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By Malinvaud E & Bacharach M

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Extra resources for Activity Analysis in the Theory of Growth and Planning: Proceedings of a Conference held by the International Economic Association

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The highest proportional growth rate subject to the condition that there be a human population is clearly IL** =2. \)y2)J is also in Z. •. •. 16 Koopmans - Economic Growth at a Maximal Rate TABLE II BASIC ACTIVITIES AT DEFINING UNIT LEVELS'*' Reproduction oft (1) (2) Rabbit Human Population Population Outputs (1) rabbits (2) people 100 Inputs (1) rabbits (2) people 1 2 500 1 • The defining activity of process (2) is not normalized. t One time-unit 25is years. commodities from the economy. Such a hierarchy has been studied by Kemeny, Morgenstern, and Thompson (1956) and by McKenzie (1963d).

And Inada, K. (1962). 'Balanced growth and intertemporal efficiency in capital accumulation', International Economic Review, vol. 3, no. 1, January 1962, pp. 94-101. Gale, D. (1956). 'The closed linear model of production', in Kuhn, H. , and Tucker, A. W. ), Linear Inequalities and Related Systems, Princeton University Press, pp. 285-303. Georgescu-Roegen, N. (1951). 'The aggregate linear production function and its applications to von Neumann's economic model', chap. iv of Koopmans, T. C. ), Activity Analysis of Production and Allocation, Wiley, New York, pp.

K. It follows that 1r(xA, yA)=O for h=1, ... , k. 1 20 Koopmans - Economic Growth at a Maximal Rate Hence p1 /P 2 is the slope of y 2 on y 1 read off from that line. In Fig. 7 this slope is uniquely determined by the smooth shape of Z. A limited indeterminacy in p 1(p 2 can arise, for instance, if z* should just happen to be a vertex of a polyhedral Z. It will be useful later if we also determine the slope of the line z in which P intersects the x1 -y 2-plane. ) From (P) we have, if y 1 = 0, P2Y2 = fL* (Ptxl + P2(1 - xt)) = P-""

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