## Interest, Own Rate of

## Interest, Own Rate of

# Interest, Own Rate of

The concept of own rates of interest can be traced back to Irving Fisher’s *Appreciation and Interest* (1896, pp. 8ff.). It was then revived and extended by Piero Sraffa (1932) to the determination of “commodity rates of interest” on all durable assets in his critique of Friedrich August Hayek’s *Prices and Production* (1931), and subsequently taken up by John Maynard Keynes in chapter 17, “The Essential Properties of Interest and Money,” in his *General Theory of Employment, Interest and Money* (1936). There Keynes used the concept to demonstrate that the rate of interest on money plays a crucial role in setting a limit to production below full employment.

Keynes used Sraffa’s notion that for every durable commodity there is a rate of interest for it in terms of itself, as, for example, a cotton rate of interest or a wheat rate of interest. Three components enter into the own-rate of interest of assets: a physical yield or output *q*, a carrying cost *c*, and its liquidity-premium *l.* Thus q* _{i}* – c

*+ l*

_{i}*is the own-rate of interest ρ*

_{i}*of any commodity*

_{i}*i*, with

*q, c*, and

*l*measured in terms of itself as the standard. These commodity rates of interest may differ between commodities, just as interest rates are likely to differ between different currency areas. For purposes of comparison, these commodity rates must be converted into a common standard of value

*(numéraire)*, usually money. Furthermore, one has to consider the expected rate of appreciation or depreciation of the price of a commodity δ

*in terms of money, determined on spot and forward markets. If, for example, the spot price of 100 quarters of wheat is*

_{i, t}*p*, the forward price in

_{t}*θ*periods

*p*, and the money rate of interest (the own-rate of interest on money) for

_{t + θ}*θ*periods

*i*, then the own rate of interest of wheat between

_{t, θ}*t*and

*t + θ*equals

If the spot price of wheat is £100, the forward price for delivery in a year hence £107, and the money rate of interest 5 percent per annum, then the wheat rate of interest is about –2 percent per year (see Keynes 1936, p. 223).

According to Keynes, the own rate of interest of any commodity *i* in terms of money thus can be written as

*i _{i, t}* = ρ

*+ δ*

_{i}*=*

_{i}*q*–

_{i}*c*+

_{i}*l*+

_{i}*δ*+

_{i}*ρ*

_{i}δ_{i}The difference between the wheat rate of interest and the money rate of interest indicates that the market for wheat is not in long-run equilibrium. Although at any moment in time there might exist as many “natural” rates of interest as there are commodities, they would not be “equilibrium” rates, as has been emphasized by Sraffa in his critique of Hayek. It is only in equilibrium that the spot and the (discounted) forward price for all commodities coincide and that “all the ‘natural’ or commodity rates are equal to one another, and to the money rate” (Sraffa 1932, p. 50), which is regarded by Sraffa as the normal rate of interest for the economy as the whole.

The latter concept has no meaning in modern general equilibrium theory of the Arrow-Debreu type, in which a complete break with the classical concern with long-period equilibria has taken place. Commodities are specified not only in physical terms, but also with regard to their date of availability. The set of intertemporal equilibrium prices consists of prices paid on current markets for commodities to be traded at a future date. Although there is some technical similarity in the calculation of own rates of interest with a multiplicity of these rates in intertemporal equilibrium, there remains the crucial difference that the concept of a long-run equilibrium, in which all rates of interest are equal in terms of the standard of value and equal to the own rate of interest of that numéraire, is missing.

In contrast to modern general equilibrium theory, there are no complete future markets in Keynes’s economics. In his *General Theory* Keynes came to the conclusion that in the long run, the economy may end up in an unemployment equilibrium, and that, in absence of rigid money wages, it is the level of the money rate of interest that rules the roost and creates a barrier to full employment. The reasons are to be found in three essential properties of money: (1) (near) zero elasticity of production, which makes it scarce because it cannot be produced privately; (2) (near) zero elasticity of substitution, a potential bottomless sink for purchasing power when money demand increases; and (3) a yield of nil with negligible carrying costs while comprising a substantial liquidity premium. This opens the way for the “liquidity trap” as the decisive cause for the money rate of interest to fall inadequately. Keynes used Sraffa’s ideas in his analysis of the determination of the volume of investment. However, it is doubtful whether Keynes fully understood Sraffa’s arguments (Kurz 2000). This is reflected in Keynes’s ambiguous use of a short-run rate of interest and a long-run equilibrium rate of interest, and in the fact that his schedule of marginal efficiency of capital cannot be independent of the rate of interest (Barens and Caspari 1997).

**SEE ALSO** *Arrow-Debreu Model; Carrying Cost; General Equilibrium; Keynes, John Maynard; Liquidity; Liquidity Premium; Liquidity Trap; Long Period Analysis; Sraffa, Piero; Yield*

## BIBLIOGRAPHY

Barens, Ingo, and Volker Caspari. 1997. Own-Rates of Interest and Their Relevance for the Existence of Underemployment Equilibrium Positions. In *A “Second Edition” of the General Theory*, Vol. 1, eds. Geoffrey C. Harcourt and Peter A. Riach, 283–303. London and New York: Routledge.

Fisher, Irving. 1896. *Appreciation and Interest.* New York: Macmillan.

Hayek, Friedrich A. 1931. *Prices and Production.* London: Routledge and Kegan Paul.

Keynes, John Maynard. 1936. *The General Theory of Employment, Interest and Money.* London: Macmillan.

Kurz, Heinz D. 2000. The Hayek-Keynes-Sraffa Controversy Reconsidered. In *Critical Essays on Piero Sraffa’s Legacy in Economics*, ed. Heinz D. Kurz, 257–301. Cambridge, U.K.: Cambridge University Press.

Sraffa, Piero. 1932. Dr. Hayek on Money and Capital. *Economic Journal* 42 (1): 42–53.

*Harald Hagemann*