workers and capitalists. Using the model, we analyze the short-run and the long-run equilibrium. In the analysis we consider two kinds of effects caused by a rise in the employment rate. First, a rise in the employment rate exerts an upward pressure on wages (i.e., a reserve army effect). Second, a rise in the employment leads capitalists to adopt labor saving technology in order to intentionally create reserve armies of labor (i.e., a reserve army creation effect). These two effects are based on the idea of Karl Marx. The stability of the long-run equilibrium depends on the reserve army effect, the reserve army creation effect, and the relative bargaining power between workers and capitalists. In addition, the stability and results of comparative statics analysis depend on which regime is realized in the short-run equilibrium. If the short-run equilibrium is the wage-led growth and stagnationist regime, the long-run equilibrium is likely to be unstable with the strong reserve army effects, the weak reserve army creation effect, and the weak bargaining power of capitalists. These factors, on the other hand, lead the long-run equilibrium to be stable if the short-run equilibrium is the profitled growth and exhilarationist regime. If the short-run equilibrium is the profit-led growth and stagnationist regime, the long-run equilibrium is stable irrespective of the size of such effects. We investigate the relationship between bargaining power and unemployment in the long run. In the wage-led growth regime an increase in the bargaining power of workers lowers the unemployment rate while in the profit-led growth regime a decrease in the bargaining power of workers lowers the unemployment rate. In this way the relationship between bargaining power and unemployment depends on the regime which realizes in the goods market.

抄録全体を表示

Japanese corporate sector has continued to depress wages, while the current profits increased for the sixth consecutive year, and the dividends to shareholders reached their record levels in the consolidated financial statements at the end of March of 2008. This paper investigates the increased dividends to shareholders and depressed wages in the recent Japanese economy, from the viewpoint of the aims and consequences of the deregulation of M&A (mergers and acquisitions) activities since the late 1990s. Section 1 shows an increase in current profits, remuneration for directors and stock repurchases, along with stagnating wages, for firms with capital more than 1 billion yen, following the economic recovery of 2002, using the Financial Statements Statistics of Corporations by the Ministry of Finance. Section 2 investigates the deregulation of business activities under the pressure of the Japanese business circles and the United States. The Japanese business circles demanded the government to deregulate laws to promote concentration in core competence, aiming at overcoming the protracted recession and surviving the global competition. The United States demanded the Japanese government to lift the control on M&A activities through the cross-border share swap, as a way of promoting US direct investment in Japan. In line with these demands, the following deregulations were realized: the ban on pure holding companies was lifted in 1997; the share swap system and the share transfer system were introduced in 1999; the corporate divestiture system was introduced in 2001; the corporate law was revised to permit the cross-border triangular mergers in May 2007. Section 3 investigates the increased dividends to shareholders and depressed wages against the background of increased M&A activities. The above deregulations promoted M&A activities since 1997, with a rapid increase in M&A among domestic firms and in M&A of Japanese firms by foreign firms. Now that the ban on M&A through share swaps had been lifted, firms were forced to keep their stock prices up, emphasizing the return on equity. To this end, firms increased dividends to shareholders and implemented stock repurchases, with the help of stock options, while keeping wages at the same or lower level. This section shows that those industries with a higher percentage owned by foreign investors tended to have higher growth rate of total dividends relative to the growth rate of wages per capita, between 2001 and 2006, using the data from the Tokyo Stock Exchange and the Ministry of Finance. In conclusion, the deregulation of M&A activities since the late 1990s diversified the procedures for corporate restructuring and dividend payment, and affected the distribution of ownership of firms, with corporate management increasingly dependent on stock prices, and with employee wages kept at the same or lower level.

抄録全体を表示