Abstract
In this chapter we go from the sphere of the production of commodities to the sphere of their circulation, by means of the theoretical as well as the empirical investigation of the Classical concept of prices of production which is based on the principle that there is a single uniform rate of profit for all activities that are organized on a profit-oriented basis. We start the Classical theory of price formation at first in its most basic setup, and then with increasing generality, in order to show how long-period prices of production may be formulated in more and more general models of production. We also provide a brief survey on the mathematical tools that are needed for the proof of basic Classical assertions on the properties of such long-period accounting prices which shows that indeed quite sophisticated mathematical theorems are needed for this purpose, for proving things that the Classical authors (including Marx) simply took for granted. Our findings will be that the search for the foundations of a Classical theory of competition has by no means been a successful one so far. On the theoretical level, we find that the analysis of the process of the circulation of capital has by and large ignored the many factual accounting principles that are involved in and indeed are governing this process and that are needed for proper production price calculations in general production systems. And on the empirical side, we come to the conclusion that the principle of imposing a single uniform rate of profit on all profit-oriented activities of the (world) economy is simply going too far in the pursuit of finding useful and applicable long-period prices for the factual analysis of existing economies. Sectoral profitability studies are urgently needed for the proper formulation of long-period prices but are rarely done by the proponents of the Classical theory of prices of production.
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- 1.
Note that we here assume as in the crude state of the society that wages are paid ex ante and thus represent capital advanced on which profits have to be earned.
- 2.
The type wage profit curve here considered need not be strictly convex in higher dimensional commodity spaces.
- 3.
In the present case the real wage ω is still equal to the consumption basket c of worker households, since this basket here consists of the corn commodity solely. We therefore allow now for variable real wages (which leads us away from the pure subsistence level assumption), but not yet for multiple commodities in workers’ physical consumption.
- 4.
since real wages \(\omega= w/{p}_{1}\) are paid ex ante.
- 5.
\(\bar{\upsilon }\) the velocity with which the quantity of money M is turned over.
- 6.
We do not consider here as in Sraffa (1960) wages that are paid ex post, but refer the reader to Chap. 9 for their treatment as surplus wages or deficit wages with respect to the here considered given consumption basket of workers. The reader is referred to Kurz and Salvadori (1995), Schefold (1997) and Bidard (2004) for detailed treatments of many aspects of Sraffa’s (1960) approach to the production of commodities by means of commodities.
- 7.
This price concept is not restricted to the consideration of production prices schemes.
- 8.
Note also that the matrix A 11 represents a principal minor of the matrix A.
- 9.
This is a quite natural assumption, since the matrix A 22 neglects all inputs of the basic sector into the sector of the non-basic commodities.
- 10.
and old machine vintages if fixed capital is considered in addition.
- 11.
The input and output structure A, B may be called decomposable if there is a proper subset of goods that can be produced by using only inputs from this proper subset.
- 12.
See Bidard (1986) for details.
- 13.
With straight line depreciation and immediate reinvestment of depreciation turnover-time is one-half of life span.
- 14.
This part of the chapter is based on Flaschel and Franke (2008, Chap. 4) where further details on its arguments can be found. I have to thank Reiner Franke for allowing to reuse the material from there for the following sections. The reader is moreover referred to Bródy (1970) for the general input–output methodology that is underling the following sections.
- 15.
See, e.g., Semmler (1984, p. 106) for this classification.
- 16.
- 17.
is the last year for which presently real data on depreciation are available. This is the main reason why in the empirical tables before we have not presented more recent data.
- 18.
Formally, it suffices to replace the inequality signs with an equality sign in the proof of Proposition 8.10.
- 19.
We should not, as it is possible with the other sectoral variables, use r to denote the profit rate vector, because this might lead to confusion in other parts of the book where r as a uniform rate is just a scalar. On the other hand, we do not wish to employ another letter for this purpose. Therefore the compromise with the (otherwise unnecessary) vector arrow above the letter r, which we below we equally apply to the vector of the differentiated real wage rates (ω1, … ω n ).
- 20.
The basic idea of the following treatment can be found in Giannini (1976), though his wages are still uniform.
- 21.
We have checked this by magnifying and also distorting the proportions of this panel. The phenomenon is interesting since the consumption vector still differs (not too much but significantly) from the right-hand eigen-value x k of the matrix \(A{D}_{k}^{r}{(I - A)}^{-1}\), where the relevance of this observation derives from the fact that the ω k -r k relationship is linear if ω k is expressed in terms of x k.
- 22.
The following sections are based on Flaschel and Franke (2008) and the reader is referred to this work for the flow matrices here referred to. The inclusion of the following discussion, taken from Flaschel and Franke (2008), here serves the sole purpose to show that prices of production are much too simplistic and restrictive in their formulation from the empirical point of view. Moreover they are not needed for the analysis of the implications of factual average price changes as we have shown in the second part of Chap. 3.
- 23.
The coefficients k ij can be added up in a column j if we recall that empirically they all have the unit ‘worth 1 mill. Euro in prices of 1995’. Naturally, the same applies to the κ i .
- 24.
Since after 1995 wages and depreciation are only available as nominal data, we used nominal data for the whole decade. This, in particular, means that the capital stock coefficients here obtained are nominal magnitudes, which does not matter as long as we are only interested in the profit rates.
- 25.
The best year was 2000, for which unfortunately we have not sufficient data to continue our computations.
- 26.
see Bródy (1970) for the needed changes in treating such issues.
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Flaschel, P. (2010). In Search of Foundations for a Classical Theory of Competition. In: Topics in Classical Micro- and Macroeconomics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00324-0_8
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