Download PDF by Prof. Martin J. Beckmann (auth.), Prof. Dr. Gerhart: Contributions to the Von Neumann Growth Model: Proceedings

By Prof. Martin J. Beckmann (auth.), Prof. Dr. Gerhart Bruckmann, Prof. Dr. Wilhelm Weber (eds.)

ISBN-10: 366222738X

ISBN-13: 9783662227381

ISBN-10: 3662246678

ISBN-13: 9783662246672

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Read Online or Download Contributions to the Von Neumann Growth Model: Proceedings of a Conference Organized by the Institute for Advanced Studies Vienna, Austria, July 6 and 7, 1970 PDF

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Additional resources for Contributions to the Von Neumann Growth Model: Proceedings of a Conference Organized by the Institute for Advanced Studies Vienna, Austria, July 6 and 7, 1970

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237, 238). 1. M is compact. Proof. It sufficies to show that M is closed in C* (G). ) is in N X yn+l, I shall write i (g)= i,x (g)= x, and y 1 (g)= Yi> j = 1, ... , n. 6). 2). Let (ma) be a sequence in M, converging to m in C* (G). ) converges to Pm• where Pm,. and Pm are considered as elements of C* (S), with the C (S), or weak*, topology on C* (S). ) converges to qm. Since the sequence (ma) is in M, Pma = qm,. 3) Furthermore, for eacll i in N define a function hi on S by ~ (;, x) s Give N the discrete topology, the product topology.

Let (gO, :n°, x 0 , p 0) be any von Neumann solution. It is well known that g 1 > g0 > g,, so that we suppose g1 ~ g0 > gi+ 1 for some i. Now partition x0 and p 0 into r classes, respectively. Then we find that either x(~) =F 0 for some s i, or 0 P<~> =I= 0 for some 8 < i. Otherwise we would obtain x0 B p = 0 because of the triangularity of B, so that (g 0 , :n°, x 0 , p 0) could not be a solution. Suppose x<~> =F 0 for some 8 i. Then it is obvious from the definition of the sth Consumption-investment Frontier that g 0 cannot be greater than g 8 • But g0 g1+ 1, a contradiction.

It is well known that g 1 > g0 > g,, so that we suppose g1 ~ g0 > gi+ 1 for some i. Now partition x0 and p 0 into r classes, respectively. Then we find that either x(~) =F 0 for some s i, or 0 P<~> =I= 0 for some 8 < i. Otherwise we would obtain x0 B p = 0 because of the triangularity of B, so that (g 0 , :n°, x 0 , p 0) could not be a solution. Suppose x<~> =F 0 for some 8 i. Then it is obvious from the definition of the sth Consumption-investment Frontier that g 0 cannot be greater than g 8 • But g0 g1+ 1, a contradiction.

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Contributions to the Von Neumann Growth Model: Proceedings of a Conference Organized by the Institute for Advanced Studies Vienna, Austria, July 6 and 7, 1970 by Prof. Martin J. Beckmann (auth.), Prof. Dr. Gerhart Bruckmann, Prof. Dr. Wilhelm Weber (eds.)


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