Commodity Interest Rates

What will be the various commodity-rates of interest over 1 year for different types of assets?

Each commodity is a standard.

The returns on each commodity must be reckoned in this context as being measured in terms of itself.

There are 3 attributes which different types of assets possess in different degrees:

1. Some assets produce a yield or output q, measured in terms of themselves, by assisting some process of production or supplying services to a consumer.

2. Most assets, except money, suffer some wastage or involve some cost through the mere passage of time (apart from any change in their relative value), irrespective of their being used to produce a yield;

i.e. they involve a carrying cost c measured in terms of themselves.

It does not matter for our present purpose exactly where we draw the line between the costs which we deduct before calculating q and those which we include in c, since in what follows we shall be exclusively concerned with q - c.

3. The power of disposal over an asset during a period may offer a potential convenience or security, which is not equal for assets of different kinds, though the assets themselves are of equal initial value.

There is nothing to show for this at the end of the period in the shape of output; yet it is something for which people are ready to pay something.

The amount (measured in terms of itself) which they are willing to pay for the potential convenience or security given by this power of disposal (exclusive of yield or carrying cost attaching to the asset), we shall call its liquidity-premium l.

It follows that the total return expected from the ownership of an asset over a period is equal to its yield minus its carrying cost plus its liquidity-premium, i.e. to q - c + l. That is to say, q - c + l is the own-rate of interest of any commodity, where q, c and l are measured in terms of itself as the standard.

It is characteristic of instrumental capital (eg. a machine) or of consumption capital (eg. a house) which is in use, that its yield should normally exceed its carrying cost, whilst its liquidity-premium is probably negligible; of a stock of liquid goods or of surplus laid-up instrumental or consumption capital that it should incur a carrying cost in terms of itself without any yield to set off against it, the liquidity-premium in this case also being usually negligible as soon as stocks exceed a moderate level, though capable of being significant in special circumstances; and of money that its yield is nil, and its carrying cost negligible, but its liquidity-premium substantial.

Different commodities may, indeed, have differing degrees of liquidity-premium amongst themselves, and money may incur some degree of carrying costs, eg. for safe custody.

But it is an essential difference between money and all (or most) other assets that in the case of money its liquidity-premium much exceeds its carrying cost, whereas in the case of other assets their carrying cost much exceeds their liquidity-premium.

Let us assume that on houses:

• the yield is q1
• the carrying cost and liquidity-premium negligible

On wheat:

• the carrying cost is c2
• the yield and liquidity-premium negligible

On money,

• the liquidity-premium is l3
• the yield and carrying cost negligible.

q1 is the house-rate of interest -c2 is the wheat-rate of interest l3 is the money-rate of interest

To determine the relationships between the expected returns on different types of assets which are consistent with equilibrium, we must also know what the changes in relative values during the year are expected to be.

Taking money as our standard of measurement, let the expected percentage appreciation (or depreciation) of houses be a1 and of wheat a2.

ql, -c2 and l3 we have called the own-rates of interest of houses, wheat and money in terms of themselves as the standard of value.

i.e. q1 is the house-rate of interest in terms of houses, -c2 is the wheat-rate of interest in terms of wheat, and l3 is the money-rate of interest in terms of money. It will also be useful to call a1 + ql, a2 - c2, and l3, which stand for the same quantities reduced to money as the standard of value, the house-rate of money-interest, the wheat-rate of money-interest and the money-rate of money-interest respectively. With this notation it is easy to see that the demand of wealth-owners will be directed to houses, to wheat or to money, according as a1 + q1 or a2 - c2, or l3, is greatest. Thus in equilibrium the demand-prices of houses and wheat in terms of money will be such that there is nothing to choose in the way of advantage between the alternatives; — i.e. a1 + q1, a2 - c2 and l3 will be equal. The choice of the standard of value will make no difference to this result because a shift from one standard to another will change all the terms equally, i.e. by an amount equal to the expected rate of appreciation (or depreciation) of the new standard in terms of the old. Now those assets of which the normal supply-price is less than the demand-price will be newly produced, and these will be those assets of which the marginal efficiency would be greater (on the basis of their normal supply-price) than the rate of interest (both being measured in the same standard of value whatever it is). As the stock of the assets, which begin by having a marginal efficiency at least equal to the rate of interest, is increased, their marginal efficiency (for reasons, sufficiently obvious, already given) tends to fall. Thus a point will come at which it no longer pays to produce them, unless the rate of interest falls pari passu. When there is no asset of which the marginal efficiency reaches the rate of interest, the further production of capital-assets will come to a standstill. Let us suppose (as a mere hypothesis at this stage of the argument) that there is some asset (eg. money) of which the rate of interest is fixed (or declines more slowly as output increases than does any other commodity’s rate of interest); how is the position adjusted? Since a1 + q1, a2 - c2 and l3, are necessarily equal, and since l3 by hypothesis is either fixed or falling more slowly than q1 or -c2, it follows that a1 and a2, must be rising.

In other words, the present money-price of every commodity other than money tends to fall relatively to its expected future price. Hence, if q1 and -c2, continue to fall, a point comes at which it is not profitable to produce any of the commodities, unless the cost of production at some future date is expected to rise above the present cost by an amount which will cover the cost of carrying a stock produced now to the date of the prospective higher price. It is now apparent that our previous statement to the effect that it is the money-rate of interest which sets a limit to the rate of output, is not strictly correct. We should have said that it is that asset’s rate of interest which declines most slowly as the stock of assets in general increases, which eventually knocks out the profitable production of each of the others, — except in the contingency, just mentioned, of a special relationship between the present and prospective costs of production. As output increases, own-rates of interest decline to levels at which one asset after another falls below the standard of profitable production; — until, finally, one or more own-rates of interest remain at a level which is above that of the marginal efficiency of any asset whatever. If by money we mean the standard of value, it is clear that it is not necessarily the money-rate of interest which makes the trouble. We could not get out of our difficulties (as some have supposed) merely by decreeing that wheat or houses shall be the standard of value instead of gold or sterling. For, it now appears that the same difficulties will ensue if there continues to exist any asset of which the own-rate of interest is reluctant to decline as output increases.

It may be, for example, that gold will continue to fill this role in a country which has gone over to an inconvertible paper standard.

III

In attributing, therefore, a peculiar significance to the money-rate of interest, we have been tacitly assuming that the kind of money to which we are accustomed has some special characteristics which lead to its own rate of interest in terms of itself as standard being more reluctant to fall as output increases than the own-rates of interest of any other assets in terms of themselves. Is this assumption justified? Reflection shows, I think, that the following peculiarities, which commonly characterise money as we know it, are capable of justifying it. To the extent that the established standard of value has these peculiarities, the summary statement, that it is the money-rate of interest which is the significant rate of interest, will hold good. (i) The first characteristic which tends towards the above conclusion is the fact that money has, both in the long and in the short period, a zero, or at any rate a very small, elasticity of production, so far as the power of private enterprise is concerned, as distinct from the monetary authority; — elasticity of production[2] meaning, in this context, the response of the quantity of labour applied to producing it to a rise in the quantity of labour which a unit of it will command. Money, that is to say, cannot be readily produced; — labour cannot be turned on at will by entrepreneurs to produce money in increasing quantities as its price rises in terms of the wage-unit. In the case of an inconvertible managed currency this condition is strictly satisfied. But in the case of a gold-standard currency it is also approximately so, in the sense that the maximum proportional addition to the quantity of labour which can be thus employed is very small, except indeed in a country of which gold-mining is the major industry.

Now, in the case of assets having an elasticity of production, the reason why we assumed their own-rate of interest to decline was because we assumed the stock of them to increase as the result of a higher rate of output. In the case of money, however — postponing, for the moment, our consideration of the effects of reducing the wage-unit or of a deliberate increase in its supply by the monetary authority — the supply is fixed. Thus the characteristic that money cannot be readily produced by labour gives at once some prima facie presumption for the view that its own-rate of interest will be relatively reluctant to fall; whereas if money could be grown like a crop or manufactured like a motor-car, depressions would be avoided or mitigated because, if the price of other assets was tending to fall in terms of money, more labour would be diverted into the production of money; — as we see to be the case in gold-mining countries, though for the world as a whole the maximum diversion in this way is almost negligible.

2. Obviously, however, the above condition is satisfied, not only by money, but by all pure rent-factors, the production of which is completely inelastic. A second condition, therefore, is required to distinguish money from other rent elements. The second differentia of money is that it has an elasticity of substitution equal, or nearly equal, to zero; which means that as the exchange value of money rises there is no tendency to substitute some other factor for it; — except, perhaps, to some trifling extent, where the money-commodity is also used in manufacture or the arts. This follows from the peculiarity of money that its utility is solely derived from its exchange-value, so that the two rise and fall pari passu, with the result that as the exchange value of money rises there is no motive or tendency, as in the case of rent-factors, to substitute some other factor for it.

Thus, not only is it impossible to turn more labour on to producing money when its labour-price rises, but money is a bottomless sink for purchasing power, when the demand for it increases, since there is no value for it at which demand is diverted — as in the case of other rent-factors — so as to slop over into a demand for other things. The only qualification to this arises when the rise in the value of money leads to uncertainty as to the future maintenance of this rise; in which event, a1 and a2 are increased, which is tantamount to an increase in the commodity-rates of money-interest and is, therefore, stimulating to the output of other assets. (iii) Thirdly, we must consider whether these conclusions are upset by the fact that, even though the quantity of money cannot be increased by diverting labour into producing it, nevertheless an assumption that its effective supply is rigidly fixed would be inaccurate. In particular, a reduction of the wage-unit will release cash from its other uses for the satisfaction of the liquidity-motive; whilst, in addition to this, as money-values fall, the stock of money will bear a higher proportion to the total wealth of the community. It is not possible to dispute on purely theoretical grounds that this reaction might be capable of allowing an adequate decline in the money-rate of interest. There are, however, several reasons, which taken in combination are of compelling force, why in an economy of the type to which we are accustomed it is very probable that the money-rate of interest will often prove reluctant to decline adequately= (a) We have to allow, first of all, for the reactions of a fall in the wage-unit on the marginal efficiencies of other assets in terms of money; — for it is the difference between these and the money-rate of interest with which we are concerned. If the effect of the fall in the wage-unit is to produce an expectation that it will subsequently rise again, the result will be wholly favourable. If, on the contrary, the effect is to produce an expectation of a further fall, the reaction on the marginal efficiency of capital may offset the decline in the rate of interest.[4] (b) The fact that wages tend to be sticky in terms of money, the money-wage being more stable than the real wage, tends to limit the readiness of the wage-unit to fall in terms of money. Moreover, if this were not so, the position might be worse rather than better; because, if money-wages were to fall easily, this might often tend to create an expectation of a further fall with unfavourable reactions on the marginal efficiency of capital. Furthermore, if wages were to be fixed in terms of some other commodity, eg. wheat, it is improbable that they would continue to be sticky. It is because of money’s other characteristics — those, especially, which make it liquid — that wages, when fixed in terms of it, tend to be sticky.[4]

3. The characteristics of money which satisfy liquidity-preference is most important here.

For, in certain circumstances such as will often occur, these will cause the rate of interest to be insensitive, particularly below a certain figure,[5] even to a substantial increase in the quantity of money in proportion to other forms of wealth. In other words, beyond a certain point money’s yield from liquidity does not fall in response to an increase in its quantity to anything approaching the extent to which the yield from other types of assets falls when their quantity is comparably increased. In this connection the low (or negligible) carrying-costs of money play an essential part. For if its carrying-costs were material, they would offset the effect of expectations as to the prospective value of money at future dates. The readiness of the public to increase their stock of money in response to a comparatively small stimulus is due to the advantages of liquidity (real or supposed) having no offset to contend with in the shape of carrying-costs mounting steeply with the lapse of time.

In the case of a commodity other than money a modest stock of it may offer some convenience to users of the commodity. But even though a larger stock might have some attractions as representing a store of wealth of stable value, this would be offset by its carrying-costs in the shape of storage, wastage, etc. Hence, after a certain point is reached, there is necessarily a loss in holding a greater stock. In the case of money, however, this, as we have seen, is not so, — and for a variety of reasons, namely, those which constitute money as being, in the estimation of the public, par excellence “liquid.” Thus those reformers, who look for a remedy by creating artificial carrying-costs for money through the device of requiring legal-tender currency to be periodically stamped at a prescribed cost in order to retain its quality as money, or in analogous ways, have been on the right track; and the practical value of their proposals deserves consideration. The significance of the money-rate of interest arises, therefore, out of the combination of the characteristics that, through the working of the liquidity-motive, this rate of interest may be somewhat unresponsive to a change in the proportion which the quantity of money bears to other forms of wealth measured in money, and that money has (or may have) zero (or negligible) elasticities both of production and of substitution. The first condition means that demand may be predominantly directed to money, the second that when this occurs labour cannot be employed in producing more money, and the third that there is no mitigation at any point through some other factor being capable, if it is sufficiently cheap, of doing money’s duty equally well. The only relief — apart from changes in the marginal efficiency of capital — can come (so long as the propensity towards liquidity is unchanged) from an increase in the quantity of money, or — which is formally the same thing — a rise in the value of money which enables a given quantity to provide increased money-services. Thus a rise in the money-rate of interest retards the output of all the objects of which the production is elastic without being capable of stimulating the output of money (the production of which is, by hypothesis, perfectly inelastic).

The money-rate of interest, by setting the pace for all the other commodity-rates of interest, holds back investment in the production of these other commodities without being capable of stimulating investment for the production of money, which by hypothesis cannot be produced. Moreover, owing to the elasticity of demand for liquid cash in terms of debts, a small change in the conditions governing this demand may not much alter the money-rate of interest, whilst (apart from official action) it is also impracticable, owing to the inelasticity of the production of money, for natural forces to bring the money-rate of interest down by affecting the supply side.

In the case of an ordinary commodity, the inelasticity of the demand for liquid stocks of it would enable small changes on the demand side to bring its rate of interest up or down with a rush, whilst the elasticity of its supply would also tend to prevent a high premium on spot over forward delivery. Thus with other commodities left to themselves, “natural forces,” i.e. the ordinary forces of the market, would tend to bring their rate of interest down until the emergence of full employment had brought about for commodities generally the inelasticity of supply which we have postulated as a normal characteristic of money. Thus in the absence of money and in the absence — we must, of course, also suppose — of any other commodity with the assumed characteristics of money, the rates of interest would only reach equilibrium when there is full employment. Unemployment develops, that is to say, because people want the moon; — men cannot be employed when the object of desire (i.e. money) is something which cannot be produced and the demand for which cannot be readily choked off. There is no remedy but to persuade the public that green cheese is practically the same thing and to have a green cheese factory (i.e. a central bank) under public control. It is interesting to notice that the characteristic which has been traditionally supposed to render gold especially suitable for use as the standard of value, namely, its inelasticity of supply, turns out to be precisely the characteristic which is at the bottom of the trouble. Our conclusion can be stated in the most general form (taking the propensity to consume as given) as follows. No further increase in the rate of investment is possible when the greatest amongst the own-rates of own-interest of all available assets is equal to the greatest amongst the marginal efficiencies of all assets, measured in terms of the asset whose own-rate of own-interest is greatest. In a position of full employment this condition is necessarily satisfied.

But it may also be satisfied before full employment is reached, if there exists some asset, having zero (or relatively small) elasticities of production and substitution,[6] whose rate of interest declines more slowly, as output increases, than the marginal efficiencies of capital-assets measured in terms of it. IV We have shown above that for a commodity to be the standard of value is not a sufficient condition for that commodity’s rate of interest to be the significant rate of interest. It is, however, interesting to consider how far those characteristics of money as we know it, which make the money-rate of interest the significant rate, are bound up with money being the standard in which debts and wages are usually fixed. The matter requires consideration under two aspects. In the first place, the fact that contracts are fixed, and wages are usually somewhat stable, in terms of money unquestionably plays a large part in attracting to money so high a liquidity-premium. The convenience of holding assets in the same standard as that in which future liabilities may fall due and in a standard in terms of which the future cost of living is expected to be relatively stable, is obvious.

At the same time the expectation of relative stability in the future money-cost of output might not be entertained with much confidence ff the standard of value were a commodity with a high elasticity of production. Moreover, the low carrying-costs of money as we know it play quite as large a part as a high liquidity-premium in making the money-rate of interest the significant rate.

What matters is the difference between:

• the liquidity-premium and
• the carrying-costs.

In the case of most commodities, other than gold, silver, and bank-notes, the carrying-costs are at least as high as the liquidity-premium ordinarily attaching to the standard in which contracts and wages are fixed.

• Even if the liquidity-premium now attaching to (e.g.) sterling-money were to be transferred to (eg.) wheat, the wheat-rate of interest would still be unlikely to rise above zero.

It remains the case, therefore, that, whilst the fact of contracts and wages being fixed in terms of money considerably enhances the significance of the money-rate of interest, this circumstance is, nevertheless, probably insufficient by itself to produce the observed characteristics of the money-rate of interest. The second point to be considered is more subtle.

The normal expectation that the value of output will be more stable in terms of money than in terms of any other commodity, depends of course, not on wages being arranged in terms of money, but on wages being relatively sticky in terms of money. What, then, would the position be if wages were expected to be more sticky (i.e. more stable) in terms of some one or more commodities other than money, than in terms of money itself?

Such an expectation requires, not only that the costs of the commodity in question are expected to be relatively constant in terms of the wage-unit for a greater or smaller scale of output both in the short and in the long period, but also that any surplus over the current demand at cost-price can be taken into stock without cost, i.e. that its liquidity-premium exceeds its carrying-costs (for, otherwise, since there is no hope of profit from a higher price, the carrying of a stock must necessarily involve a loss).

If a commodity can be found to satisfy these conditions, then, assuredly, it might be set up as a rival to money. Thus it is not logically impossible that there should be a commodity in terms of which the value of output is expected to be more stable than in terms of money. But it does not seem probable that any such commodity exists.

I conclude, that the commodity, in terms of which wages are expected to be most sticky, cannot be one whose elasticity of production is not least, and for which the excess of carrying-costs over liquidity-premium is not least.

In other words, the expectation of a relative stickiness of wages in terms of money is a corollary of the excess of liquidity-premium over carrying-costs being greater for money than for any other asset. Thus we see that the various characteristics, which combine to make the money-rate of interest significant, interact with one another in a cumulative fashion.

The fact that money has low elasticities of production and substitution and low carrying-costs tends to raise the expectation that will be relatively stable.

This expectation enhances money’s liquidity-premium and prevents the exceptional correlation between the money-rate of interest and the marginal efficiencies of other assets which might, if it could exist, rob the money-rate of interest of its sting.

Professor Pigou has been accustomed to assume that there is a presumption in favour of real wages being more stable than money-wages. But this could only be the case if there were a presumption in favour of stability of employment. Moreover, there is also the difficulty that wage-goods have a high carrying-cost.

If some attempt were made to stabilise real wages by fixing wages in terms of wage-goods, the effect could only be to cause a violent oscillation of money-prices.

For every small fluctuation in the propensity to consume and the inducement to invest would cause money-prices to rush violently between zero and infinity. That money-wages should be more stable than real wages is a condition of the system possessing inherent stability. Thus the attribution of relative stability to real wages is not merely a mistake in fact and experience.

It is also a mistake in logic, if we are supposing that the system in view is stable, in the sense that small changes in the propensity to consume and the inducement to invest do not produce violent effects on prices.