### The Classical Theory of the Rate of Interest

# WHAT is the Classical Theory of the Rate of Interest?

It
is something upon which we have all been brought up and which we have
accepted without much reserve until recently. Yet I find it difficult to
state it precisely or to discover an explicit account of it in the
leading treatises of the modern classical school.

^{}It is fairly clear, however, that this tradition has regarded the rate of interest as the factor which brings the demand for investment and the willingness to save into equilibrium with one another. Investment represents the demand for investable resources and saving represents the supply, whilst the rate of interest is the “price” of investable resources at which the two are equated. Just as the price of a commodity is necessarily fixed at that point where the demand for it is equal to the supply, so the rate of interest necessarily comes to rest under the play of market forces at the point where the amount of investment at that rate of interest is equal to the amount of saving at that rate.

The above is not to be found in Marshall’s

*Principles*in so many words. Yet his theory seems to be this, and it is what I myself was brought up on and what I taught for many years to others. Take, for example, the following passage from his

*Principles*: “Interest, being the price paid for the use of capital in any market, tends towards an equilibrium level such that the aggregate demand for capital in that market, at that rate of interest, is equal to the aggregate stock forthcoming at that rate”. Or again in Professor Cassel’s

*Nature and Necessity of Interest*it is explained that investment constitutes the “demand for waiting” and saving the “supply of waiting”, whilst interest is a “price” which serves, it is implied, to equate the two, though here again I have not found actual words to quote. Chapter vi. of Professor Carver’s

*Distribution of Wealth*clearly envisages interest as the factor which brings into equilibrium the marginal disutility of waiting with the marginal productivity of capital.

^{}Sir Alfred Flux (

*Economic Principles*, p. 95) writes: “If there is justice in the contentions of our general discussion, it must be admitted that an automatic adjustment takes place between saving and the opportunities for employing capital profitably. ... Saving will not have exceeded its possibilities of usefulness ... so long as the rate of net interest is in excess of zero.” Professor Taussig (

*Principles,*vol., ii. p. 29) draws a supply curve of saving and a demand curve representing “the diminishing productiveness of the several instalments of capital”, having previously stated (p. 20) that “the rate of interest settles at a point where the marginal productivity of capital suffices to bring out the marginal instalment of saving”. Walras, in Appendix I. (III.) of his

*éléments d'Économie pure,*where he deals with “l'échange d'épargnes contre capitaux neufs”, argues expressly that, corresponding to each possible rate of interest, there is a sum which individuals will save and also a sum which they will invest in new capital assets, that these two aggregates tend to equality with one another, and that the rate of interest is the variable which brings them to equality; so that the rate of interest is fixed at the point where saving, which represents the supply of new capital, is equal to the demand for it. Thus he is strictly in the classical tradition.

Certainly the ordinary man — banker, civil servant or politician — brought up on the traditional theory, and the trained economist also, has carried away with him the idea that whenever an individual performs an act of saving he has done something which automatically brings down the rate of interest, that this automatically stimulates the output of capital, and that the fall in the rate of interest is just so much as is necessary to stimulate the output of capital to an extent which is equal to the increment of saving; and, further, that this is a self-regulatory process of adjustment which takes place without the necessity for any special intervention or grandmotherly care on the part of the monetary authority. Similarly — and this is an even more general belief, even to-day — each additional act of investment will necessarily raise the rate of interest, if it is not offset by a change in the readiness to save.

Now the analysis of the previous chapters will have made it plain that this account of the matter must be erroneous. In tracing to its source the reason for the difference of opinion, let us, however, begin with the matters which are agreed.

Unlike the neo-classical school, who believe that saving and investment can be actually unequal, the classical school proper has accepted the view that they are equal. Marshall, for example, surely believed, although he did not expressly say so, that aggregate saving and aggregate investment are necessarily equal. Indeed, most members of the classical school carried this belief much too far; since they held that every act of increased saving by an individual necessarily brings into existence a corresponding act of increased investment. Nor is there any material difference, relevant in this context, between my schedule of the marginal efficiency of capital or investment demand-schedule and the demand curve for capital contemplated by some of the classical writers who have been quoted above. When we come to the propensity to consume and its corollary the propensity to save, we are nearer to a difference of opinion, owing to the emphasis which they have placed on the influence of the rate of interest on the propensity to save. But they would, presumably, not wish to deny that the level of income also has an important influence on the amount saved; whilst I, for my part, would not deny that the rate of interest may perhaps have an influence (though perhaps not of the kind which they suppose) on the amount saved

*out of a given income.*All these points of agreement can be summed up in a proposition which the classical school would accept and I should not dispute; namely, that, if the level of income is assumed to be given, we can infer that the current rate of interest must lie at the point where the demand curve for capital corresponding to different rates of interest cuts the curve of the amounts saved out of the given income corresponding to different rates of interest.

But this is the point at which definite error creeps into the classical theory. If the classical school merely inferred from the above proposition that, given the demand curve for capital and the influence of changes in the rate of interest on the readiness to save out of given incomes, the level of income and the rate of interest must be uniquely correlated, there would be nothing to quarrel with. Moreover, this proposition would lead naturally to another proposition which embodies an important truth; namely, that, if the rate of interest is given as well as the demand curve for capital and the influence of the rate of interest on the readiness to save out of given levels of income, the level of income must be the factor which brings the amount saved to equality with the amount invested. But, in fact, the classical theory not merely neglects the influence of changes in the level of income, but involves formal error.

For the classical theory, as can be seen from the above quotations, assumes that it can then proceed to consider the effect on the rate of interest of (

*e.g.*) a shift in the demand curve for capital, without abating or modifying its assumption as to the amount of the given income out of which the savings are to be made. The independent variables of the classical theory of the rate of interest are the demand curve for capital and the influence of the rate of interest on the amount saved out of a given income; and when (

*e.g*.) the demand curve for capital shifts, the new rate of interest, according to this theory, is given by the point of intersection between the new demand curve for capital and the curve relating the rate of interest to the amounts which will be saved out of the given income. The classical theory of the rate of interest seems to suppose that, if the demand curve for capital shifts or if the curve relating the rate of interest to the amounts saved out of a given income shifts or if both these curves shift, the new rate of interest will be given by the point of intersection of the new positions of the two curves. But this is a nonsense theory. For the assumption that income is constant is inconsistent with the assumption that these two curves can shift independently of one another. If either of them shift, then, in general, income will change; with the result that the whole schematism based on the assumption of a given income breaks down. The position could only be saved by some complicated assumption providing for an automatic change in the wage-unit of an amount just sufficient in its effect on liquidity-preference to establish a rate of interest which would just offset the supposed shift, so as to leave output at the same level as before. In fact, there is no hint to be found in the above writers as to the necessity for any such assumption; at the best it would he plausible only in relation to long-period equilibrium and could not form the basis of a short-period theory; and there is no ground for supposing it to hold even in the long-period. In truth, the classical theory has not been alive to the relevance of changes in the level of income or to the possibility of the level of income being actually a function of the rate of the investment.

The above can be illustrated by a diagram as follows:

#### In this diagram the amount of investment (or saving) I is measured vertically, and the rate of interest

*r*horizontally. X

_{1}X

_{1}' is the first position of the investment demand-schedule, and X

_{2}X

_{2}' is a second position of this curve. The curve Y

_{1}relates the amounts saved out of an income Y

_{1}to various levels of the rate of interest, the curves Y

_{2}, Y

_{3}, etc., being the corresponding curves for levels of income Y

_{2}, Y

_{3}, etc. Let us suppose that the curve Y

_{1}, is the Y-curve consistent with an investment demand-schedule X

_{1}X

_{1}', and a rate of interest

*r*

_{1}. Now if the investment demand-schedule shifts from X

_{1}X

_{1}' to X

_{2}X

_{2}', income will, in general, shift also. But the above diagram does not contain enough

*data*to tell us what its new value will be; and, therefore, not knowing which is the appropriate Y-curve, we do not know at what point the new investment demand-schedule will cut it. If, however, we introduce the state of liquidity-preference and the quantity of money and these between them tell us that the rate of interest is

*r*, then the whole position becomes determinate. For the Y-curve which intersects X

_{2}X

_{2}' at the point vertically above

*r*

_{2}, namely, the curve Y

_{2}, will be the appropriate curve. Thus the X-curve and the Y-curves tell us nothing about the rate of interest. They only tell us what income will be, if from some other source we can say what the rate of interest is. If nothing has happened to the state of liquidity-preference and the quantity of money, so that the rate of interest is unchanged, then the curve Y'

_{2}which intersects the new investment demand-schedule vertically below the point where the curve Y

_{1}intersected the old investment demand-schedule will be the appropriate Y-curve, and Y'

_{2}will be the new level of income.

Thus the functions used by the classical theory, namely, the response of investment and the response of the amount saved out of a given income to change in the rate of interest, do not furnish material for a theory of the rate of interest; but they could be used to tell us what the level of income will be, given (from some other source) the rate of interest; and, alternatively, what the rate of interest will have to be, if the level of income is to be maintained at a given figure (

*eg.*the level corresponding to full employment).

The mistake originates from regarding interest as the reward for waiting as such, instead of as the reward for not-hoarding; just as the rates of return on loans or investments involving different degrees of risk, are quite properly regarded as the reward, not of waiting as such, but of running the risk. There is, in truth, no sharp line between these and the so-called “pure” rate of interest, all of them being the reward for running the risk of uncertainty of one kind or another. Only in the event of money being used solely for transactions and never as a store of value, would a different theory become appropriate.

^{}

There are, however, two familiar points which might, perhaps, have warned the classical school that something was wrong. In the first place, it has been agreed, at any rate since the publication of Professor Cassel’s

*Nature and Necessity of Interest,*that it is not certain that the sum saved out of a given income necessarily increases when the rate of interest is increased; whereas no one doubts that the investment demand-schedule falls with a rising rate of interest. But if the Y-curves and the X-curves both fall as the rate of interest rises, there is no guarantee that a given Y-curve will intersect a given X-curve anywhere at all. This suggests that it cannot be the Y-curve and the X-curve alone which determine the rate of interest.

In the second place, it has been usual to suppose that an increase in the quantity of money has a tendency to reduce the rate of interest, at any rate in the first instance and in the short period. Yet no reason has been given why a change in the quantity of money should affect either the investment demand-schedule or the readiness to save out of a given income. Thus the classical school have had quite a different theory of the rate of interest in Volume I. dealing with the theory of value from what they have had in Volume II. dealing with the theory of money. They have seemed undisturbed by the conflict and have made no attempt, so far as I know, to build a bridge between the two theories. The classical school proper, that is to say; since it is the attempt to build a bridge on the part of the neo-classical school which has led to the worst muddles of all. For the latter have inferred that there must be two sources of supply to meet the investment demand-schedule; namely, savings proper, which are the savings dealt with by the classical school,

*plus*the sum made available by any increase in the quantity of money (this being balanced by some species of levy on the public, called “forced saving” or the like). This leads on to the idea that there is a “natural” or “neutral”

^{[6]}or “equilibrium” rate of interest, namely, that rate of interest which equates investment to classical savings proper without any addition from “forced savings”; and finally to what, assuming they are on the right track at the start, is the most obvious solution of all, namely, that, if the quantity of money could only be kept

*constant*in all circumstances, none of these complications would arise, since the evils supposed to result from the supposed excess of investment over savings proper would cease to be possible. But at this point we are in deep water. “The wild duck has dived down to the bottom — as deep as she can get — and bitten fast hold of the weed and tangle and all the rubbish that is down there, and it would need an extraordinarily clever dog to dive after and fish her up again.”

Thus the traditional analysis is faulty because it has failed to isolate correctly the independent variables of the system. Saving and Investment are the determinates of the system, not the determinants. They are the twin results of the system’s determinants, namely, the propensity to consume, the schedule of the marginal efficiency of capital and the rate of interest. These determinants are, indeed, themselves complex and each is capable of being affected by prospective changes in the others. But they remain independent in the sense that their values cannot be inferred from one another. The traditional analysis has been aware that saving depends on income but it has overlooked the fact that income depends on investment, in such fashion that, when investment changes, income must necessarily change in just that degree which is necessary to make the change in saving equal to the change in investment.

Nor are those theories more successful which attempt to make the rate of interest depend on “the marginal efficiency of capital”. It is true that in equilibrium the rate of interest will be equal to the marginal efficiency of capital, since it will be profitable to increase (or decrease) the current scale of investment until the point of equality has been reached. But to make this into a theory of the rate of interest or to derive the rate of interest from it involves a circular argument, as Marshall discovered after he had got half-way into giving an account of the rate of interest along these lines. For the “marginal efficiency of capital” partly depends on the scale of current investment, and we must already know the rate of interest before we can calculate what this scale will be. The significant conclusion is that the output of new investment will be pushed to the point at which the marginal efficiency of capital becomes equal to the rate of interest; and what the schedule of the marginal efficiency of capital tells us, is, not what the rate of interest is, but the point to which the output of new investment will be pushed, given the rate of interest.

The reader will readily appreciate that the problem here under discussion is a matter of the most fundamental theoretical significance and of overwhelming practical importance. For the economic principle, on which the practical advice of economists has been almost invariably based, has assumed, in effect, that,

*cet. par.,*a decrease in spending will tend to lower the rate of interest and an increase in investment to raise it. But if what these two quantities determine is, not the rate of interest, but the aggregate volume of employment, then our outlook on the mechanism of the economic system will be profoundly changed. A decreased readiness to spend will be looked on in quite a different light if, instead of being regarded as a factor which will,

*cet. par.,*increase investment, it is seen as a factor which will,

*cet. par.,*diminish employment.