# Own Rates of Interest

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_1540

## Abstract

*Prices and Production*(1931), and was later taken up, and labelled, by Maynard Keynes in his analysis of the role of money in the theory of employment (1936, ch. 17). Sraffa introduced the concept by means of the example of a cotton spinner who borrows money to purchase a quantity of raw cotton today (at the spot price) which he simultaneously sells forward (Sraffa 1932, p. 50). The spinner is actually borrowing cotton for the period of the transaction, say, one year. The own-rate of interest on cotton is then the spot price of a bale of cotton for divided by the future price of a bale discounted at the going money rate of interest; less one. So if the price of 100 bales of cotton for delivery today is $20, and the price to be paid for delivery of 100 bales in one year’s time is $21.40, whilst the money rate of interest is 5%, then the own-rate of interest on cotton is

*not*that it was simply the rate of interest on a numeraire. ‘Money’ in his discussion, is the actual financial medium. So the money rate represents the normal rate of interest (which is assumed equal to rate of profit) in the economy as a whole. The difference between the money rate and own-rate of interest on a commodity therefore indicates that the

*spot market*for that commodity is not in normal long-run equilibrium.

*Prices and Production*(1931), and was later taken up, and labelled, by Maynard Keynes in his analysis of the role of money in the theory of employment (1936, ch. 17). Sraffa introduced the concept by means of the example of a cotton spinner who borrows money to purchase a quantity of raw cotton today (at the spot price) which he simultaneously sells forward (Sraffa 1932, p. 50). The spinner is actually borrowing cotton for the period of the transaction, say, one year. The own-rate of interest on cotton is then the spot price of a bale of cotton for divided by the future price of a bale discounted at the going money rate of interest; less one. So if the price of 100 bales of cotton for delivery today is $20, and the price to be paid for delivery of 100 bales in one year’s time is $21.40, whilst the money rate of interest is 5%, then the own-rate of interest on cotton is

*not*that it was simply the rate of interest on a numeraire. ‘Money’ in his discussion, is the actual financial medium. So the money rate represents the normal rate of interest (which is assumed equal to rate of profit) in the economy as a whole. The difference between the money rate and own-rate of interest on a commodity therefore indicates that the

*spot market*for that commodity is not in normal long-run equilibrium.

In equilibrium the spot and forward price coincide, for cotton as for any other commodity; and all the ‘natural’ or commodity rates are equal to one another, and to the money rate. But if, for any reason, the supply and the demand for a commodity are not in equilibrium (*i.e.*, its market price exceeds or falls short of its cost of production), its spot and forward prices diverge, and the ‘natural’ rate of interest on that commodity diverges from the ‘natural’ rates on other commodities. Suppose there is a change in the distribution of demand between various commodities; immediately some will rise in price, and other will fall; the market will expect that after a certain time, the supply of the former will increase, and the supply of the latter fall, and accordingly the forward price, for the date on which equilibrium is expected to be restored, will be below the spot price in the case of the former and above it in the case of the latter; to the effecting of the [restoration of equilibrium] as is the divergence of prices from the costs of production; it is, in fact, another aspect of the same thing (1932, p. 50).

In terms of the example, the equilibrium price is $21.40 and the equilibrium rate of interest is 5%. However, the current price of 100 bales of cotton is $20, which invested at the going rate of interest, would be worth only $21, at the end of a year, and this would buy c.98 bales of cotton at the equilibrium price then ruling. Thus the own-rate of interest on cotton is c. –2%. The concept of the own-rate of interest on a commodity interpreted in this way, can only be defined with respect to normal prices and to the normal interest rate, represented by the money rate of interest. For example, if the money rate of interest in the above instance were 10% the own-rate of interest on cotton would be c. 3%; if 0%, then c. –7%.

Keynes used Sraffa’s idea in his analysis of the determination of the level of investment. His theory of the rate of interest was derived from an analysis of the demand for the stock of monetary assets – that demand being the sum of transactions, precautionary, and speculative demands – with only the latter being regarded as a function of the rate of interest.

The elasticity of the liquidity preference schedule with respect to the rate of interest was based on two rates of interest, the rate which actually holds, and the rate which is expected to hold in the future (the long-run rate). The ambiguity introduced into Keynes’s analysis by the construction of the liquidity preference schedule on the basis of the short-run and the long-run rate of interest was not totally clear in the *General Theory*, other than in Keynes’s ambivalence over whether the rate of interest was a ‘psychological’ or a ‘conventional’ variable (see Keynes 1936, pp. 200–202). The reference to ‘convention’ established the idea that ‘institutional’ or ‘historical’ factors might be the underlying determinants of the long-run rate of interest; he is content to point to forces other than supply and demand and leave the issue there.

The ambiguity in Keynes’s theory is exposed in his theory of investment. There, he associates the equalization of rates of return on different categories of assets with the determination of the volume of investment. The idea that rates of return are equalised is characteristic of long-run analyses. Yet Keynes is suggesting that this equality is attained with respect to a rate of interest which is determined as a short-run phenomenon. This ambiguity is unresolved in the *General Theory*. Subsequent discussion by Kaldor (1960) although the issue was clearly identified, left the problem unresolved.

The definition and interpretation of the own-rate of interest in modern general equilibrium theory (see Debreu 1959) are quite different from those advanced by Sraffa – although there is a formal similarity in the method of calculation. The set of equilibrium prices refer to commodities located at different points in time and yet include no interest charge. The price are discounted prices *which would be paid today* for commodities to be traded at a future date. The rate of interest at which the prices are discounted is not specified.

*t*to time

*t*+1, is defined as the ratio of the appropriate discounted prices, less one: i.e., the own-rate of interest on commodity

*q*over the time period

*t*is

*q*available at the beginning (resp. the end) of period

*t*, the prices being determined in the manner shown. The calculation jsut shown contains no reference to a normal rate of interest. The own-rate of return is defined independently of any normal or money rate. By analogy with the case of a-capitalistic production, the ratio of the discounted prices \( {p}_{qt},{p}_{qt+1} \) is equal to the marginal rate of substitution in consumption between

*q*

_{t}and \( {q}_{t+1} \), and to the marginal rate of transformation in production.

So although commodities *q*_{t} and \( {q}_{t+1} \), are defined as *different* commodities for the purpose of price determination, they are regarded as the *same* commodity for the purpose of the definition of the own-rate of interest, the difference in the prices being due to their temporal location.

Although there is some technical similarity in the calculation of the own-rate of interest on a commodity by both Sraffa and Debreu, the definition advanced by Sraffa is quite different from that adopted by Debreu. This difference stems from their different conceptions of prices and their formation. In Sraffa’s formulation the own-rate of interest is a reflection of the divergence of the market price from normal equilibrium price (and the normal rate of interest). In Debreu’s definition this latter distinction has no meaning. The discounted prices used in his calculation are equilibrium prices, but there is no normal rate of interest of normal long-run prices in the Marshallian sense of those terms. Thus differences in the own-rate of interest as between commodities arise not out of market price ‘deviations’, but out of his definition of a ‘commodity’.

It should also be noted that markets of the type referred to by Debreu, on which payment is made today for commodities to be traded in the future, do not exist. On such futures markets as there are the prices set are those which will be paid at the time the trade is actually made (Debreu 1959, p. 33). Such prices could not be the basis for the calculation of the own-rate of interest on a commodity in the manner of Debreu.

### Bibliography

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