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A Reflection on Sraffa’s Revolution in Economic Theory
The aim of this chapter is to contribute to our understanding of the relation between Leontiefbased and Sraffabased modelling. To this end we take a second look at the core properties of models belonging to either of these ‘schools’. We focus on the wellknown open static Leontief model with one primary factor, and explore how this model behaves if we replace the traditional input coefficients matrix by a matrix of extended input coefficients that capture the real pay accruing to the wage earners. We show that capital can be straightforwardly introduced, and that this model generates a precise expression for the relation between the rate of profits and the wage rate. We finish by discussing the connections between this ‘extended’ Leontief model and Sraffa’s single product models.
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In this context the term ‘primary’ means that the production of this factor is not explained by the model.
Matrices and vectors are in bold type, scalars in standard. Vectors are column vectors, row vectors are indicated by an apostrophe.
See also the next section on additional properties of the system.
We assume that each industry employs labour, thus
l′ > 0.
Each element of the vector
f/
L is equal to the corresponding element of the vector
f divided by
L.
Note: if
p′(
f/
L) = 1
and L = 1,
w stands for the value of the economy’s net income.
These properties are basically selfevident. Indecomposability e.g. prevents that there are subsystems capable of (re)production without inputs, directly or indirectly, from sectors not belonging to that subsystem. The full rank property means that there are no industries using the same technology. A dominant eigenvalue smaller than 1 guarantees that a surplus is possible. For further details, see e.g. Takayama (
1974) or Seneta (
1981).
See also footnote 4. With
f > 0 and
l′ > 0 also matrix (
f/
L)
l′ > 0 and, consequently, matrix
M.
That is, each element of
A is multiplied by α in the new configuration.
For further background, see Steenge and Serrano (
2012), or Steenge (2015).
However, we should point out again that the choices we have made in this section only are one example of possible extensions. Future work may be called for to explore further possibilities.
Matrix
A in this model is assumed to have the same properties as matrix
A in the Leontief model of Sect.
2.
Symbols have the same interpretation as before.
We observe that vectors
f and
x are not proportional to each other, so there is no role for the Standard commodity, see the next section.
Sraffa is of course aware of the possibility that wages may at least in part consist ‘of the necessary subsistence of the workers’ and would thus enter ‘the system on the same footing as the fuel for the engines or the feed for the cattle’ (Sraffa
1960, p. 9). However, he decides to ‘follow the usual [postclassical] practice of treating the whole of the wage as variable’ (Sraffa
1960, p. 10).
Different types of closure in the two cases of stationary (or semistationary) conditions and of sustained growth are discussed in Quadrio Curzio and Scazzieri (
1986), who introduce a distinction between the representations of production technology corresponding to the two above states of the economy (
transformation apparatus and
structural apparatus, respectively).
The concept of ‘Take Out’ has been introduced in John Hicks’s
Capital
and Time as ‘the difference between value of output and value of input’ (Hicks
1973, p. 30). Here it is used as a general expression to denote what is left after subtracting from the gross product the physical quantities needed to cover the selfreplacement of means of production and workers’ consumption.
See Morishima (
1966, p. 521) for an alternative proof of this proposition.
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The Socialist Price Mechanism, Durham, NC, Duke University Press.
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Resources, Production and Structural Dynamics, Cambridge, Cambridge University Press, pp. 107–25.
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The Structure of American Economy
, 1919–1929, Cambridge, Harvard University Press.
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Structural Change and Economic Dynamics, 2 (1, June), pp. 181–212.
go back to reference Morishima, M. (1966) ‘Refutation of the Nonswitching Theorem’, The Quarterly Journal of Economics, 80 (4, November), pp. 520–25, https://doiorg.ezp.lib.cam.ac.uk/10.2307/1882913 (accessed 25.2.2020). Morishima, M. (1966) ‘Refutation of the Nonswitching Theorem’,
The Quarterly Journal of Economics, 80 (4, November), pp. 520–25,
https://doiorg.ezp.lib.cam.ac.uk/10.2307/1882913 (accessed 25.2.2020).
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Foundations of Economics. Structures of Inquiry and Economic Theory, Oxford and New York, Basil Blackwell, pp. 377–407.
go back to reference Sinha, A. (2016) A Revolution in Economic Theory: The Economics of Piero Sraffa, Basel, Springer. CrossRef Sinha, A. (2016)
A Revolution in Economic Theory: The Economics of Piero Sraffa, Basel, Springer.
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go back to reference Sraffa, P. (1960) Production of Commodities by Means of Commodities, Cambridge University Press. Sraffa, P. (1960)
Production of Commodities by Means of Commodities, Cambridge University Press.
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Resources, Production and Structural Dynamics, Cambridge, Cambridge University Press, pp. 107–25.
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go back to reference Steenge, A. (2020) ‘From Multipliers to the Distribution of Income: Connecting Leontief and Sraffa’, this volume. Steenge, A. (2020) ‘From Multipliers to the Distribution of Income: Connecting Leontief and Sraffa’, this volume.
go back to reference Quadrio Curzio, A. (1967) Rendita e distribuzione in un modello economico plurisettoriale, Milano, Giuffrè. Quadrio Curzio, A. (1967)
Rendita e distribuzione in un modello economico plurisettoriale, Milano, Giuffrè.
go back to reference Seton, F. (1977) ‘The Question of Ideological Obstacles to Rational Price Setting in Communist Countries’, in A. Abouchar (ed.), The Socialist Price Mechanism, Durham, NC, Duke University Press. Seton, F. (1977) ‘The Question of Ideological Obstacles to Rational Price Setting in Communist Countries’, in A. Abouchar (ed.),
The Socialist Price Mechanism, Durham, NC, Duke University Press.
 Title
 From Multipliers to the Distribution of Income: Connecting Leontief and Sraffa
 DOI
 https://doi.org/10.1007/9783030472061_12
 Author:

Albert E. Steenge
 Publisher
 Springer International Publishing
 Sequence number
 12
 Chapter number
 Chapter 12