Abstract
In this chapter we provide some continuity results for Sraffa price system which include subsistence consumption in the matrix of intermediate inputs, but which allow for wage level fluctuations around the subsistence wage level, assuming thereby ex post wage payments only with respect to this deviation from the subsistence wage level. These continuity results all concern a neighborhood of the maximum rate of profit R derived from the subsistence wage situation. An economic consequence of theses mathematical results is that the concept of ‘basic commodities’ needs reformulation from the empirical point of view, since it may (on the physical level) include basics of very minor importance (‘pencils’). These types of commodities must in some way or another be classified as non-basics. They should also not be considered as giving rise to switches of techniques when ball-pens are replacing pencils, in case this latter commodity is no longer available. From a broader perspective, these observation again suggest that the basic/non-basic distinction cannot be meaningfully applied to the highest level of disaggregation (the physical level), but must be reconsidered in its usefulness after some aggregation for appropriately chosen aggregated sets of commodities and aggregated methods of production. This again suggests that an input–output oriented approach as in Bródy (1970), concerning fixed capital, semi-finished products, and now also the notion of basic commodities will be the better choice compared to the physical one that was chosen by Sraffa and his followers.
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Notes
- 1.
A ≥ 0 is the quadratic matrix of physical inputs of a simple input–output system and is assumed to be productive, i.e., \(y = x - Ax > 0\) for a given x = (x 1, …, x n )t (a column), the gross industry output vector. l > 0 (a row) is the vector of direct labor inputs and p, w, r ≥ 0 denote the usual system of production prices (a row) and its wage and profit rate; for details see Pasinetti (1977, Chap. 5) or Weizsäcker (1971, Part II).
- 2.
I the identity matrix
- 3.
λ(A), R(A), if explicit reference to the matrix A is necessary.
- 4.
This notation means that the point R is to be excluded.
- 5.
cf. also the exchange of views between Sraffa and Newman in Bharadwaj (1970).
- 6.
The first s commodities then describe the basic sector of the given input–output system.
- 7.
Example: Electric energy. This condition implies that R is finite and that the economy cannot be decomposed into two unconnected parts.
- 8.
cf. Sraffa (1976, Appendix B).
- 9.
- 10.
Cf. Appendix 6 in Sraffa (1976).
- 11.
\(M(n \times n; \mathcal{R})\) the vector-space of all n ×n-matrices with real coefficients.
- 12.
for simplicity written as ‘A’ in the following.
- 13.
We do not question here the analytical usefulness of such a theory.
- 14.
One may think of a commodity which normally will be used as a consumption good only, but is also used as an input in the production of a ‘true basic’ in a very small amount.
References
Bharadwaj, K. (1970). On the maximum number of switches between two production systems. Schweizerische Zeitung für Volkswirtschaft und Statistik, 106, 409–429
Blackley, G. R., & Gossling, W. F. (1967). The existence, uniqueness and stability of the standard system. Review of Economic Studies, 34, 427–431
Bródy, A. (1970). Proportions, prices and planning. North Holland: Amsterdam
Diedonné, J. (1960). Foundations of modern analysis. New York: Academic
Miyao, T. (1977). A generalization of Sraffa’s standard commodity and its complete characterization. International Economic Review, 18, 151–162
Nikaido, H. (1968). Convex structures and economic theory. New York: Academic
Pasinetti, L. (1977). Lectures on the theory of production. London: Macmillan
Schefold, B. (1976). Relative prices as a function of the rate of profit: A mathematical note. Zeitschrift für Nationalökonomie, 36, 21–48
Seneta, E. (1973). Non-negative matrices. London: George Allen & Unwin
Sraffa, P. (1976). Warenproduktion mittels Waren. Frankfurt a.M.: Edition Suhrkamp, Bd. 780
Varga, R. (1962). Matrix iterative analysis. Englewood Cliffs, New Jersey: Prentice Hall
Weizsäcker, C. C. V. (1971): Steady State Capital Theory. Heidelberg: Springer
Zaghini, E. (1967). On non-basic commodities. Schweizerische Zeitschrift für Volkswirtschaft und Statistik, 103, 257–266
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Flaschel, P. (2010). Some Continuity Properties of a Reformulated Sraffa Model. In: Topics in Classical Micro- and Macroeconomics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00324-0_10
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