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Further Mathematics for Economic Analysis

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Additional info for An Outline of the Dialectic of Capital: Volume 2

Sample text

Thus, the present theory requires that the switching of the old for a new technique should be accomplished with the shortest delay, subject to the condition aE(T) = K{T) at the terminal point. Let X(t) be the output of cotton yarn produced with the innovative technique, and Y(t) that produced with the conventional technique. ] X(t). (1) Let Z(t) be the social demand for cotton yarn, which, for simplicity, may be assumed to grow exponentially at rate g, so that Z(0 = V". (2) If X(t) is the proportion of X(t) in the total output of cotton yarn, we have I X(t)Z(t) = X(t), I [1 - X(f)]Z(f) = y(0, where 0 g X(t) S 1, X(0) = 0.

Thus, in the simplified context in which only one capital good exists, fixed capital does not exist, and all turnover frequencies of capital are equal to one, the first law of average profit has been demonstrated. More complicated cases have been treated elsewhere (see The Dialectic of Capital, vol. 2). Let us revert to the numerical example (T*) above, and assume that (18) holds. 00416. Hence, we have (Q* 9>. 631), 28 The Doctrine of Distribution and it turns out, by chance, that k = ky. 631) Jtz < k.

They are subject to contingencies and cannot be predicted due to varying combinations of technical and commodity-economic factors. 38 The Doctrine of Distribution What is required of the theory here is to explain the method of synthesising the "value-determining social technique" from the concurrently employed multiple techniques, once given any arbitrary set of marginal response ratios. The same social technique can be used to determine the marketregulating production-price. 1368. 1737. The difference between the market and the individual production-price measures the surplus profit (positive or negative) earned by the technique, per unit of the commodity.