ON THE LOGICAL CONSISTENCY OF SRAFFA'S ECONOMIC THEORY : A COMMENT ON SAVRAN AND STEEDMAN

Transcription

1 ON THE LOGICAL CONSISTENCY OF SRAFFA'S ECONOMIC THEORY : A COMMENT ON SAVRAN AND STEEDMAN Hugh V. McLachlan A.T. O'Donnel l J.K. Swales In a recent article in Capital and C/ass, Savran (1979, p. 131) argues that '... Sraffa's economics is inconsistent and untenable even within its own theoretical framework' and '... that logical consistency requires that Sraffa's theory itself be abandoned' (Savran, 1979, p. 137). In neo- Ricardian analysis, the wage/profit frontier for the economic system as a whole is constructed using data for the technological conditions of production in all industries (Figure 1). The prior specification of one of the distributional parameters (say the wage rate, w a ) determines the value of the other distributional parameter (ra) and the prices of all the commodities. Savran maintains that it is not logically possible to 'close' Sraffa's system in this way. His main objection is that it cannot be known a priori whether a wage rate which has been so determined will be high enough to cover subsistence consumption. Steedman (1979) states that such criticism is misplaced and that Sraffa's system does not suffer from these alleged logical flaws. Whilst we agree with many of the points that Steedman makes, we feel that his summary treatment of Savran's argument is a little misleading. Steedman, quite rightly, treats Sraffa's book, Production of Commodities by Means of Commodities, as having as its central concern :... the relationships which necessarily hold between wages, profits and prices, for given conditions of production, when the wage rate, the rate of profit and the price of each commodity are uniform throughout the economy (Steedman, 1977, p. 13). Wages (Standard figure 1 Commodity Units) Rate of Profit

2 160 CAPITAL & CLASS When Sraffa's analysis is so conceived, it is, as Steedman (1979) shows, clearly immune from the criticisms made by Savran. However, it is common to regard Sraffa's work as more than the mere elaboration of a logical theorem : it is often thought that Sraffa is presenting a rudimentary economic theory of distribution in a capitalist economy. That is to say, Sraffa is interpreted as making the claim that, in a capitalist economy, one of the distributional parameters is determined independently of the value of the other distributional parameter and the relative prices of commodities. The value taken by this exogenously determined distributional parameter, together with the characteristics of the existing technology, then determines all other prices in the system.[1 ] We shall try to show that when Sraffa's work is interpreted in this way, many of the issues raised by Savran are relevant. However, we shall also show that even with this interpretation it is incorrect to say that Sraffa's system is logically inconsistent : rather it is merely underspecified. Finally, we shall question the notion that a logically inconsistent theory should necessarily be abandoned. Let us consider first the possibility that the wage rate is determined as a vector of physical quantities of wage goods. Steedman (1979, p. 71) argues : Since Sraffa's purpose was, in part, to examine how wages, profits and prices vary together, what is in question here is not the possibility of taking a particular given aggregate of commodities as the real wage and then determining the corresponding profit rate and prices of production. The question is rather whether it is possible in Sraffa's analysis to consider a variable wage, paid in advance and consisting of a bundle of commodities in fixed proportions but of varying absolute size. Steedman represents Sraffa's system here as a set of mathematical relationships by means of which one can speculate about possible worlds. But if Sraffa's work is interpreted as an economic theory of a capitalist economy, then clearly the question is whether it is plausible that the real wage would be set in terms of a bundle of physical quantities of wage goods, prior to the 'determination of relative prices. We find this implausible, as does Sraffa (1960, p. 33).[2] Even if the wage rate were at a mere subsistence level, it is likely that there are a number of possible subsistence consumption vectors, a-1, a_2,..., a_ n. In this case the relevant consumption vector, i.e. the one which maximises the rate of profit, will be determined simultaneously with relative prices. [3] If the view that the wage rate is determined as a vector of physical quantities of wage goods is untenable, then a fortiori it is implausible that the wage should be set in terms of the Standard Commodity. This lead Sraffa to prefer the rate of profit as the independently determined distributional variable. A second, separate set of issues tackled by both Savran and Steedman involves the complex nature of the payment to labour in the Sraffian system. In order that the economic system be reproduced, the workers must be reproduced. This implies that a part of the payment to labour is necessary for the reproduction of the system, and that the commodities

3 DEBATE: VALUE - THEOR Y 161 which make up such necessary consumption appear to be basic commodities. However, generally, part of the payment to labour is also a share in the economic surplus. Sraffa (1960, p. 10), as Savran points out, wants to incorporate necessaries as quasi-basics which exert `... their influence on prices and profits.. in devious ways'. However, this cannot be. We have already seen that Sraffa favours the rate of profit as the independently determined distributional variable : the wage rate is a residual. Here, clearly, a change in the technique of production of a wage good which is not a part of the Standard Commodity has no effect on the price of other commodities or the rate of profit. The standard of living of the workers will generally change, but this will have no effect on the other variables in the system.[4] Steedman (1979) argues against this position. He maintains that changes in the technology for producing the necessaries of consumption can have the fundamental effects on the economic system normally associated with changes in the technology for the production of basic commodities. He makes two separate points. First, a necessary of consumption might be, quite separately, a basic commodity. This is clearly an unsubstantial argument, as the effect on Sraffa's system is here generated through the commodity's acting qua basic rather than qua necessary. Secondly, as we have seen already, Steedman argues that the wage rate might be given in terms of a vector of physical quantities of commodities. One or more of these commodities might be a necessary or might be produced using necessaries as inputs. If this is so, a change in the technology for the production of one of these necessaries will change the rate of profit that rules with a given wage rate. In this sense necessaries mimic the action of basics. Again, treating Sraffa's system as a logical theorem, if all the necessaries are included in the vector of physical quantities that make up the wage rate then all necessaries produce effects on the economic system as a whole similar to the effects produced by basics. However, there is one important problem with this argument. The effect on Sraffa's system is not caused by the necessary's acting as an essential requirement for the reproduction of the systems. Rather, the effect is caused by the necessary acting as one of the elements in the standard by which the wage rate is measured. Clearly there is no logical reason why luxury goods (such as Sraffa's racehorses) should not be included in this standard. Moreover, as we shall discuss in greater detail later, even if the wage were to be limited to a vector of quantities of wage goods, it is unlikely in fact that all, or even most, wage goods are necessaries. We feel that despite Steedman's valid comments, Savran is substantially correct when he argues that in the normal formulation of Sraffa's analysis, necessaries are not basics and therefore play a subsidiary role.[5] A third issue raised by Savran is clearly closely related to the issues that have been discussed already. He argues that Sraffa does not include in the formal framework of his theory the requirement that the system reproduces the work force. He maintains that Sraffa's exogenously determined rate of profit might imply a wage rate not large enought to cover the subsistence needs of the workers. Consider first an extreme example given by Savran (1979, p. 139, footnote 11). Imagine that the exogenously given

4 162 CAPITAL & CLASS rate of profit is greater than R, the maximum rate of profit consistent with non-negative wages. Such a system will not reproduce itself. The case against Sraffa's economic theory implied here is this : if the rate of profit is truly determined independently of the values taken by the parameters of the productive system, there is no reason to believe that the resulting wage rate will 'be non-negative. Whilst this is true, we do not feel that such criticism is substantial enough to require '... that Sraffa's theory itself be abandoned'. First, Sraffa's theory does show the limits within which the rate of profit must' lie for the wage rate to be non-negative. Secondly, the production system does not precisely determine either the wage rate or the rate of profit. However, Savran's main argument might be rather that Sraffa's theory seems wrongly to imply that all rates of profit between 0 and R (Figure 1) are attainable. Workers require to be produced by the economic system. It is generally the case that certain values of the rate of profit will imply a residual real wage which is too small to cover subsistence. However, as Steedman points out, Sraffa himself suggests a way in which his analysis can be re-interpreted to deal with such a possibility : In view of this double character of the wage it would be appropriate, when we come to consider the division of the surplus between capitalists and workers, to separate the two component parts of th wage and regard only the 'surplus' part as variable ; whereas the goods necessary for the subsistence of the workers would continue to appear, with the fuel etc., amongst the means of production (Sraffa, 1960, pp. 9-10). Whilst Sraffa actually chooses not to present it in this way, he argues that his analysis '... can easily be adapted to the more appropriate, if unconventional, interpretation of the wage suggested above' (Sraffa, 1960, p. 10). This reformulation has two analytical advantages over the conventional presentation of Sraffa's system. First necessaries of consumption become basics : secondly, all non-negative wage rates are large enough to reproduce the labour force. Moreover, these analytical gains are not made at the expense of elegance. It is curious therefore that Sraffa did not choose to present his analysis in this reformulation. The reason might be this : that whilst the analysis would gain as a logical theorem, it would loose as an economic theory. The wage rate which is used to calculate the reformulated wage-profit frontier no longer corresponds to the wage rate used in other theories or calculated in empirical studies. Also the reformulated theory requires that there is a given subsistence set of wage goods whose consumption is necessary for survival and whose consumption is maintained even when income rises above subsistence levels. First, we have questioned already the notion that the subsistence set of consumption goods can be chosen prior to the determination of relative prices. Secondly, as income rises, the whole pattern of consumption changes : not only are extra goods and services consumed but higher quality commodities are substituted for lower quality ones. This process of substitution means that very few commodities consumed by a person on Social Security will also be consumed by Rod Stewart.

5 DEBA TE : VALUE - THEORY 163 However there is an alternative reformulation of Sraffa's theory which explicitly takes into account the need to reproduce the workforce. For a given exogenously determined rate of profit (r a ) there corresponds a wage rate (wa ) and a price vector (p- a). Such a set of prices is consistent with the reproduction of the system so long as the minimum value a-11 p_, a-2. p-a,, a_n, p-a is less than or equal to w a, and ra is greater than zero. ~fhe first condition here is simply that the wage rate, measured in Standard Commodity units, must be large enough to purchase at least one subsistence set of wage goods. Wages (Standard commodity Units) figure 2 I I N 0 R Rate of Profit The problem of an exogeneously determined rate of profit's implying a wage insufficient to cover subsistence is tackled explicitly by Kaldor (1960, pp ). He states that his theory is applicable only where the resulting wage rate is above subsistence. Is it therefore sufficient, following Harcourt (1972, p. 209) and Steedman (1979), to limit the applicability of Sraffa's theory to implied wage rates above some minimum level, wmin (and therefore profit rates below r max )? In general : no. This is because a change in the wage rate is generally accompanied by changes in the prices of wage goods. With joint production, it is possible for a wage increase to cause an even faster rise in the price of wage goods (Sraffa, 1960, pp ). This means that it is possible for a fall in the rate of profit, with its associated rise in the wage rate measured in Standard Commodity units, to cause the workers' standard of living to fall below subsistence. If a wage/profit frontier which takes explicit account of the need to reproduce the labour force is drawn, it might well look like Figure 2. Here the broken segments of the line represent values of the wage rate not large enough to cover subsistence consumption. However, the greater the choice of subsistence consumption sets, the more likely it is that the system will be viable at relatively high rates of profit. Savran argues that Sraffa's theory should be abandoned on the grounds that it is logically contradictory.[ 61 Before considering the logical status of Sraffa's system, we shall examine Savran's implicit assumption that theories which involve logical contradiction should be abandoned. A logical contradiction is the simultaneous assertion and denial of the same proposition. A theory, T, will be logically contradictory if it contains the

6 164 CAPITAL & CLASS elements (i) p and (ii) not-p. If T consists solely of (i) and (ii) then T will be vacuous since what is asserted by (i) is denied by (ii) and vice versa. Hence, overall, T would contain nothing which could be accepted or abandoned. Suppose that T contain elements other than (i) and (ii). T could be rendered consistent by eliminating either (i) or (ii) or both of them. (It does not appear that the addition of assumptions could render T consistent.) Here, whether it would be more rational to abandon T or to modify it cannot be settled a priori. Hence, even if Savran could show that Sraffa's economic theory contains a contradiction, his argument would not have sufficient force to establish that the theory should be totally abandoned rather than pruned. However we maintain that Savran has not shown that Sraffa's system contains a contradiction. Savran (1979, pp ) correctly claims that in Sraffa's theory, as it is generally presented in Production of Commodities by Means of Commodities, '... there is nothing to guarantee that the commodities necessary for the subsistence of the workers will accrue to them. When the prices are determined, the wage may well turn out to be below this subsistence level'. But the truth of this statement does not imply that none of the methods for determining the independent distributional variable '... can logically yield a solution which satisfies the task set by Sraffa for the system of prices of production' (Savran, 1979, p. 133). Rather, it is the case that, under Sraffa's specifications, it is logically possible that such a solution might not be reached. But that is not to say that the system contains a logical contradiction : it is to say that it is underspecified. This seems to be the point that Steedman (1979, p. 5) is making when he states that 'Savran is attempting to produce a conjuror's mystery out of a black box'. For no elements of Sraffa's system need be removed to render it consistent. We have added assumptions to Sraffa's system need be removed to render it consistent. We have added assumptions to Sraffa's system and produced a consistent, more highly specified system which is immune to Savran's attempted criticism. But the mere addition of assumptions could not render a theory consistent if it had previously contained a contradiction. We have seen that Sraffa's analysis is logically consistent : Savran's objections do not show it to be logically contradictory. However, it is a necessary but not a sufficient condition for the acceptance of a theory that it be logically consistent and Savran's objections, particularly those concerning the nature of the payment to labour in Sraffa's system, do raise problems for those who wish to interpret Sraffa's work as an elementary theory of distribution in a capitalist economy. 'NOTES The authors, who teach at Newcastle Polytechnic, Glasgow University and Strathclyde University respectively, would like to thank the editorial committee of Capital and Class for comments on an earlier version. 1 This clearly seems to be the view expressed in Sraffa (1960, p. 33). 2 An example of wages being set this way would be if wages were some multiple of the retail price index (RPI) and the basket of goods on which the RPI were calculated remained unchanged.

7 DEBA TE: VALUE-THEORY In a system with no joint products, the problem is simply solved by successively reducing the wage rate in terms of the Standard Commodity. As the wage rate falls, the number of attainable subsistence consumption sets also falls. At some low wage, workers will just be able to afford only one subsistence consumption set. This will be the wage which maximises the rate of profit. With joint products, the problem is more complex, because the price of subsistence wage goods might fall faster than the wage rate. 4 Providing, of course, that the labour force is receiving a real income which covers subsistence. 5 It is interesting to note that Sraffa gives only one example of necessaries influencing prices and profits in devious ways. This is that the methods of production of necessaries set '... a limit below which the wage cannot fall' (Sraffa, 1960, p. 10). 6 We shall adopt Savran's terminology and treat logically 'inconsistent' and logically 'contradicting' as synonymus. Similarly we cannot detect a distinction between the term 'theoretically consistent' and 'logically consistent'. REFERENCES Harcourt, G. C., 1972, Some Cambridge Controversies in the Theory of Capital, Cambridge : Cambridge University Press. Kaldor, N., 1960, Essays on Value and Distribution, London : Duckworth. Savran, S., 1979, 'On the Theoretical Consistency of Sraffa's Economics', Capital and Class, vol. 7, pp Sraffa, P., 1960, Production of Commodities by Means of Commodities, Cambridge : Cambridge University Press. Steedman, I., 1977, Marx after Sraffa, London : New Left Books. Steedman, I., 1979, 'On an Alleged Inconsistency in Sraffa's Economics', Capital and C/ass, vol. 9, pp