Abstract
Picking up with the results of the discussion of the thirties, demonstrated in Chapter 2, Section 2.3, we want to show now that as early as 1937 the von Neumann-model indicated a way out of the theoretical dead-end, in which Austrian capital and interest theory found itself.
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This chapter is to a great extent identical with Faber and Irsigler [1978], the latter again is a reworked rendition of the third part of Faber [1973].
With the exception of Schumpeter [1911] and von Hayek [1941] the most important representatives of the Austrian capital theory as Wicksell, Akerman/ von Stackelberg and the neo-Austrian as Bernholz, Fehl, Hicks, Jaksch, Reetz, and von Weizsäcker are not Austrians.
A demonstration of these theorems and corresponding literature can be found in Morishima [19643.
Beckmann [1971] demonstrates how von Böhm-Bawerk’s concept of a production period can be introduced into the von Neumann-model and which relations exist between it and some other economic variables, especially the capital stock.
It was pointed out (Faber [1973,p.29]) that the structure of von Neumann ‘s model is more encompassing than those of the von Böhm-Bawerk-Wicksell systems. Under certain circumstances the von Neumann-model can be given an Austrian, intertemporal interpretation. Burmeister [1974] showed this for a generalized von Neumann-model in which one primary factor, labor, and one consumption good are explicitly considered. Burmeister’s conclusion goes even further in that he demonstrates that an intertemporal interpretation of this type can under certain conditions also be applied to the technology of Hicks’[1973] model, which encompasses the Austrian approach. See also Faber [1975] and Chapter 9 below.
H.J.Jaksch called our attention to a problem of this interpretation for the following reason: As capital goods are subject to continual quality change, and as each can be utilized within the limits of its capacity there are an infinite number of goods to be considered. It follows, that there are more than a finite number of components to every process and/or there are more than countably many activities. This means that the conditions of finite-dimensional production technology no longer hold.
Until von Neumann published his paper, equilibrium had almost always implied a stationary system.
This condition was first formulated by Kemeny, Morgenstern and Thompson [1956], It guarantees equality of α anβ $ which was no longer insured after Assumption 3.3 had been exchanged for 3.3′; furthermore it excludes certain pathological cases which could occur in the original von Neumann model. (See Kemeny, Morgenstern and Thompson [1956, p.118]).
Using weaker conditions than Gale, Jaksen [1977] states necessary and sufficient conditions of equality between α and ß.
Economically this precondition means: it is impossible to disaggregate the economy into two or more parts such that the subsystems are independent of one another, that is to find divisions which produce goods only needed in that system. — The condition of irreducibility is also guaranteed by von Neumann’s Assumption 3.3.
One result of this generalization (Morishima [19643) is that the equilibrium interest rate equals the ratio between the steady state growth rate and the capitalists’ saving propensity. For a short description see Burmeister [1970].
In the 1970s von Weizsäcker [1971a] and Fehl [1976] redefined the concept of the average production period for steady state growth paths under the following assumptions: fix capital does not exist and labor is the only primary factor.
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© 1979 Springer-Verlag Berlin Heidelberg
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Faber, M. (1979). The von Neumann-Model and its Relations to Austrian Capital and Interest Theory. In: Introduction to Modern Austrian Capital Theory. Lecture Notes in Economics and Mathematical Systems, vol 167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48310-3_3
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DOI: https://doi.org/10.1007/978-3-642-48310-3_3
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