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A note on re-switching, the average period of production and the Austrian business-cycle theory

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Abstract

According to a new formulation, the average period of production is calculated by taking the shares of costs referable to each period out of the total amount of costs as weights. Once this notion had been introduced, its inverse relationship with the rate of interest prompted some scholars to believe that it could serve as a good measure of capital intensity, expecially in view of a possible resumption of the Austrian business-cycle theory. As will be shown, however, this new average period poses some problems. On the one hand, the inverse relationship mentioned above does not preclude the re-switching of production methods. On the other, if re-switching occurs, the most roundabout method may paradoxically be the one that gives the smallest net output per worker. This result can affect the revival of the Austrian business-cycle theory.

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Notes

  1. An analysis of the different positions of the various authors lies beyond the aims of the present paper. Here we refer in general to the view of the rate of interest as the variable that brings households’ decisions about capital supply, in terms either of value or of ‘waiting’, into equilibrium with firms’ decisions about the employment needed to put optimal production plans into effect.

  2. In Böhm-Bawerk’s words:

    The adoption of capitalist methods of production is followed by two consequences, equally characteristic and significant. One is an advantage, the other a disadvantage. The advantage […] consists in the greater technical productiveness of those methods. With an equal expenditure of the two originary productive forces (that is to say, labour and valuable natural powers) more or better goods can be produced by a wisely chosen capitalist process than could be by direct unassisted production. […]

    The disadvantage connected with the capitalist method of production is its sacrifice of time. The roundabout ways of capital are fruitful but long; they procure us more or better consumption goods, but only at a later period of time. (Böhm-Bawerk 1891, p. 82.)

  3. While this is not the goal of the present paper, a couple of brief remarks can be made on this point. First, since capital is not a factor of production, it cannot have a real marginal product. Second, since the rate of interest is not the price for the use of capital, its equality with an alleged ‘marginal product of capital’ is essentially meaningless.

  4. See Lewin and Cachanosky (2018a) for a reconstruction of the history of the concept of the average period of production.

  5. For some critical assessments of these contributions, see Hagemann and Kurz (1976), Orosel (1979, 1990), Howard (1980) and Fratini (2013, 2014).

  6. Similar claims can also be found in Cachanosky and Lewin (2016) and Braun (2017).

  7. Cachanosky and Lewin have made a number of contributions on capital theory in recent years. An in-depth analysis of their standpoint goes far beyond the aims of this note, in which we will instead try to focus attention on this specific statement.

  8. We discuss here a typical Austrian model in which output is obtained by the employment of labour at different dates. In this model, capital is the amount of value invested in order to pay wages in advance, before the output is obtained and sold.

  9. Similar figures can be found, for example, in Jevons (1888, p. 229) and Wicksell (1934, pp. 152 and 159).

  10. All the figures presented in the present paper are based on the following numerical example. Method A: a1 = 2; a2 = 7; a3 = 1. Method B: b1 = 8; b2 = 2; b3 = 2. Readers can use these coefficients to obtain the results discussed here. Similar examples can be found, for instance, in Samuelson (1966, p. 569), Harcourt (1972, pp. 151−52), Steedman (1972, p. 45) and Yager (1976, pp. 317–18).

  11. As is known, ‘labour commanded’ is a measure of value adopted by Adam Smith. The value of a commodity in terms of labour commanded is the amount of labour that can be purchased with one unit of this commodity.

  12. Since we are studying price-taker firms’ decisions, the rate of interest can be considered as an exogenous variable and we can give it arbitrary values.

  13. In fact: \( d\left({p}_a/{p}_b\right)/ dR=\left[\left(d{p}_a/ dR\right){p}_b-\left(d{p}_b/ dR\right){p}_a\right]/{p}_b^2=\left({p}_a/{p}_b\right)\left({\Theta}_a-{\Theta}_b\right)/R \).

  14. See, for instance, von Weizsäcker (1971, p. 65) and Malinvaud (2003, p. 518).

  15. Similar reasoning and figure can be found in Sraffa (1960, p. 38).

  16. Since in the present analysis, for the sake of simplicity, we can consider the participation rate as independent from the price system, the variations of the output per capita go in the same direction as the variations of the output per worker.

  17. It can be incidentally stressed that, in Samuelson’s view, the possibility of an ‘unconventional relation’ between the rate of interest and the final output is ‘the single most surprising revelation from the re-switching discussion’ (1966, p. 577, footnote 6).

  18. For an in-depth reconstruction of the working of the Austrian business-cycle theory and the Hayek-Keynes-Sraffa controversy on it, we can refer the reader to Kurz (2000, 2015).

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Acknowledgements

Thanks are due to C. Gehrke, G.C. Harcourt, H.D. Kurz and two anonymous referees for comments and suggestions. The usual caveat applies.

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  1. Dipartimento di Economia, Università di Roma Tre, Via Silvio D’Amico, 77, 00145, Rome, Italy

    Saverio M. Fratini

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Fratini, S.M. A note on re-switching, the average period of production and the Austrian business-cycle theory. Rev Austrian Econ 32, 363–374 (2019). https://doi.org/10.1007/s11138-019-0432-0

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