for the first compounding period, of the services which constitute the original principal in the case; the second is the advance, for the second compounding period, of services which constitute the original principal (the services a') plus services which constitute the interest (a") of the first advance; the third is the advance, for the third compounding period, of services which constitute the principal of the second advance plus services which constitute the interest of the second advance; and so on. In commercial transactions the length of the compounding period is fixed by law or by contract, usually as six months or one year. Ideally, however, it should be infinitesimal; for the advance of services for the least time conceivable

b' b' has ideally, on account of the relation of to already b" b

explained, some nominal value, however small, and an advance for an appreciable time really involves the making of a series of advances, each for an infinitesimal period and each of services constituting the principal plus the interest of the previous advance of the series.

§ 60. The question now arises: What is the effect, if any, on the rate of loan interest of the customary adoption, in accordance with law or contract, of so extended a compounding period as six months or a year? It is to raise that rate, above what it would be if the compounding period were infinitesimal, enough to make the return to the lender just what it would be if the compounding period were infinitesimal.

CHAPTER VI

CAUSES OF THE NORMAL RATE OF INTEREST

§ 61. Usually, when people speak or write of the "causes of interest," they mean the causes of a positive rate, a rate above zero. What we want, however, is more than that: we want a comprehensive list of the causes that raise and the causes that lower the rate.

§ 62. In undertaking to determine these causes our first thought is that since I is the formula for the

b'b" bb"" normal rate of interest, whatever increases

raise the rate, and whatever decreases

b'b"

must lower

bb""

the rate. That is, of course, true; but as a criterion of the causes of effects on the rate it is not nearly so serviceable as that furnished by Diagram II (of § 41), in which the rate is represented by the length of a line, WV. The advantage for our present purpose of that diagram, which is reproduced with a slight addition below, is that it reveals the causes of the length of WV, which represents the rate of interest, as divisible into two groups, those on the value side, as we may call them, and those on the cost side. For the length of WV is fully determined by the height above the base-line of the point W. But that point, we know, must be on both the curve OR and the

100

UNIV. OF

curve CH. So the conditions or causes of the rate WV must be susceptible of division into two groups, those that determine the course of the curve OR where it is to cross the curve CH, and those that determine the course of the curve CH where it is to cross OR. Nothing can be a cause, on the value side, of a rise or a fall in the normal rate of interest except a change of conditions that respectively raises or lowers the curve OR so as to raise or lower the point of intersection W; and nothing

-H

-R

DIAGRAM IV

can be a cause, on the cost side, of a rise or a fall in the normal rate of interest except a change of conditions that respectively raises or lowers the curve CH so as to raise or lower the point of intersection W. All this will become clear as we proceed to apply it.

§ 63. What possible conditions, then, on the value side might raise the normal rate of interest? Applying the criterion derived from the diagram, we answer: Any conditions that change the course of OR so as to raise the point of its intersection with CH.

Among such conditions, clearly, are those changes that open opportunities for making advances to nature considered better than those previously considered mar

ginal. (In this connection recall §§ 37-40 above, especially § 40.) For example suppose the time in question to be that of the first successful application of electricity to the propelling of street-cars; suppose the series of all the natural capitals- if I may use such a form of expression in existence and yielding as much as the normal rate of interest at the time to be represented by LI; and suppose the invention as we call it — of the electric car to reveal opportunities for the investment of services, up to an amount represented objectively by a sixteenth of an inch on LI, in advances to nature estimated to be more valuable or advantageous than those standing at the point V in the series. In that case services, in the form of the labor of artisans, represented objectively by a sixteenth of an inch on LI, which would have been devoted, if the invention had not been made, to making and repairing horse-cars and horse-buses, harnesses, and various other sorts of natural capital now displaced in the series, are now diverted to producing electric cars and all their accessories; and the effect of this on the curve OR is to raise its course from that pointsay N in Diagram IV above-at which the electric cars and accessories standing highest take their place in the general series, on towards R or rather towards a point somewhat above R. The dotted line in Diagram IV indicates the course of the curve after the supposed effect of the invention has been felt. It is apparent that although the conditions determining the course of the curve CH, which are the causes of the rate of interest on the cost side, have remained unchanged, the point of intersection of the two curves is no longer W, but X,

MIA OL

which is higher than W. In other words the rate of interest has been raised. We may therefore declare, with an assurance impossible, as it seems to me, to any economist hitherto, that inventions may be causes, on the value side, of a rise in the rate of interest.

Discoveries, as of new lands or of unknown resources in old lands, may have on the rate of interest the same effect as inventions, and for the same reasons.

So also may an extension among men generally of the scientific knowledge already possessed by a few; so may an increase, on the part of laborers, of skill in the handling of machinery; so may an increase of painstaking in the handling of machinery; so, indeed, may any change whatever that raises OR so as to raise its intersection with CH when the course of CH itself remains unchanged.

One more class of these changes that may raise OR so as to raise its intersection with CH demands special explanation. I refer to changes that affect opportunities for making advantageous advances to nature of a sort seldom recognized as advances at all. Let me explain. A young man is really making an advance to nature when he undergoes pain and expense in training himself or educating himself in order to increase the economic value of his services, per unit of their cost, later. Consider the case of a lad who spends money perhaps borrowed money - and works painfully hard to give himself a medical education. Though most of his expenses are for board and lodging, which he is unquestionably "consuming" if a person ever consumes anything, those very "expenses for consumption," as