ON THE CONVERGENCE OF MARX'S 'TRANSFORMATION'PROCEDURE

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  • Marxの「転形」手続の収束性
  • Marx ノ テンケイ テツズキ ノ シュウソクセイ

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Abstract

In the chapter 9 in "Das Kapital, " Vol. III, Marx gave the following procedure to transform "value" into "production price"; Wt+1=(1+rt)AWt rt=e(E-A)Wt/eAWt (*) where e=(1, 1, …, 1) and W1t Wt= A=Wnt aij=(Cij+Vij)/Wj0 Wi0=∑jCij+∑jVij+Mi.<br>W0, Wt denote "value" vector and the t-th "transformed value" respectively. ∑Cij is "constant capital" in terms of "value" in the i-th sector. ∑Vij is "variable capital". Mi denotes "surplus value" in the i-th sector. rt shows the average rate of profit at Wt.<br>Marx himself showed only the first step by a numercial example; W1=(1+r0)AW0=(1+r0)(C+V) r0=e(E-A)W0/eAW0=∑Mi/∑Ci+∑Vi where C1+V1 Ci=∑Cij C+V= CN+VN Vi=∑Vij.<br>In this note we show the convergence of Marx's transformation procedure (*); limt→∞ Wt=W* limt→∞ rt=r*

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