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Weight of Commercial Sector and Reproduction Scheme Hiroshi ONISHI Keio University, JAPAN

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Japanese Tradition of Mathematical Marxism Nobuo Okishio

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Reproduction Scheme with Commercial Sector W1=c1+v1+m1 W2=c2+v2+m2 Wc=cc+vc+mc In this case, total supply = demand of the means of production 　c1+v1+m1=c1+c2+cc ⇒　v1+m1=c2+cc total supply = demand of the means of consumption 　c2+v2+m2=v1+m1+v2+m2+vc+mc ⇒　 c2=v1+m1+vc+mc

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commercial sector is not productive substituting the above 2nd equation for the 1st equation leads v1+m1=c2+cc=v1+m1+vc+mc+cc ⇒ 0= cc+vc+mc= Wc It means commercial sector is not productive at all.

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In the case of Extended Reproduction Scheme W1=c1+v1+m1(c)+m1(v)+m1(k) W2=c2+v2+m2(c)+m2(v)+m2(k) Wc=cc+vc+mc(c)+mc(v)+mc(k) In this case, also Wc=cc+vc+mc(c)+mc(v)+mc(k)=0

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additional surplus value > cost and transferred surplus of commercial sector . Where r is the profit rate of one turnover.

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Ratio of (Cc+Vc)/(Cp+Vp) Just a transform from the above inequality leads On the equilibrium

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Ratio of Wc/(W1+W2) If we set z=, and profit rate is equalized between both sectors, Wc=z (W1+W2) =z (c1+c2+v1+v2+m1+m2) But, how can we determine average profit rate r ? For this question, we need to solve the transformation problem.

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Iterative Method of Transformation from Value to Price of Production W1=c1+v1+m1 W2=c2+v2+m2

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transform 3 equation system in the same way W1=c1+v1+m1 W2=c2+v2+m2 Wc=z (c1+c2+v1+v2+m1+m2)

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Implications of the that equation system ①The first two equations and W1*+W2*=W1+W2 can determine three variables: W1*, W2* and r* independently from the commercial sector. ②Sale and Profit in the commercial sector Wc* are z times larger than in the industrial sectors. ③z is determined by the technologies Δp, Δc and Δc’ and by r* which is determined by the industrial sectors.