THE DEFECT IN RICARDO’S ARGUMENT FOR THE 93 PER CENT LABOUR THEORY OF VALUE‘:’

WILLIAM COLEMAN

Victoria University of Wellington

In the third edition of the Principles Ricardo advanced a n argument which claims t o show that changes in the rate of profit can affect relative prices by, a t most, six o r seven per cent. Ricardo used this proposition to argue that relative prices would be roughly equal to relative labour inputs. Stigler (1965) has dubbed Ricardo’s argument and conclusion “The 93 Per Cent Labour Theory of Value”.

Several criticisms of the 9 3 per cent labour theory of value were canvassed in the discussion which followed Stigler’s paper. Stigler (1965) criticised all labour theories of value for assuming that, (i) land is immobile between industries, (ii) machinery is produced by labour alone, and (iii) goods are produced a t constant marginal cost. Wilson and Pate (1968) emphasised that, even within the framework established by these assumptions, the 93 per cent version of the theory requires arbitrary assumptions about relative time periods of production if point-input - point-output tecchnology is assumed.

There has, however, been little critical examination of the argument for the 93 per cent theory which Ricardo actually presented in the Principles.’ This note reviews this neglected argument, and shows that it rests on a n extremely arbitrary assumption about technology. Once this assumption is dropped, Ricardo’s own theory allows the profit rate to have a very large effect on relative values. Thus Ricardo’s argument is shown to be a bad one.

The paper goes on to suggest, that even though the argument is defective, it may have played an important role in the evolution of Ricardo’s thought by promoting his confidence in a barely qualified labour theory of value.

I. RICARDO’S ARGUMENT

Ricardo’s argument (1951, p. 33-36) relies on a numerical example. It involves the comparison of a good produced without machinery (“corn”) and a good produced with machinery (“manufactures” or “cloth”).

Ricardo begins his argument by stating some technological assumptions. (The italics are ours).

” I am grateful to Geoff Bertram, Neil Quigley and two anonymous referees for helpful comments and criticisms.

‘The argument has been summarised in Hollander (1979) among others, but without its deficiencies being analysed.

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Suppose two men employ one hundred men each for a year in the construction of two machines, and another man employs the same number of men in cultivating corn, . . . Suppose one of the owners of one of the machines to employ it, with theassistance of one hundred men, the following year in making cloth, . . . , while the farmer continues to employ one hundred men as before in the cultivation of corn . . .

Ricardo then introduces some assumptions about wage rates and deduces the equilibrium prices of corn and machines.

Suppose that for the labour of each workman 50 1. per annum were paid, or that 5,000 1. capiial were employed and profits were 10 per cent, the value of each of the machines as well as of the corn, a t the end of the first year, would be 5,500 1.

Ricardo then deduces the equilibrium price of manufactures.

The second year the manufacturers and farmers will again employ 5,000 1. each in the support of labour, and will therefore again sell their goods for 5,500 1.; but the men using the macchines, to be on a par with the farmer, must not only obtain 5,500 1. for the equal capitals of 5,000 1. employed on labour, but they must obtain a further sum of 550 1. for the profit on 5,500 I., which they have invested in the machinery, and consequently their goods must sell for 6,050 1.

Ricardo then calculates the effect of a variation in factor prices on the prices of corn and manufactures.

Suppose then, that owing to a rise in wages, profits fall from 10 to 9 per cent, instead of adding 550 1. to the common price of their goods (to 5,500 1.) for the profits on their fixed capital, the manufacturers would only add 9 per cent on that sum, or 495 I., consequently the price would be 5995 1. instead of 6050 1. As the corn would continue to sell for 5,500 1. the manufactured goods in which more fixed capital was employed, would fall relatively to corn . . .

Ricardo then draws his conclusion

The reader, however, should remark that this cause of the variation of commodities is comparatively slight in its effects. With such a rise in wages as should occasion a fall of 1 per cent in profits, goods produced under the circumstances I have supposed vary in relative value only 1 per cent; they fall with so great a fall in profits from 6050 1. to 5995 1. The greatest effects which could be produced on the relative prices of these goods from a rise in wages could not exceed 6 or 7 per c e n t . . .

11. RICARDO’S ARGUMENT I N ALGEBRA

In order t o get to grips with this argument it should be expressed in algebra.

The argument evidently involves a comparison of the prices of two goods; corn and manufactures. It is assumed corn is produced by labour alone, and that there is a lag of one period between the input of labour and the output of corn. Thus,

Pc = a c w ( l + r )

a , = labour requirement per unit of corn

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Manufactures, by contrast, are produced by the joint application of machinery and labour.2 Like corn, however, the production of manufactures requires a one period lag between input and output. It is also implicitly assumed that the machinery employed in manufactures is infinitely durable. Thus, the equilibrium condition for the price of manufactures is

P , =urn w ( I + r ) + b, Pk r

a, = labour requirement per unit of manufactures

b, = machinery requirement per unit of manufactures

pk = price of the machine

Machines are produced by labour alone. Consequently,

Pk = ak ( l + r ) w

ak = labour requirement per unit of machines

(3)

Equations ( l ) , (2) and (3) solve to provide the price of manufactures relative to corn, P “ ;

(4) can be simplified using an innocuous assumption which Ricardo makes about technology. The second and third italicised sections of the quoted passages make it plain that Ricardo assumes that the labour requirement in corn (ie. 100 men) equals the direct labour requirement in the manufactured good, (z.e. 100 men). In algebraic terms, ac = a,. This assumption is just a matter of convenience; the units in which corn is measured can always be defined so that the labour required for one “unit” or corn is the same as the labour required for one unit of manufactures. This assumption means that (4) can be simplified to,

To obtain the conclusion that r only has a small effect on P“, we must introduce one further assumption which Ricardo makes about technology. This assumption is crucial. It concerns the amount of labour used directly in manufactures, a,, compared to the amount which is used indirectly through machinery, b, a k . The first and third italicised passages in the quote indicate that Ricardo assumes that 100 men are used to build the machine and 100 men are used t o operate it. In other words, Ricardo is assuming that the indirect labour requirement in manufactures equals the direct labour requirement; ak b, = a,. This assumption means the equation for relative price simplifies to;

2Contrary to the impression which may be given by reading Wilson and Pate (1968), Ricardo did not use a point input-point output technology.

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(6) implies that the semi-elasticity of relative prices to the rate of profit is approximately one.

In Ricardo’s words, “With a fall of 1 per cent in profits, goods produced under the circumstances I have supposed vary in relative value only 1%’’ (p. 36). This means that significant fluctuations in the rate of profit will only have an insignificant impact on relative prices. Consider, for example, a decline in the profit rate from ten per cent t o the rate which Ricardo considers to be the bare minimum; three per cent. Such a decline would reduce relative prices from 1.1 to 1.03, a cut of only about seven per cent. Thus the effect of variation in profit rates on relative values is “comparatively slight in its effect”.

111. THE DEFECT

Ricardo’s conclusion that changes in r will only have a slight effect on P* depends crucially on his assumption that the ratio of indirect to direct labour inputs in manufactures is one. Recalculating the semi-elasticity of relative prices without that assumption yields,

If we allow (b , a k ) / a , to assume any non-negative value ( and not just one), then the semi-elasticity may assume a wide range of values. Table I shows the value of the semi- elasticity for various values of ( b , ak)/a,.

TABLE I

Value of (dP’:?/dr) P“

( b , ak) la , = 0 (b , a k ) / a m = 1 0 1 1 /r

(b , ak) lam = m

The lowest value of the semi-elasticity is zero; this would occur when n o machinery was used in the production of manufactures. The highest value is l/r. This would occur if an only infinitesimal amount of labour was used directly in the production of manufactures. How large is l/r? If we allow Ricardo’s assumption of a minimum profit rate of three per cent, then l l r could be as large as 33.3 Thus the if we allow ( b , a k ) / a , to assume any non- negative value then the semi-elasticity could be as large as 33.

Ricardo’s argument for a 93 per cent labour theory of value would only carry weight if he could show that it is reasonable to assume that the indirect labour requirement is roughly

3What if we allowed r to be as low as zero? Inspection of (8) indicates that when r = O the semi-elasticity equals (b,ak)/a,. Since (bmak/a,) could be very large, the semi-elasticity could be very large i f r = 0.

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equal to the direct labour requirement (i.e. b , ak = u,). Since Ricardo makes no attempt to show this, his argument must be considered very weak.4

IV. THE ARGUMENTS PLACE I N THE EVOLUTION OF RICARDO’S THOUGHT

We have shown that Ricardo’s argument for a 93 per cent labour theory of value is dependent upon the existence of a very particular technology. It is unclear to what extent Ricardo was aware of his argument’s dependence on its technological assumptions. Certainly, he realized that if the direct labour requirement in manufactures was zero then the semi-elasticity of P“ to rwould be large. In the first and second editions of the Principles he calculated the effect on P” of a fall in r from ten per cent to three per cent when the machinery-using good was completely unmanned; ie. a, = 0.5 Ricardo showed that if the machine lasted only one period the effect on relative prices would only be six per cent. But, he also noted, if the machine lasted 100 years the effect would be 68 per cent.6

Of course, the assumption that machinery is completely unmanned does seem intolerably unrealistic. It appears that in the preparation of the third edition of the Principles Ricardo turned his mind to analysing the much more realistic case of a good produced by a machine which was manned. As we have seen, this analysis concluded that, even if the machine was infinitely durable, a one point fall in rwould change P” by only one per cent. Is it far fetched to suppose that this result gave a certain satisfaction to Ricardo? It seemed to show that by

4Barkai (1967) also asserts that Ricardo’s argument rests on special technology. However, Barkai’s argument is a t some points obscureand at others highlycontrary to Ricardo’s. In his presentation there are two goods; good 1 (manufactures) and good 2 (corn). Both use fixed capital of infinite durability.

p i = wnl( l+r ) + r k i , p2 = wa2(l+r) + rk2

kj =value of fixed capital per unit of output i

Consequently, the relative price of goods is,

Unfortunately, Barkai does not state what he is assuming about the determination of k,, something which is vital for his argument. He then states without proof;

Having arrived, by some means, a t this expression Barkai goes o n to make three further assumptions. First,itisassumedr=O.Ol anddr=0.01. Second,itisassumed t h a t b l = b 2 + l .Third, i t isassumed that a 1 = 1 and a 2 = 0. The addition of these three assumptions “imply” a one percentage point change in r changes p1/p2 by 0.8 of one per cent, roughly what Ricardo concluded. But a 2 = 0 is a very strange assumption to make; it means the direct labour input in corn is zero, something Ricardo never assumed!

’See Goenewegen (1972).

‘These conclusions are congruent with our own analysis. When the direct labour requirement becomes infinitesimally small the semi-elasticity in our analysis approaches l / r . Consequently, if r = 10% (as Ricardo assumes) the semi-elasticity is ten. Ten is also roughly the semi-elasticity in Ricardo’s calculations when the life-span of the machine is 100 years (68%/70/0 = 10).

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incorporating the realistic assumption of machinery being manned, the importance of profits in determining values was greatly diminished, and the realism of the labour theory of value was greatly enhanced. And that allowed a welcome simplification of the Theory of Value in general. Is it implausible to conjecture that this “discovery” was central to what was (according to most critics)’ a more emphatic advocacy of the labour theory of value in third edition of the Principles? Certainly, there is a n association between the new argument and the new emphasis; two of the four new remarks which Sraffa mentions as minimizing the qualifications to the theory occur just after the argument in question.’

As we have pointed out, Ricardo was mistaken in concluding that the “manning” of machinery implies that the profit rate has only a slight influence on relative prices. But we are left with some interesting speculations. If the defect in his argument had been brought to his attention, would Ricardo have retreated from a labour theory of value? Would his insistence o n this doctrine have receded in a hypothetical fourth edition of the Principles? And in that case, would Marx have adopted the doctrine with such ardour?

REFERENCES

Barkai, H. (1967), “The Empirical Assumptions of Ricardo’s 93 Per Cent Labour Theory of Value”, Economica, vol. 34.

Groenewegen, P.D. (1972), “Three Notes on Ricardo’s Theory of Value and Distribution”, Australian Economic Papers, vol. 9.

Hollander, S. (1979), The Economics of David Ricardo (Toronto: University of Toronto Press).

Ricardo, D. (1951), THe Principles of Political Economy and Taxation, P. Sraffa (ed.), (Cambridge:

Stigler, G.J. (1965), “Ricardo and the 93 Per Cent Labor Theory of Value”, Essays in the History of

Cambridge University Press).

Economics (Chicago: University of Chicago Press).

Wilson, G.W. and Pate, J.L. (1968), “Ricardo’s 93 Per Cent Labor Theoryof Value: A Final Comment”, lournal of Political Economy, vol. 76.

’According to Hollander (1979), qualifications to the labour theory of value “are present in abundance in 1817, while the quantitative significance of these qualifications is actually increasingly played down in subsequent years”. Sraffa (1951, p. xxxix) also suggests the changes in the third edition tend to minimise qualifications to the Labour Theory of Value.

*Sraffa’s introduction to Ricardo’s Principles (1951, p. xxxix)