The purpose of this paper is to make clear the following points. The significance and the limitation of Marx's reproduction theory lies in grounding the economic crisis structually, by setting so called "inner contradiction," i.e. one between the tendency of capital to develope the production without limit and the relations of reproduction to limit it: proportions of industrial branches and limited consumption as a mediater, into the schema of reproduction, i.e. a manifestation of ideal self-reproduction system of a bourgeois society abstracting foreign trades in the world of value or surplus value. Tomizuka Theory, in which Marx's crisis theory seems to be reorganized as a. kind of expanding equilibrium model with limit, is characterlized especially by the unique comprehension of the relationship between crisis theory and reproduction theory, where the schema of reproduction is considered an apparatus not for affirming the contradiction in the structure but for detecting disequilibrium in the "dynamic state". In the meantime Prof. Tomizuka elaborates the equilibrium conditions and assers that so called "equilibrium accumulation track", which is a kind of expanding equilibrium one to keep the given proportion of productive branches constant, belongs to Marx. But the formative process of Marx's reproduction theory shows that Prof's comprehension and assertion is different from what Marx intended. That is, it can be admitted that Marx used the inner relationship of unity of capitals as the detective standard of disequilibrium in relating the so called "Original Schema" with crisis theory in "Grundrise", but it is because he considered the crisis theory in competitive rather than in structual at that time, however,we can also find the origin of the structual achievement there. But, on the other hand, the formative process shows that such a weekpoint, together with other ones that the branches expand with the same proportion (rates) and that the revolution in productive force is treated simultaneously, is rectified through "Mehrwert". We cannot admit that Prof. Tomizuka takes such process in consideration. Kuruma Theory is also characterilized by the unique comprehension of the relationship between reproduction theory and crisis theory which denies so called "inner contradiction". That is, Prof. Kuruma maintains that the point in the reproduction theory is the logic that the fluctuation of accumulation rate produces "troubles" through changing the ratio of branches, which is connected with another unique understanding that the fall of the profit rate makes the accumulation rate fall and thus crisis breaks out. But the theory of the "transision from simple reproduction to extended': lying under such comprehension and consisting its basis, has lost its ground finally with the appearance of the 8th maniscript of "Kapital" II. The ruin of the "transision theory" and the confirmation of the theory of accumulation mechanism by the manuscript, together with the formative process, seems to force both Tomizuka and Kuruma Theories that deny the contradiction in the structure to be reconsidered.

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With respect to the relation of depreciation and replacement of fixed capital in simple reproduction, K. Marx solved this problem in his "Das Kapital". But the problem on expanded reproduction is not yet fully discussed. This article is devoted to the analysis of the some pending questions related to the movement of fixed capital in the condition of expanded reproduction of social gross capital. In expanded reproduction, depreciation (D) and replacement (R) of fixed capital is not equal in the amount, and D is inevitably greater than R. The difference of D and R, (D-R), is realised by the additional expenditure on fixed capital. This additional expenditure of (D-R) is requisite condition of normal expanded reproduction process. The money used for this additional expenditure must be mobilized from the depreciation funds that are free in this period. As a result of the realisation of (D-R), the amount of fixed capital in natural increase and the reproduction on expanded scale occures without capital accumulation, i, e., conversion of surplus value into capital. Owing to the peculiar nature of turnover of fixed capital, the total value of fixed capital has dual form in natura and money. The realisation of (D-R) which is achieved by the free depreciation funds brings about the value of fixed capital in natura and the decrease of the same value of fixed capital in money form. Therefore, total value of fixed capital remains unchanged after the realisation of (D-R). In respect of fixed capital, two conditions, D=R+(D-R) and (D-R)< the amount of the free depreciation funds in this period, are nothing but requsite coditions for the normal proceeding of expanded reproduction. The anarchic nature of capitalist reproduction process, however, converts the above two conditions into one for the abnormal proceeding of expanded reproduction.

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本稿は,江戸時代後半(18世紀半ば以降)における武士,なかでもとくに大名家臣を対象として彼らの人口再生産レベルを検討した。江戸時代の武士については,人口のすら困難であったと推測されてきた。たしかに,これまでいくつかの藩の大名家臣に関しては,彼らの出生力は低かったことが報告されている。しかしながら,低出生力とはいえ,それがを下回る水準にあったかどうかは検討されていない。なぜなら武士人口を考察する際に利用されるおもな記録史料である系譜からはそれを検討するための再生産率などの出生力指標が得られないからである。そこでマイクロシミュレーションの手法を用いて,この間題に接近した。いくつかの藩では,大名家臣の系譜から,当主がもうけた成人男子の平均や既婚当主がもうけた男子の平均などがすでに求められている。それらとシミュレーションの結果との比較によって,再生産レベルを推測することができると考えた。用いたプログラムはケンブリッジグループにおいて開発されたCAMSIMである。このシミュレーションプログラムによって,を実現する仮想人口を作り出した。さらに,シミュレーションのなかで"当主"を定義したうえで,"当主"のもうけた,15年以上生存した男子の平均や既婚"当主"のもうけた男子の平均を計算した。そして,系譜から求められているそれぞれの数値との比較を試みた。シミュレーションの結果から得られた数値と系譜から求めた数値はほぼ等しかった。このことから,少なくとも,これまで平均男子数が求められているいくつかの藩の大名家臣については,自らによって人口を再生産していた可能性が十分にあることを指摘することができた。

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Examinations to carry out the formation of the optimum distribution of resources and labor by the calculation of labor expenditure without using money, was performed among socialists before. This thought was inherited in the Soviet Union. When it thinks that it can produce stock such as machinery by labor and stock, it is labor that is scarce eventually. But when think in each period; stock which received from the before period is limited and total labor in this period is limited, so that consumption in this period decreases when labor and stock which are necessary for increase the stock, are allocated. Therefore, when products are evaluated by the value that economists in classical school and Marx calculated by labor, we cannot achieve the optimum allocation. In the Soviet Union, Novozirof (1959) and Kantorovich (1959) are showed the optimum allocation in the solution of linear programming, but they did not succeed in leading it only from labor expenditure. In this paper I show the calculation formula of the appropriate evaluation of products by labor expenditure which can lead the optimum solution. We can calculate the quantity of labor necessary directly and indirectly to produce one unit of product from using simultaneous equations. It is equal to the quantity of labor that is necessary to produce a unit of net product. Similarly we can calculate the quantity of stock directly and indirectly to produce one unit of product from using similar simultaneous equations. Even if stock consists of having many kinds, when the stock is produced in labor and stock, we can add it up by the quantity of labor that is necessary to produce it directly and indirectly. I'll call 'cost' that x+ξ・z; x is the quantity of labor necessary to produce one unit of net product, z is the quantity of stock evaluated by labor that is necessary to produce it directly and indirectly, and hung a coefficient ξ for saving stock. Because the government appoints an appropriate coefficient ξ and companies choose production methods to minimize costs, we can achieve the most suitable production formation. What we should pay attention to is for the profit that is income not to enter in a calculation formula. The coefficient for saving stock is not income. Another point to pay attention to is that the production price in capitalist production system is approximation of the most suitable calculation by labor. But concerning space, I am going to explain it in detail in the next article in this connection. In addition, in a sign, y is durability, ζ is the quantity of the stock necessary for production per a unit and z is its total evaluation by labor. And c is consumer goods, e is first producer's goods, d is second producer's goods. About subscript, lower first is a number of output products, lower second is a number of in-put goods, upper (right corner shoulder) is a number of production methods.

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