Nerio Naldi
4. The grounds for Sraffa’s approach: some hypotheses
First of all, we may stress that the fact that Sraffa believed that the cotton-rate of interest could be expressed in terms of bales contracted for spot delivery is not as
obvious at it may appear from Keynes’s second letter. The text published by Sraffa, just like the typescript he had submitted to Keynes and all the preparatory notes known to us (SP D3/9), does not state that the cotton-rate of interest should be defined in terms of
spot bales. This possibility emerges from Keynes’s comments, and it may be recognized
in the text of Sraffa’s article only if we assume that when Sraffa mentioned the number of bales that can be purchased with the amount of money corresponding to the cost of
borrowing cotton he implicitly referred to spot bales. To study the question it may then
be appropriate to consider two different directions of enquiry. First, we may consider which reasons might have led Sraffa to refrain, in his 1932 article, from providing a full specification of a formula apt to calculate the value of the natural, or commodity, rate of interest. Second, we may consider which reasons might have led Sraffa, in private discussions to favour a definition of that rate in terms of spot bales.
Let us start from the question of the absence, in Sraffa’s 1932 article, of the full specification of a formula apt to calculate the value of commodity rates of interest in a monetary economy. To explore this direction of research, we must start from some
10 This remark rules out the possibility that the price referred to by Sraffa could have been the spot price currently quoted at the time of delivery referred to in the relevant forward contract, which, in Keynes’s opinion, would give rise to a payment in arrear just like the forward price.
premises. First of all, we may take as a fact that Sraffa’s wording, when he referred to the number of bales that can be purchased with the amount of money corresponding to the cost of borrowing cotton, was genuinely ambiguous and that he was aware of that ambiguity (indeed, had he not already been aware of it, the remarks contained in Keynes’s two letters could not have failed to alert him). Granting this, we may stress that Sraffa did not discuss commodity rates of interest in order to develop a theory of those magnitudes, but only to show the inconsistency of Hayek’s approach and of his prescriptions for monetary management. Given this aim, it may be argued that establishing a relationship between divergences between spot and forward prices, demand and supply for commodities, and commodity rates of interest was sufficient to serve Sraffa’s purpose. Indeed, within the compass of his analysis, it would have been irrelevant whether the monetary cost of borrowing cotton was divided by the spot or forward price of cotton: in both cases the relationships between commodity rate, money rate and spot and forward prices would have been going in the same directions and the same would have applied to the effects of differences between spot and forward prices. Furthermore, this conclusion is also consistent with the possibility that Sraffa preferred contrasting Hayek’s views on rates of interest in a non-monetary economy by studying commodity-loans in a monetary economy because he was convinced that discussions of non-observable cases should be dealt with with special caution, if not avoided at all.11 In this sense, an additional reason to refrain from presenting a complete formula designed to calculate the value of commodity rates of interest in a monetary economy could have been that he was determined to avoid any risk of mechanical applications of such a formula to the case of a non-monetary economy.
This explanation addresses Sraffa’s approach exactly as it emerges from the text of his article. The same explanation, however, cannot account for Keynes’s remarks as far as they may be interpreted as implying that Sraffa, in private discussions, had maintained that an alternative definition of the concept of commodity rate of interest was to be preferred to the one proposed by Keynes, and, in particular, that the monetary economy analogue of the concept of commodity rate of interest as defined in a non- monetary economy should be arrived at by expressing the cost of borrowing a commodity in terms of spot quantities of that very commodity.
11 In the opening pages of his article Sraffa had accepted the idea of ‘a comparison between the conditions
of a specified non-monetary economy and those of various monetary systems’ (Sraffa 1932: 43), but within the discussion of commodity rates he almost ridiculed the perspective of a direct examination of such a case: ‘we need not to stretch our imagination and think of an organised loan market amongst savages bartering deer for beavers’ (Sraffa 1932: 49).
As already noted, if, in a monetary economy, we wish to borrow cotton, we must
start by borrowing money. The cost of the whole operation is a monetary cost, and in order to express that cost as a rate it may be obvious to divide it by the amount of money initially borrowed. If we borrow money in order to borrow (or, more precisely,
buy and later sell) 100 bales of cotton, the monetary rate of interest paid on that
operation may be calculated by dividing its monetary cost by S c balesP
100 , as in equation [5]. In this sense, dividing by S
c
P would be incomplete; dividing by PcF or by F c balesP 100 would be meaningless. [5] S c bales bales F c S c bales S c m c P P P P i i 100 100 ) ( 100
Such a rate may be understood as a commodity rate because it pertains to the
operation of borrowing a commodity. Sraffa’s reference to that rate as a number of bales and, consequently, to the division of the cost of borrowing cotton by the price of
cotton (which we may now take to have been S c
P ) rather than by the amount of money
initially borrowed ( S c balesP
100 ) may be understood as a way to emphasize the analogy between that rate as may be calculated within a monetary economy and the rate which would apply on a commodity-loan in the case of a non-monetary economy. Use of analogy instead of full analytical exposition is a shortcut that Sraffa could take because he was not developing a theory; he was just manoeuvring on Hayek’s ground in order to criticize him. His statement, however, could also be justified by the fact that, when the quantity of cotton initially borrowed (or, more precisely, bought) is 100 bales, or could
be reduced to 100 bales,12 the rate envisaged as a number of bales numerically
corresponds to the value of the cotton-rate of interest as defined in equation [5]. Dividing the monetary cost of borrowing cotton by S
c
P would then reflect two aspects
of Sraffa’s argument. On the one hand, it would reflect Sraffa’s view that in a monetary economy the commodity rate of interest is a monetary rate of interest. On the other hand,
it would reflect Sraffa’s strategy of developing an argument concerning a non-monetary economy by considering data and facts as may be observed in a monetary economy— i.e., it would reflect his way to bridge the gap between an observable case and a non- observable case.
This seems to offer a sound explanation for Sraffa’s supposed preference for dividing the monetary cost of borrowing cotton by S
c
P , as seems to be implicit in
Keynes’s letters. Keynes would then be wrong in stating that Sraffa was depicting a
12 Sraffa’s wording was as follows: ‘the rate of interest which he pays, per hundred bales of cotton, is the number of bales that can be purchased with the following sum of money […]’ (Sraffa 1932: 50, our emphasis).
reward paid in advance rather than in arrear—i.e., a discount, rather than an interest.
The real point separating their approaches seems to be that the operation that, following Keynes’s letters, can be recognized as envisaged by Sraffa may be described as borrowing cotton, but it only implies buying cotton today and selling that very quantity of cotton at the end of the period, while it is money which is initially borrowed and later returned augmented by an interest. Keynes, on the contrary, conceived an operation implying, at the end of the period, the calculation of the quantity of cotton which should be sold in order to repay the amount of money initially borrowed and the corresponding monetary interest—that is to say, it implied the equivalent of returning an augmented amount of cotton (not of money!) at the end of the borrowing period. This may not be immediately evident if Keynes’s view is formalized on the basis of Sraffa’s approach to the concept of commodity rate of interest (as in equation [4]). But the point was crystal clear to Keynes, who stated that ‘we have to find how many forward bales can be obtained by parting with a given number of spot bales’ (letter from Keynes to Sraffa, 21.12.1931). This is the way he was to follow in the General Theory and we may see
how it relates to equations [1] and [4]: [6] F c bales bales F c S c bales S c m bales F c bales F c S c bales S c m bales bales F c S c bales m S c S c F c P P P P i P P P P i P P i Q Q Q 100 100 ) ( 100 100 100 ) ( 100 100 100 100 ) 1 (
If Keynes, having in mind equation [1], wanted to calculate F
Q , he may have seen
that to that effect the monetary cost of borrowing cotton was to be divided by F P .13
This presupposition probably led him to overlook the fact that Sraffa’s wording was not directed at identifying a number of bales of cotton as such but a percentage, and, consequently to overlook the possibility that Sraffa’s approach was radically different from his own.
To put it in other words, Keynes proposed to replicate within a monetary economy what may be conceived as the structure of commodity-loans in a non-monetary economy. Such an operation, as shown by equation [6], may be successfully accomplished using data observable in a monetary economy. But the scheme—even though formally correct—would be totally unconnected to the logic of observable economic behaviour in a monetary economy, where, in ordinary circumstances, no one calculates that sort of returns. It is for this reason—we may presume—that Keynes’s view might have been judged by Sraffa as wrong (letter from Keynes to Sraffa,
13 As a matter of fact, dividing the monetary cost of borrowing cotton by F
P we obtain QF QS, not
F Q .
21.12.1931). Sraffa’s approach, on the other hand, would follow the logic of the assessment of costs and profitability as universally applied in monetary economies, where agents are interested in monetary costs and returns and pay no attention to
commodity-costs and commodity-returns.