The Online Library of Liberty

A project of Liberty Fund, Inc.

• Errata
• Preface
• Suggestions to Readers
• Part I.: Introduction
• Part I, Chapter I: Income and Capital 2
• Part I, Chapter II: Money Interest and Real Interest
• Part I, Chapter III: Some Common Pitfalls
• Part II.: The Theory In Words
• Part Ii, Chapter IV: Time Preference (human Impatience)
• Part Ii, Chapter V: First Approximation to the Theory of Interest Assuming Each Person's Income Stream Foreknown and Unchangeable Except By Loans
• Part Ii, Chapter VI: Second Approximation to the Theory of Interest Assuming Income Modifiable (1) By Loans and (2) By Other Means
• Part Ii, Chapter VII: The Investment Opportunity Principles
• Part Ii, Chapter VIII: Discussion of the Second Approximation
• Part Ii, Chapter IX: Third Approximation to the Theory of Interest Assuming Income Uncertain
• Part III.: The Theory In Mathematics
• Part Iii, Chapter X: First Approximation In Geometric Terms
• Part Iii, Chapter XI: Second Approximation In Geometric Terms
• Part Iii, Chapter XII: First Approximation In Terms of Formulas
• Part Iii, Chapter XIII: Second Approximation In Terms of Formulas
• Part Iii, Chapter XIV: The Third Approximation Unadapted to Mathematical Formulation
• Part IV.: Further Discussion
• Part Iv, Chapter XV: The Place of Interest In Economics
• Part Iv, Chapter XVI: Relation of Discovery and Invention to Interest Rates
• Part Iv, Chapter XVII: Personal and Business Loans
• Part Iv, Chapter XVIII: Some Illustrative Facts
• Part Iv, Chapter XIX: The Relation of Interest to Money and Prices
• Part Iv, Chapter XX: Objections Considered 73
• Part Iv, Chapter XXI: Summary
• Appendix to Chapter I
• Appendix to Chapter X
• Appendix to Chapter Xii
• Appendix to Chapter Xiii
• Appendix to Chapter Xix
• Appendix to Chapter Xx
• Bibliography

PART II.

THE THEORY IN WORDS

PART II, CHAPTER IV

TIME PREFERENCE (HUMAN IMPATIENCE)

§1. Preference for Present over Future Income

IN the preceding chapter we mentioned some pitfalls in the explanation of interest. We are now ready to consider more searchingly the fundamental causes which determine the rate of interest. We shall find a place for each of the partial truths contained in the inadequate theories.

Many people think of interest as dependent directly on capital. As already suggested, it will help the reader to proceed in the following analysis if he will try to forget capital and instead think exclusively of income. Capital wealth is merely the means to the end called income, while capital value (which is the sense in which the term capital is ordinarily used by interest theorists) is merely the capitalization of expected income.

The theory of interest bears a close resemblance to the theory of prices, of which, in fact, it is a special aspect. The rate of interest expresses a price in the exchange between present and future goods. Just as, in the ordinary theory of prices, the ratio of exchange of any two articles is based, in part, on a psychological or subjective element—their comparative marginal desirability—so, in the theory of interest, the rate of interest, or the premium on the exchange between present and future goods, is based, in part, on a subjective element, a derivative of marginal desirability; namely, the marginal preference for present over future goods. This preference has been called time preference, or human impatience. The chief other part is an objective element, investment opportunity. It is the impatience factor which we shall now discuss, leaving the investment opportunity factor for discussion in later chapters.

Time preference, or impatience, plays a central rôle in the theory of interest. It is essentially what Rae calls the "effective desire for accumulation," and what Böhm-Bawerk calls the "perspective undervaluation of the future." It is the (percentage) excess of the present marginal want for29 one more unit of present goods over the present marginal want for one more unit of future goods. Thus the rate of time preference, or degree of impatience, for present over future goods of like kind is readily derived from the marginal desirabilities of, or wants for, those present and future goods respectively.30

§2. Reduction to Enjoyment Income

What are these goods which are thus contrasted? At first sight it might seem that the goods compared may be indiscriminately wealth, property, or services. It is true that present machines are in general preferred to future machines; present houses to future houses; land possessed today to land available next year; present food or clothing to future food or clothing; present stocks or bonds to future stocks or bonds; present music to future music, and so on. But a slight examination will show that some of these cases of preference are reducible to others.

When present capital wealth, or capital property, is preferred to future, this preference is really a preference for the income expected to flow from the first capital wealth, or capital property, as compared with the income from the second. The reason why we would choose a present fruit tree rather than a similar tree available in ten years is that the fruit yielded by the first will come earlier than the fruit yielded by the second. The reason one prefers immediate tenancy of a house to the right to occupy it in six months is that the uses of the house under the first leasehold begin six months earlier than under the second. In short, capital wealth, or capital property, available early is preferred to the capital wealth, or capital property of like kind, available at a more remote time simply and solely because the income from the former is available earlier than the income from the latter.

Thus all time preference resolves itself in the end into the preference for comparatively early income over comparatively remote, or deferred, income. Moreover, the preference for early, or prompt, income over late, or deferred, income resolves itself into the preference for early enjoyment income over deferred enjoyment income. Any income item which consists merely of an interaction or, otherwise expressed, of a preparatory service31 (that is, an item which, while it is income from one species of capital, is outgo in respect to another species) is wanted for the sake of the enjoyment income to which that interaction paves the way. The consumer prefers the service of milling flour in the present to milling flour in the future because the enjoyment of the resulting bread is available earlier in the one case than in the other. The manufacturer prefers present weaving to future weaving because the earlier the weaving takes place the sooner will he be able to sell the cloth and realize his enjoyment income.

To him, early sales are more advantageous than deferred sales, not because he desires the cloth to reach its ultimate destination sooner, but because he will the sooner be in a position to make use of the purchase price for his own personal uses—the shelter and comforts of various kinds constituting his income.

The manufacturer is conscious of only one step toward the ultimate goal of clothes—the money he expects to get for the cloth from the jobber to whom he sells it. But this money payment in turn discounts a further step. To the jobber this money he pays is the discounted value of the money he will receive from the wholesaler, and so on through the retailer, tailor and wearer. The result is that each is unconsciously discounting, as the ultimate link in the chain, the enjoyment to be derived by the wearer of the clothes. Of course this is not the whole story, but it represents the main parts relevant to the present problem.

All preference, therefore, for present over future goods resolves itself, in the last analysis, into a preference for early enjoyment income over deferred enjoyment income. This simple proposition would have received definite attention earlier in the history of economics had there been at hand a clear-cut concept of income. The stream of future enjoyment income plays the essential rôle.

But, as explained in Chapter I, for practical purposes we may well stop at the objective services of wealth, as measured by its cost—the cost of living—that is, the money values of nourishment, clothing, shelter, amusements, the gratifications of vanity, and the other miscellaneous items in our family budget. It is the money value of this income stream upon which attention now centers. Henceforth, we may think of time preference as the preference for a dollar's worth of early real income over a dollar's worth of deferred real income. It is assumed, then, that the income goods are reduced to a common money denominator, and that the prices of all items of real income—the prices of nourishment, shelter, clothing, amusements, etc.—are predetermined.

In these cases, as already noted, no appreciable time elapses between valuation and realization. We pay for a basket of fruit and eat it forthwith. But we pay for a fruit tree and wait years for the fruit. So in the prices of many other enjoyable services—nourishment, shelter, etc.—no discount element, or rate of interest, enters or, at any rate, it does not enter in the direct way in which it enters in case of interactions.32 That is, in the present, the price of present real income contains no appreciable interest to complicate the problem because these goods are consumed so soon after purchase; and for the same reason in the future price of future real income there is no appreciable interest element. When, however, any goods other than enjoyable goods are considered, their values already contain a rate of interest. The price of a house is the discounted value of its future income. Hence, when we compare the values of present and future houses, both terms of the comparison already involve a rate of interest. Although, as will be noted more specifically later, such a complication would not necessarily beg the question, its elimination simplifies the picture.

§3. Impatience Depends on Income

Time preference, a concept which psychologically underlies interest, lends itself to express any situation, either preference for present as against future goods or preference for future as against present goods or for no preference. The term impatience carries with it the presumption that present goods are preferred. But I shall treat the two terms (impatience and time preference) as synonymous. Henceforth the term impatience will be the one chiefly used partly because its meaning is more self-evident, partly because it is shorter, and partly because it does carry a presumption as to the usual direction of the time preference. The degree of impatience varies, of course, with the individual, but when we have selected our individual, the degree of his impatience depends on his entire income stream, beginning at the present instant and stretching indefinitely into the future; that is, on the amount of his expected real income and the manner in which it is expected to be distributed in time. It depends in particular on the relative abundance of the early as compared with the remote income items—or what we shall call the time shape of the expected income stream. If income is particularly abundant in the future; that is, if the person expects an increase in his income stream, he would willingly promise to sacrifice out of that increase, when it comes, a relatively large sum for the sake of receiving a relatively small sum at once. Thus the possessor of a strawberry patch might, in winter, be willing to exchange two boxes of strawberries, due in six months, for one available today. On the other hand, if immediate income is abundant but future income scarce, the opposite relation may exist. In strawberry season, the same man might willingly give up two boxes of his then abundant crop for the right to only one box in the succeeding winter. That is, time preference may not always be a preference for present over future goods; it may, under certain conditions, be the opposite. Impatience may be and sometimes is negative!

It is, therefore, not necessary in beginning our study of interest to distinguish, as many writers do, between the principles which lead to the existence of interest and those which regulate the rate of interest. By the existence of interest these writers mean that the rate is greater than zero. It seems preferable to reverse the order of the two problems and seek first to find the principles which fix the terms on which present and future goods exchange, without restricting ourselves in advance to the thesis that, always and necessarily, present goods command a premium over future goods. If our principles permit the deviations from par to be in either direction, this will mean that the rate of interest may under certain circumstances be zero (i.e., non-existent), or even negative, so that, in such a case, future goods would command a premium over present. After these general principles have been established a special study will then be in order to discover why the rate of interest is, in actual experience, almost never zero or negative.

We noted, in Chapter II, that when gold, or any other durable commodity capable of being stored or kept without cost, is the standard of comparison, the rate of interest in terms of that standard cannot fall below zero. Does the reason why interest is, in general experience, positive rather than negative lie entirely in human nature? Or does it lie partly in the income stream? These special questions can best be answered after we have found the general principles by which the rate of interest, be it positive, negative, or zero, is determined.

§4. Interest and Price Theory

The preference of any individual for early over deferred income depends upon his present as compared with his prospective income and corresponds to the ordinary theory of prices, which recognizes that the marginal want for any article depends upon the quantity of that article available. Both propositions are fundamental in their respective spheres.

The relationship of these problems, and others, may be schematized roughly as shown in Chart 4 which follows.

In this chart A and B represent present prices of enjoyable goods; and A' and B' prices of future enjoyable goods. A and A' refer to different years in the same place, say New York; B and B' are similar except that they relate to a different place, say London.

All problems of local prices, exchange, and interest, act and react on each other in many ways. The problem of "time" foreign exchange, or forward foreign exchange, is indicated by the diagonals, and involves both interest and foreign exchange, i.e., both a time to time factor and a place to place factor combined in the same transaction. Both exchange and interest rates, as well as local prices, would be, theoretically, combined if, say, present New York wheat were quoted in terms of future London coal.

In this book, for simplicity, the problems of price determinations, in one place and at one time, are supposed to have been solved.33 We start with the values of the items in the income stream ready made. Likewise we neglect the problem of foreign exchange; we are studying only the problem of interest.

§5. Specifications of Income

In the above schematic picture only two periods of time are represented. In actual life there are many periods—an indefinite number of them. Theoretically there might be a rate of interest connecting every pair of possible dates. For instance, there might be a rate of interest between the present and one year hence, another between one year hence and two years hence, and so on, all these rates being quotable in today's markets. In practice no rates are actually quoted except those connecting the present (which, of course, merely means a future date near the present) with several more remotely future dates. A rate on a five year contract may be considered as a sort of an average of five theoretically existing rates, one for each of the five years covered.

Except when the contrary is specifically mentioned, it will henceforth be understood, for the sake of simplicity, that there is only one rate of interest, the rate of interest, applicable to all time intervals. This may be most conveniently pictured to mean the rate connecting today with one year hence. Even this rate of interest connecting two specific dates separated by one year depends on (or, in technical terminology, is a function of) conditions not only at these two dates but at many other dates. When it is said that the impatience of an individual depends on his future income stream, it is meant that the degree of his impatience for, say, $100 worth of this year's income over $100 worth of next year's income depends upon the entire character of his expected income stream pictured as beginning today and extending into the indefinite future, with specific increases or decreases at different periods of time.

If we wish to be still more meticulous, we may note that a person's income stream is made up of a large number of different elements, filaments, strands, or fibers, some of which represent nourishment, others shelter, others amusement, and so on—all the components of real income. In a complete enumeration of these elements, we should need to distinguish the use of each different kind of food, and the gratification of every other variety of human want. Each of these constitutes a particular thread of the income stream, extending out from the present into the indefinite future, and varying at different points of time in respect to size and probability of attainment. A person's time preference, or impatience for income, therefore, depends theoretically on the size, time shape, and probability (as looked at in the present) of this entire collection of income elements as we may picture them stretching out into the entire future.

In summary, we may say then that an individual's impatience depends on the following four characteristics of his income stream:

• 1. The size (measured in dollars) of his expected real income stream.
• 2.Its expected distribution in time, or its time shape—that is, whether it is constant, or increasing, or decreasing, or sometimes one and sometimes the other.
• 3.Its composition—to what extent it consists of nourishment, of shelter, of amusement, of education, and so on.
• 4.Its probability, or degree of risk or uncertainty.

We shall consider these four in order.

§6. The Influence of Mere Size

Our first step, then, is to show how a person's impatience depends on the size of his income, assuming the other three conditions to remain constant; for, evidently, it is possible that two incomes may have the same time shape, composition and risk, and yet differ in size, one being, say, twice the other in every period of time.

In general, it may be said that, other things being equal, the smaller the income, the higher the preference for present over future income; that is, the greater the impatience to acquire income as early as possible. It is true, of course, that a permanently small income implies a keen appreciation of future wants as well as of immediate wants. Poverty bears down heavily on all portions of a man's expected life. But it increases the want for immediate income even more than it increases the want for future income.

This influence of poverty is partly rational, because of the importance, by supplying present needs, of keeping up the continuity of life and thus maintaining the ability to cope with the future; and partly irrational, because the pressure of present needs blinds a person to the needs of the future.

As to the rational aspect, present income is absolutely indispensable, not only for present needs, but even as a pre-condition to the attainment of future income. A man must live. Any one who values his life would, under ordinary circumstances, prefer to rob the future for the benefit of the present—so far, at least, as to keep life going. If a person has only one loaf of bread he would not set it aside for next year even if the rate of interest were 1000 per cent; for if he did so, he would starve in the meantime. A single break in the thread of life suffices to cut off all the future. We stress the importance of the present because the present is the gateway to the future. Not only is a certain minimum of present income necessary to prevent starvation, but the nearer this minimum is approached the more precious does present income appear relative to future income.

As to the irrational aspect of the matter, the effect of poverty is often to relax foresight and self-control and to tempt us to "trust to luck" for the future, if only the all-engrossing need of present necessities can be satisfied.

We see, then, that a small income, other things being equal, tends to produce a high rate of impatience, partly from the thought that provision for the present is necessary both for the present itself and for the future as well, and partly from lack of foresight and self-control.

§7. The Influence of Time Shape

The concept of time shape of the income stream34 is best treated not apart from size but as combined with size and thus will constitute a complete specification of the size at each successive period of time. Types of income of different time shapes are shown on the charts in Chapter I. Uniform income is represented in Chart 1; increasing income in Chart 2; decreasing income in Chart 3. Fluctuating income is represented in both Charts 2 and 3.

The fact that a person's income is increasing tends to make his preference for present over future income high, as compared with what it would be if his income were flowing uniformly or at a slackening rate; for an increasing income means that the present income is relatively scarce and future income relatively abundant. A man who is now enjoying an income of only $5000 a year, but who expects in ten years to be enjoying one of $10,000 a year, will today prize a dollar in hand far more than the prospect of a dollar due ten years hence. His great expectations make him impatient to realize on them in advance. He may, in fact, borrow money to eke out this year's income and promise repayments out of his supposedly more abundant income ten years later. On the other hand, a progressively dwindling income, one such that present income is relatively abundant and future income relatively scarce, tends to appease impatience—i.e., to reduce the want for present as compared with that for future income. A man who has a salary of $10,000 at present but expects to retire in a few years on half pay will not have a very high rate of preference for present over future income. He may even want to save from his present abundance in order to provide for coming needs.

These are, of course, only some of the various effects which various time shapes have on time preference. The important point is that it does make a difference to a man's time preference whether his income has one time shape or another, just as it makes a difference whether his income is, as a whole, larger or smaller.

The extent of these effects will, of course, vary greatly with different individuals. If two persons both have exactly the same sort of ascending income, one may have a rate of time preference, or degree of impatience, indicated by 10 per cent, while the other may have one of only 4 per cent. What we need to emphasize here is merely that, if for either man a descending income were substituted for an ascending income, he would experience a reduction of impatience; the first individual's might fall from 10 to 7 per cent, and the second's from, say, 4 to 3 per cent.

If, now, we consider the combined effect on time preference of both the size and the time shape of income, we shall observe that those with small incomes are much more sensitive to time shape in their feeling of impatience than are those with larger incomes. For a poor man, a very slight stinting of the present suffices to enhance enormously his impatience for present income; and oppositely, a very slight increase in his present income will suffice enormously to diminish that impatience. A rich man, on the other hand, presumably requires a relatively large variation in the comparative amounts of this year's and next year's income in order to suffer any material change in his time preference.

It will be clear to readers of Böhm-Bawerk that the dependence of time preference on the time shape of a person's income stream is practically identical with what he called the "first circumstance" making for the superiority of present over future goods:

The only important difference between this statement and that here formulated is that in this book the "provision" has the definite meaning contained in the income concept.

It is only for completeness that I have included in the list of characteristics of income affecting interest the composition of the income. It recognizes the fact that, strictly speaking, a man's real income is not one simple homogeneous flow of money, but a mosaic or skein of threads of many heterogeneous elements of psychic experience. An income of $5000 may comprise for one individual one set of enjoyable services, and for another, an entirely different set. The inhabitants of one country may have relatively more house shelter and less food in their real incomes than those of another. Those differences will have, theoretically, an influence in one direction or the other upon the time preference. Food being a prime necessity, a decrease of the proportion of food, or nourishment, even though total income remain the same, will have an effect upon the impatience similar to the effect of the diminution of total income.

For practical purposes, however, we may ordinarily neglect the characteristic of income called composition; for ordinarily any variation in the mere composition of family budgets will very seldom be sufficient to have any appreciable effect on the rate of interest.

Hereafter, therefore, all the elements of income will be considered as lumped together in a single sum of money value. Our picture of income henceforth may be considered as a flag or pennant without regard to stripes but seen as a whole, stretching out into the future. Each man's pennant has a definite width varying with the distance from the flagstaff.

§8. The Influence of Risk

We come finally to the element of risk. Future income is always subject to some uncertainty, and this uncertainty must naturally have an influence on the rate of time preference, or degree of impatience, of its possessor. It is to be remembered that the degree of impatience is the percentage preference for $1 certain of immediate income, over $1, also certain, of income of one year hence, even if all the income except that dollar be uncertain. The influence of risk on time preference, therefore, means the influence of uncertainties in the anticipated income of an individual upon his relative valuation of present and future increments of income, both increments being certain.

The manner in which risk operates upon time preference will differ, among other things, according to the particular periods in the future to which the risk applies. If, as is very common, the possessor of income regards his immediately future income as fairly well assured, but fears for the safety or certainty of his income in a more remote period, he may be aroused to a high appreciation of the needs of that remote future and hence may feel forced to save out of his present relatively certain abundance in order to supplement his relatively uncertain income later on. He is likely to have a low degree of impatience for a certain dollar of immediate income as compared with a certain dollar added to a remoter uncertain income.

Such a type of income is, in fact, not uncommon. The remote future is usually less known than the immediate future, a fact which of itself means risk or uncertainty. The chance of disease, accident, disability, or death is always to be reckoned with; but under ordinary circumstances this risk is greater in the remote future than in the immediate future. As a result, uncertainty has a tendency to keep impatience down. This tendency is expressed in the phrase "to lay up for a rainy day." The greater the risk of rainy days in the future, the greater the impulse to provide for them at the expense of the present.

But sometimes the relative uncertainty is reversed, and immediate income is subject to higher risk than remote income. Such is the case in the midst of a war, in a strike, or other misfortune, believed to be temporary. Such is also the case when an individual is assured a permanent position with a salary after a certain date, but, in the meantime, must obtain a precarious subsistence. In these cases the effect of the risk element is to enhance the estimation in which immediate income is held.

Again, the risk, instead of applying especially to remote periods of time or especially to immediate periods, may apply to all periods alike. Such a general risk largely explains why salaries and wages, being relatively assured, are generally lower than the average earnings of those who take the risks incident to being their own employers. It also explains why the bondholder is content with a lower average return than the stockholder. The bond-holder chooses fixed and certain income rather than a variable and uncertain one, even if the latter is, on the average, larger. In short, a risky income, if the risk applies evenly to all parts of the income stream, is equivalent to a low income. And, since a low income, as we have seen, tends to create a high impatience, risk, if distributed in time, uniformly or fairly so, tends to raise impatience.

It follows, then, that risk tends in some cases to increase and in others to decrease impatience, according to the time incidence of the risk. But there is a common principle in all these cases. Whether the result is a high or a low time preference, the primary fact is that the risk of losing the income in a particular period of time operates, in the eyes of most people, as a virtual impoverishment of the income in that period, and hence increases the estimation in which a unit of certain income in that particular period is held. If that period is a remote one, the risk to which it is subject makes for a high regard for remote income; if it is the present (immediate future), the risk makes for a high regard for immediate income; if the risk applies to all periods of time alike, it acts as a virtual decrease of income all along the line.

There are, however, exceptional individuals of the gambler type in whom caution is absent or perverted. Upon these, risk will have quite the opposite effects. Some persons who like to take great speculative chances are likely to treat the future as though it were especially well endowed, and are willing to sacrifice a large amount of their exaggerated expectations for the sake of a relatively small addition to their present income. In other words, they will have a high degree of impatience. The same individuals, if receiving an income which is risky for all periods of time alike, might, contrary to the rule, have, as a result, a low instead of a high degree of impatience.

The income to which risk applies may be, of course, either the income from articles of capital external to man or the income from man himself, considered as an income producer. In the latter case, often called earned income, the risk of losing the income is the risk of death or invalidism. This risk—the uncertainty as to human life, health and income producing power—is somewhat different from the uncertainty of income flowing from objective capital: for the cessation of life not only causes a cessation of the income produced by the dying human machine, but also a cessation of the enjoyment of all income whatsoever—or rather a transfer of the enjoyment to posterity of any income continuing after death. This is because the individual is in the double capacity of being at once a producer and a consumer.

The effect of risk, therefore, is manifold, according to the degree and range of application of risk to various periods of times. It also depends on whether or not the risk relates to the continuation of life; and if so, according to whether or not the individual's interest in the future extends beyond his own lifetime. The manner in which these various tendencies operate upon the rate of interest will be discussed in Chapter IX.

§9. The Personal Factor

The proposition that, in the theory of interest, the impatience of a person for income depends upon the character of his income—as to its size, time shape, and probability—does not deny that it may depend on other factors also, just as, in the theory of prices, the proposition that the marginal want for an article depends upon the quantity of that article does not deny that it may depend on other elements as well.

But the dependence of impatience on income is of chief importance; for impatience, whatever else it depends on, is always impatience for income—exactly as the dependence of the marginal want for bread on the quantity of bread is more important than the dependence of this marginal want for bread on the quantity of some other commodity, such as butter.36

We have seen, therefore, how a given man's impatience depends both upon the characteristics of his expected income stream, and on his own personal characteristics. The rate of impatience which corresponds to a specific income stream will not be the same for everybody. This has already been noted, incidentally, but requires special discussion here. One man may have an annual rate of time preference of 6 per cent, and another 10 per cent, although both have the same income. Impatience differs with different persons for the same income and with different incomes for the same person. The personal differences are caused by differences in at least six personal characteristics37 : (1) foresight, (2) self-control, (3) habit, (4) expectation of life, (5) concern for the lives of other persons, (6) fashion.

(1) Generally speaking, the greater the foresight, the less the impatience, and vice versa.38 In the case of primitive races, children, and other uninstructed groups in society, the future is seldom considered in its true proportions. This is illustrated by the story of the farmer who would never mend his leaky roof. When it rained he could not stop the leak, and when it did not rain there was no leak to be stopped! Among such persons, the preference for present gratification is powerful because their anticipation of the future is weak. In regard to foresight, Rae states:39

The sagacious business man represents the other extreme; he is constantly forecasting. Many great corporations, banks, and investment trusts today maintain statistical departments largely for the purpose of gauging the future developments of business. The carefully calculated forecasts made by these and independent services tend to reduce the element of risk, and to aid intelligent speculation.

Differences in degrees of foresight and forecasting ability produce corresponding differences in the dependence of time preference on the character of income. Thus, for a given income, say $5000 a year indefinitely, the reckless might have a degree of impatience or rate of time preference of 10 per cent, when the forehanded would experience a preference of only 5 per cent. In both cases, the preference depends on the size, time shape, and risk of the income; but the particular rates corresponding to a particular income will be entirely different in the two cases. Therefore, the degree of impatience, in general, will tend to be higher in a community consisting of reckless individuals than in one consisting of the opposite type.

(2) Self-control, though distinct from foresight, is usually associated with it and has very similar effects. Foresight has to do with thinking; self-control, with willing. Though a weak will usually goes with a weak intellect, this is not necessarily so, nor always. The effect of a weak will is similar to the effect of inferior foresight. Like those workingmen who, before prohibition, could not resist the lure of the saloon on the way home Saturday night, many persons cannot deny themselves a present indulgence, even when they know what the consequences will be. Others, on the contrary, have no difficulty in stinting themselves in the face of all temptations.

(3) The third characteristic of human nature which needs to be considered is the tendency to follow grooves of habit. The influence of habit may be in either direction. Rich men's sons, accustomed to the enjoyment of a large income, are likely to put a higher valuation on present compared with future income than would persons possessing the same income but brought up under different conditions. When those habituated to luxury suffer a reverse of fortune they often find it harder to live moderately than do those of equal means who have risen instead of fallen in the economic scale; and this will be true even if foresight and self-control are inherently the same in the two cases. The former, brought up in the lap of luxury, will be more likely to be the prodigal son, that is, the more impatient for present income. The lack of such traditions among the Negroes tends toward a high rate of impatience, while the traditions of thrift among the Scotch curb impatience.

Our thrift campaigns are designed to reduce impatience by cultivating certain habits of regular saving out of income. So also is the propaganda for life insurance with its high-pressure salesmanship. On the other hand, the corresponding salesmanship for installment buying tends, in the first instance, in the opposite direction. The individual can indulge himself in the immediate enjoyment of a radio or an auto. Yet, it must not be overlooked that, after the sale is made, there ensues a new responsibility to provide for the future payments agreed upon which may permanently improve the faculties of foresight and self-control.

(4) The fourth personal circumstance which may influence impatience for immediate real income has to do with the uncertainty of life of the recipient. We have already seen, in a somewhat different connection, that the time preference of an individual will be affected by the prospect of a long or short life, both because the termination of life brings the termination of the income from labor, and because it also terminates the person's enjoyment of all income.

It is the latter fact in which we are interested here—the manner in which the expectation of life of a person affects the dependence of impatience on his income. There will be differences among different classes, different individuals, and different ages of the same individual. The chance of death may be said to be the most important rational factor tending to increase impatience; anything that would tend to prolong human life would tend, at the same time, to reduce impatience. Rae goes so far as to say:40

The shortness of life thus tends powerfully to increase the degree of impatience, or rate of time preference, beyond what it would otherwise be. This is especially evident when the income streams compared are long. A lover of music will be impatient for a piano, i.e., will prefer a piano at once to a piano available next year, because, since either will outlast his own life, he will get one more year's use out of a piano available at once.

(5) But whereas the shortness and uncertainty of life tend to increase impatience, their effect is greatly mitigated by the fifth circumstance, solicitude for the welfare of one's heirs. Probably the most powerful cause tending to reduce the rate of interest is the love of one's children and the desire to provide for their good. Wherever these sentiments decay, as they did at the time of the decline and fall of the Roman Empire, and it becomes the fashion to exhaust wealth in self-indulgence and leave little or nothing to offspring, impatience and the rate of interest will tend to be high. At such times the motto, "After us the deluge," indicates the feverish desire to squander in the present, at whatever cost to the future.41

On the other hand, in a country like the United States, where parents regard their lives as continuing after death in the lives of their children, there exists a high appreciation of the needs of the future. This tends to produce a low degree of impatience. For persons with children, the prospect of loss of earnings through death only spurs them all the more to lay up for that rainy day in the family. For them the risk of loss of income through death is not very different from the risk of cessation of income from any ordinary investment; in such a case the risk of cessation of future income through death tends to lower their impatience for income. This act supplies the motive for life insurance. A man with a wife and children is willing to pay a high insurance premium in order that they may continue to enjoy an income after his death. This is partly responsible for the enormous extension of life insurance. At present in the United States the insurance on lives amounts to over $100,000,000,000. This represents, for the most part, an investment of the present generation for the next.

An unmarried man, on the other hand, or a man who cares only for self-indulgence and does not care for posterity, man, in short, who wishes to "make the day and the journey alike," will not try thus to continue the income after his death. In such a case uncertainty of life is especially calculated to produce a high rate of time preference. Sailors, especially unmarried sailors, offer the classic example. They are natural spendthrifts, and when they have money use it lavishly. The risk of shipwreck is always before them, and their motto is, "A short life and a merry one." The same is even more true of the unmarried soldier. For such people the risk of cessation of life increases their impatience, since there is little future to be patient for.

Not only does regard for one's offspring lower impatience, but the increase of offspring has in part the same effect. So far as it adds to future needs rather than to immediate needs, it operates, like a descending income stream, to diminish impatience. Parents with growing families often feel the importance of providing for future years far more than parents in similar circumstances but with small families. They try harder to save and to take out life insurance; in other words, they are less impatient. Consequently, an increase of the average size of family would, other things being equal, reduce the rate of interest.

This proposition does not, of course, conflict with the converse proposition that the same prudent regard for the future which is created by the responsibilities of parenthood itself tends to diminish the number of offspring. Hence it is that the thrifty Frenchman and Dutchman have small families.

(6) The most fitful of the causes at work is probably fashion. This at the present time acts, on the one hand, to stimulate men to save and become millionaires, and, on the other hand, to stimulate millionaires to live in an ostentatious manner. Fashion is one of those potent yet illusory social forces which follow the laws of imitation so much emphasized by Tarde,42 Le Bon,43 Baldwin,44 and other writers. In whatever direction the leaders of fashion first chance to move, the crowd will follow in mad pursuit until almost the whole social body will be moving in that direction. Sometimes the fashion becomes rigid, as in China, a fact emphasized by Bagehot;45 and sometimes the effect of a too universal following is to stimulate the leaders to throw off their pursuers by taking some novel direction—which explains the constant vagaries of fashion in dress. Economic fashions may belong to either of these two groups—the fixed or the erratic. Examples of both are given by John Rae.46 It is of vast importance to a community, in its influence both on the rate of interest and on the distribution of wealth itself, what direction fashion happens to take. For instance, should it become an established custom for millionaires to consider it "disgraceful to die rich," as Carnegie expressed it, and believe it de rigueur to give the bulk of their fortunes for endowing universities, libraries, hospitals, or other public institutions, the effect would be, through diffusion of benefits, to lessen the disparities in the distribution of wealth, and also to lower the rate of interest.

§10. The Personal Factor Summarized

Impatience for income, therefore, depends for each individual on his income, on its size, time shape, and probability; but the particular form of this dependence differs according to the various characteristics of the individual. The characteristics which will tend to make his impatience great are: (1) short-sightedness, (2) a weak will, (3) the habit of spending freely, (4) emphasis upon the shortness and uncertainty of his life, (5) selfishness, or the absence of any desire to provide for his survivors, (6) slavish following of the whims of fashion. The reverse conditions will tend to lessen his impatience; namely, (1) a high degree of foresight, which enables him to give to the future such attention as it deserves; (2) a high degree of self-control, which enables him to abstain from present real income in order to increase future real income; (3) the habit of thrift; (4) emphasis upon the expectation of a long life; (5) the possession of a family and a high regard for their welfare after his death; (6) the independence to maintain a proper balance between outgo and income, regardless of Mrs. Grundy and the high-powered salesmen of devices that are useless or harmful, or which commit the purchaser beyond his income prospects.

The resultant of these various tendencies in any one individual will determine the degree of his impatience at a given time, under given conditions with a particular income stream. The result will differ as between individuals, and at different times for the same individual.

The same individual in the course of his life may change from one extreme of impatience to the other. Such an alteration may be caused by a change in the person's nature (as when a spendthrift is reformed or a man, originally prudent, becomes, through intemperance, reckless and thriftless), or by variation in his income, whether in respect to size, distribution in time, or uncertainty. Everyone at some time in his life doubtless changes his degree of impatience for income. In the course of an ordinary lifetime the changes in a man's degree of impatience are probably of the following general character: as a child he will have a high degree of impatience because of his lack of foresight and self-control; when he reaches the age of young manhood he may still have a high degree of impatience, but for a different reason, namely, because he then expects a large future income. He expects to get on in the world, and he will have a high degree of impatience because of the relative abundance of the imagined future as compared with the realized present. When he gets a little further along, and has a family, the result may be a low degree of impatience, because then the needs of the future rather than its endowment will appeal to him. He will not think that he is going to be so very rich; on the contrary, he will wonder how he is going to get along with so many mouths to feed. He looks forward to the future expenses of his wife and children with the idea of providing for them—an idea which makes for a high relative regard for the future and a low relative regard for the present. Then when he gets a little older, if his children are married and have gone out into the world and are well able to take care of themselves, he may again have a high degree of impatience for income, because he expects to die, and he thinks, "Instead of piling up for the remote future, why shouldn't I enjoy myself during the few years that remain?"

§11. Income Rather Than Capital in the Leading Rôle

The essential fact, however, is that for any given individual at any given time, his impatience depends in a definite manner upon the size, time shape, and probability of his income stream.

This view, that the degree of impatience and, consequently, the rate of interest depend upon income, needs to be contrasted with the common view, which makes the rate of interest depend merely on the scarcity or abundance of capital. It is commonly believed that where capital is scarce, interest is high, and where capital is plentiful, interest is low. In a general way, there is undoubtedly some truth in this belief; and yet it contains a misinterpretation of borrowing and lending.

In the first place, we must distinguish between capital wealth and capital value. It is capital value of which most people think when they say capital. But capital value is merely capitalized income. Behind, or rather beyond, a capital of $100,000 is the stream of income which that capital represents, or rather the choice of any one among many possible streams. To fix attention on the $100,000 capital instead of on the income which is capitalized is to use the capital as a cloak to cover up the real factor in the case.

Moreover, capital value is itself dependent on a pre-existing rate of interest. As we know, the capital value of a farm will be doubled if the rate of interest is halved. In such a case there would seem to be more capital in farms than before; for the farms in a community would rise, say, from $100,000,000 to $200,000,000. But it is not the rise in capital value which produces this fall in interest. On the contrary, it is the fall in the interest rate which produces the rise in the capital. If we attempt to make the rate of interest depend on capital value, then, since capital value depends on two factors—the prospective income and the rate of interest—we thereby make the interest rate depend partly on income and partly on itself. The dependence on itself is of course nugatory, and we are brought back to its dependence on income as the only fact of real significance. It is present and future income that are traded against each other.

But, even as thus amended and explained, (that capital stands for income) the proposition that the rate of interest depends on the amount of capital is not satisfactory. For the mere amount of capital does not tell us enough about the income for which the capital stands. To know that one man has a capital worth $10,000,000 and another has a capital worth $20,000,000 shows, to be sure, that the latter man can have an income of double the value of the former; but it tells us absolutely nothing as to the time shapes of the two incomes actually selected; and the time shape of income has, as we have seen, a most profound influence on the time preference of its possessor, and time preference is a prime determiner of interest.

To illustrate this important fact, let us suppose that two communities differ in the amount of capital and the character of the income which that capital represents but, as far as possible, are similar in all other respects. One of these two communities we shall suppose has a capital of $100,000,000, invested, as in Nevada, in mines and quarries nearly exhausted, while in the other community there is $200,000,000 of capital invested in young orchards and forests, as in Florida. According to the theory that abundance of capital makes interest low, we should expect the Nevada community to have a high rate of interest compared with the Florida community. This would ordinarily be true if the two communities had income streams differing only in size with the same time shapes and probabilities. But, under our assumptions, it is evident that, unless other circumstances should interfere, the opposite would be the case; for Nevada, due to the progressive exhaustion of her mines, is faced by a decreasing future income, and in order to offset the depreciation of capital which follows from this condition,47 she would be seeking to lend or invest part of the income of the present or immediate future, in the hope of offsetting the decreased product of the mines in the more remote future. The Florida planters, on the contrary, would be inclined to borrow against their future crops. If the two communities are supposed to be commercially connected, it would be Nevada which would lend to Florida notwithstanding the fact that the lending community was the poorer in capital of the two. From this illustration it is clear that the mere amount of capital value is not only a misleading but a very inadequate criterion of the rate of interest.48

Apologists for the common idea that abundance or scarcity of capital lowers or raises interest might be inclined to argue that it is not the total capital, but only the loanable capital which should be included, and that the Nevada community had more loanable capital than the Florida community. But the phrase loanable capital is merely another cloak to cover the fact that it is not the amount of capital, but the decision to lend or borrow it, (or the income stream which the capital stands for) which is important.

We end, therefore, by emphasizing again the importance of fixing our eyes on income and not on capital. It is only as we look through capital value at the income beyond that we reach the effective causes which operate upon the rate of interest. It has, perhaps, been the absence of a definite theory and conception of income which has so long prevented economists from seeing these relations. Borrowing and lending are in form a transfer of capital, but they are in fact a transfer of income of which that capital is merely the present value. In our theory of interest, therefore, we have to consider not primarily the amount of capital of a community, but the future expected income for which that capital stands.

§12. Impatience Schedules

Unfortunately for purposes of exposition, the relation between impatience and income cannot be expressed in a simple schedule or a simple curve, as can the relation between demand and price, or supply and price, or marginal want and quantity consumed, for the reason that income means not a single magnitude merely, but a conglomeration of magnitudes. As mathematicians would express it, to state that income impatience depends on the character of income, its size, shape, and probability is to state that this impatience is a function of all the different magnitudes which need to be specified in a complete description of that income. A geometrical representation, therefore, of the dependence of time preference on the various magnitudes which characterize income would be impossible. For a curve can be in two dimensions only and hence can represent the dependence of a magnitude on only one independent variable. Even a surface can only represent dependence on two. But for our requirement, i.e., in order to represent the dependence of a man's impatience on the infinite number of successive elements constituting his income stream, we should need not two or three dimensions simply but a space of n dimensions.

We may represent, however, the relation between time preference and income by a schedule like the ordinary demand schedule and supply schedule, if we make a list of income streams of all possible sizes, shapes, and probabilities, specifying for each individual income all its characteristics—its size, time shape (that is, its relative magnitude in successive time intervals), and the certainty or uncertainty of its various parts, to say nothing of its heterogeneous and varying composition. Having thus compiled a list of all possible income streams, it would only be necessary for us to assign to each of them the rate of impatience pertaining to it.

Such a schedule would be too complicated and cumbersome to be carried out in detail; but the following will roughly indicate some of the main groups of which it would consist. In this schedule I have represented, by the three horizontal lines, three different classes of income—two extreme types and one mean type—so that the corresponding rates of time preference range themselves in a descending series of numbers. The three vertical columns show three different classes of individuals, two being of extreme types, and the third of a mixed or medium type. Thus, the numbers in the table grow smaller as we proceed toward the right and as we proceed downward, the smallest numbers of all being the lower right-hand corner. This represents a man whose rate of impatience is only 1 per cent, being low both because his income is large, decreasing and assured, and because his nature is farsighted, self-controlled, accustomed to save, and desirous to provide for heirs.

This schematic representation is, in the effort to be general, rather vague. We may be more specific if, instead of thinking of a man's income stream as uncertain and variable at every point, we think of it, for the moment, as certain throughout and as invariable, or frozen, at all points of time except two—the present time and one year hence.

Restricted by this highly artificial hypothesis, we can construct for the man an impatience and demand schedule and demand and supply schedules for loans and interest analogous to the ordinary utility schedule and demand or supply schedule for commodities and prices. Thus the demand schedule might be that a certain prospective borrower is willing, for each successive one hundred dollars added to his present income, to give, out of next year's income, as follows:

Such a schedule is expressed geometrically in Chapters X and XI.

Since the time preference of an individual is a derivative of his marginal want for present and his marginal want for future income, the above schedule is likewise a sort of derivative of the ordinary want schedules (utility schedules) of present and future income. But the more general schedule previously given, not restricted to two years, but recognizing uncertainty and variability of the person's income stream at all its points, is more appropriate for our present purpose.

We see then that each individual has a rate of impatience dependent on his own personal nature and on the nature of his income. If all individuals' incomes were rigid, that is, incapable of being modified, and if there were no loan or money market by which immediate and future income could be exchanged, there could be no common market rate of interest. There would be a separate rate of time preference for each individual. One man would be willing to part with $100 today for the sake of $101 next year, while another would require $200 or $1000. But nothing would happen toward equalizing these divergent rates.

But given a loan market, the individuals toward the end of the list will tend to borrow; and those toward the beginning will tend to lend. The effect of such operations is to reduce the high rates of time preference and to increase the low ones until a middle ground is reached in the common rate of interest. This process will be discussed in the following chapter.

PART II, CHAPTER V

FIRST APPROXIMATION TO THE THEORY OF INTEREST
Assuming Each Person's Income Stream Foreknown and Unchangeable Except by Loans

§1. Hypotheses of First Approximation

IN the last chapter we reached three conclusions:

• (1) that the rate of time preference, or impatience for present over future goods, is, in the last analysis, a preference for present over future enjoyment income, or, let us say, real income;
• (2) that the degree of impatience depends, for any given individual, upon the character of his real income-stream—in particular, on its size, time shape, and probability;
• (3) that the nature of this dependence differs with different individuals.

The question at once arises: will not the actual degrees of impatience of different individuals necessarily be very different, and if so, what relation do these different rates have to the market rate of interest? Is the market rate of interest a sort of average of these individual degrees of impatience, or does it equalize them?

It is doubtless true that the different rates of impatience of different individuals who are not connected through a common loan market do vary widely. In a nation of hermits, in which there existed no mutual lending and borrowing, individuals would be independent of each other. But, among ourselves who have access to a common loan market, borrowing and lending do, at least, tend to bring into equality the marginal rates of impatience in different minds. Absolute equality is not reached even among those making use of such a market; but this is because of the limitations of the market and, in particular, because of the risk element. This element will be considered in the third approximation, but for simplicity of exposition is omitted in the first two approximations.

Here we shall assume a perfectly competitive market, one in which each individual is so small a factor as to have, singly, no perceptible influence on the rate of interest, and in which there is no limitation on the amount of lending and borrowing other than that caused by the rate of interest itself. The would-be borrower is thus supposed to be able to obtain as large or small a loan as he wishes at the market price—the rate of interest. He is not cut down to $5,000 when he is willing to borrow $100,000, merely because he cannot furnish enough collateral security or a satisfactory endorser. He can buy a loan as he can buy sugar, as much or as little as he pleases, if he will pay the price.

In the actual world, of course, no such perfect market exists. While many people in New York City can obtain as large loans as they wish, there are thousands who are unable to obtain any at all. The price of a loan is paid not in the present, as the price of sugar is paid, but in the future. What the lender gets when he makes the loan is not payment but a promise of payment, and the future being always uncertain he needs some sort of assurance that this promise will be kept. We are assuming in the first and second approximations that there will never be a lack of such assurance. This amounts almost to assuming that there is no risk in the world. The element of risk is assumed to be entirely lacking, both with respect to the certainty of the expected income streams belonging to the different individuals, and with respect to the certainty of repayment for loans. In other words, we assume that each individual in the market is free to give up any part of his income during one period of time to some other person in consideration of receiving back an addition to his own income during another period of time.

We assume further that thus to buy and sell rights to various parts of his income stream is the only method open to any individual to alter his income stream. Such trading between present and future dollars may be in the form of loans, since a loan is the sale of future money for present money, or it may be in the guise of buying and selling bonds or other securities conveying title to fixed sums of money. In any case the trading reduces itself to buying and selling titles to future income. Prior to such exchange, the income stream of each individual is assumed to be fixed in size and shape. Each capital instrument which he possesses, including himself, is assumed to be capable of only a single definite series of services contributing to his income stream. Each individual is a stipendiary with a definite income which he receives and spends according to a foreknown schedule—so much next year, so much the year after, and so forth.

Thus the assumptions of our first approximation are: (1) that each man's income stream is initially certain and fixed; (2) that he is a negligible element in a vast and perfect competitive loan market; (3) that he has free access to this market, whether as borrower or lender, to any desired extent, at the market rate; (4) that his sole method of modifying his future income stream is through such borrowing or lending (or, more exactly and generally, through trading income).

§2. Income Prescribed

Such assumptions are, of course, highly theoretical. They imagine a world in which incomes are produced spontaneously, as mineral water gushes from the spring. They picture these income-bearing agents as pouring forth their income streams at rates which follow a foreknown, rigid, and unchangeable schedule. There being no flexibility in the flow from any one article, there is no flexibility in the scheme of combined flow from the whole group possessed by an individual. His total real income is scheduled in advance with no possibility of modification except by borrowing or lending, buying or selling.49

The abstract nature of this hypothesis need not greatly trouble us for two reasons: the first, and in itself quite sufficient reason, is that most of the elements of this hypothesis will be abandoned when we reach the second approximation. It is adopted temporarily merely for simplicity of exposition. Secondly, the hypothesis might easily be made more realistic without changing its essential features. We might even alter our hypothesis of a rigidly prescribed income stream to the hypothesis of an income stream which, while it may be decreased at will, cannot be increased beyond a fixed amount at each period of time. While free to decrease his income in any period, its possessor would not do so unless thereby he could secure an increase in some other period.

Not only is such an hypothesis quite thinkable, it is probably actually approximated in primitive communities. In our own day most men have opportunities (quite apart from lending to others at interest) to secure much real income in future years by temporarily sacrificing a little immediate real income as, for instance, by investing labor in building a house or machine. But we can readily suppose a situation such that this year's production and next year's production would be almost independent of each other. This situation is true of most animals and even of man in the hunting and fishing stage, and before that stage even more markedly when his only implements were his hands. And even in our own civilization, many are mere stipendiaries, virtually without any opportunity to add to future income except by lending at interest.

The essence of the hypothesis therefore on which the first approximation rests is that we are not to be bothered by the possibility of a man's thus increasing his income in one period through decreasing it in another except through the process of trading some of one year's income with another person for some of another year's income.

We may in fact for practical purposes picture the income stream of each person as thus fixed for only a few years, and assume that expectation of income beyond those years so indefinite as to have no effect on the present rate of interest. Such a community has been approximated in former years by the typical American army camp isolated in a western community in which each inhabitant, or family, had a prescribed income. A series of such hypotheses will lead us through successive approximations to an eventual picture of actuality.

§3. Equalization of Impatience

Under the hypothetical conditions which have been stated for the first approximation, the rates of time preference for different individuals will, by the process of borrowing and lending, become perfectly reconciled to the market rate of interest and to each other, for if, for any particular individual, the rate of preference differs from the market rate, he will, if he can, adjust the time shape of his income stream so as to bring his marginal preference rate into harmony with the interest rate. A man who, for a given income stream, has a rate of preference above the market rate will sell some of his surplus future income in return for an addition to his meager present income, i.e., he will borrow. This will have the effect of enhancing his want for one more dollar of future income and decreasing his want for one more dollar of present income. The process will continue until the rate of preference of this individual, at the margin, is equal to the rate of interest. In other words, under our hypothesis, a person whose preference rate exceeds the current rate of interest will borrow up to the point at which the two rates will become equal.

On the other hand, the man, whose temperament or whose income stream or both give him a preference rate below the market rate, will buy future income with some of his abundant present income, i.e., he will lend. The effect will be to increase his preference rate until, at the margin, it harmonizes with the rate of interest.

To put the matter in figures, let us suppose the rate of interest is 5 per cent, whereas the rate of preference of a particular individual is, to start with, 10 per cent. Then, by hypothesis, the individual is willing to sacrifice $1.10 of next year's income in exchange for $1 of this year's. But, in the market, he finds he is able to obtain $1 for this year by foregoing only $1.05 of next year's. To him this latter ratio is a cheap price. He therefore borrows, say, $100 for a year, agreeing to return $105; that is, he contracts a loan at 5 per cent, when he is willing to pay 10 per cent. This operation partly satisfies his hunger for present income by drawing on his future income, and thus reduces his time preference from 10 per cent to, say, 8 per cent. Under these circumstances he will borrow another $100, being willing to pay 8 per cent, but required to pay only 5. This operation will still further reduce his time preference, and so on through successive stages, until it is finally brought down to 5 per cent. Then, for the last or marginal $100, his rate of time preference will agree with the market rate of interest.50

In like manner, if another individual, entering the loan market from the opposite side, has a rate of preference of 2 per cent, he will become a lender instead of a borrower. He will be willing to lend $100 of this year's income for $102 of next year's. As he can lend at 5 per cent when he would do so at 2, he "jumps at the chance," and invests, not $100 only, but another and another. But his present income, being drawn upon by the process, is now more highly esteemed by him than before, and his future income, being supplemented, is less highly esteemed; and under the influence of successive additions to the sums lent, his rate of preference for the present will keep rising until, at the margin, it will equal the market rate of interest.

In such an ideal loan market, therefore, where every individual could freely borrow or lend, the rates of preference or impatience for present over future income for all the different individuals would become, at the margin, exactly equal to each other and to the rate of interest.

§4. Altering Income by Loans

To illustrate this reasoning by a chart, let us suppose the income stream to be represented as in Chart 5, and that the possessor wishes to obtain, by borrowing, a small item X' of immediately ensuing income in return for a somewhat larger item X'' later on, X'' being the amount of X' at interest. By such a loan he modifies his income stream from ABCD to EBD. But this change will evidently produce a change in his time preference. If the rate of time preference corresponding to the income stream represented by the unbroken line is 10 per cent, the rate of preference corresponding to the broken line will be somewhat less, say, 8 per cent. If the market rate of interest is 5 per cent, it is evident that the person will proceed to still further borrowing. By repeating the operation several times he can evidently produce almost any required conformation of his income stream.

If, instead of borrowing, he wishes to lend (Chart 6) he surrenders from his present income stream the amount X' for the sake of the larger amount X'' at a later time. After the operations are completed and the final conformations of the income streams are determined, the rates of time preference are all brought into conformity with the market rate of interest.

In practice, of course, the adjustments are never perfect and, in particular, the income stream is never a smooth curve, such as it is here for convenience represented.

In practice, also, loans are effected under the guise of money. We do not confessedly borrow and lend real incomes, but money and credit. Yet money—that universal medium in practice and universal stumbling-block in theory—merely represents real income, or capitalized real income. A hundred dollars mean the power to secure income,—any income the present value of which is $100. When, therefore, a person borrows $100 today and returns $105 next year, in actual fact he secures the title to $100 worth of income—immediately future, perhaps—and parts with the title to $105 worth of income a year later. Every loan contract, or any other contract implying interest, involves, at bottom, a modification of income streams, the usual and chief modification being as to time shape.

One reason why we often forget that a money loan represents real income is that it represents so many possible varieties of real income. A fund of money is usually the capitalization not simply of one particular future program, or lay-out, of income but of a large number of optional income streams, and is not restricted, as in the first approximation, here considered, to a simple income stream and its modification by loans or their equivalent.

We may distinguish six principal types of individuals in a loan market—three borrowing types and three lending types. The first type of borrower (Chart 7) is supposed to be possessed of an increasing, or ascending, income stream AB, a fact which, in his mind, results in a rate of preference above the market rate. This leads him to borrow, and relatively to level up his ascending income stream toward such a position as A'B'. The second type of individual already possesses a uniform income stream AB (Chart 8), but having, a strong propensity to spend, he too experiences a rate of preference above the market rate, and will therefore modify his income stream toward the curve A'B'. The third type is shown in Chart 9 and represents even more of a spendthrift. This individual has also a rate of preference in excess of the market rate, in spite of his having a declining income stream pictured by the descending curve AB. By his borrowing, he obtains a curve A'B' of still steeper descent.

In a similar way, the three types of lenders may be graphically represented. Chart 10 represents a descending income AB, which the owner, by lending present income in return for future income, converts into a relatively uniform income A'B'; Chart 11 represents a uniform income converted, by lending, into an ascending income; and Chart 12 an ascending income converted into a still more steeply ascending income.

The borrower changes his income curve by tipping it down in the future and up in the present. The lender tips his income curve in the opposite direction. Of the three types of borrowers and of lenders, the first in each group of three (see Charts 7 and 10), is the usual and normal case. In both these cases the effort is to transform the given income into a more uniform one, the rising curve (Chart 7) being lowered and the falling curve (Chart 10) being raised toward a common horizontal position. Chart 9 and Chart 12, on the other hand, represent the extreme and unusual cases of the spendthrift and the miser.

But whatever the personal equation, it remains true that, for each individual, other things being equal, the more ascending his income curve, the higher his rate of preference; and the more descending the curve, the lower the rate of preference. If the descent of the income stream is sufficiently rapid, the rate of preference could be made zero or even negative.51

These foregoing types of income streams are, of course, not the only ones which could be considered, but they are some of the more important. To them we may add the type of fluctuating income, as represented in Chart 13, which may result in alternate borrowing and lending so as to produce a more nearly uniform income stream. Such financing over the lean parts of a year is often practiced when the income is lumped at one or two spots, such as dividend dates.

It must not be imagined that the classes of borrowers and lenders correspond respectively to the classes of poor and rich. The factors, environmental and personal, discussed in Chapter IV, will determine whether a man's rate of preference is high or low, and therefore whether he will become a spender or a saver.

When we come to the second and third approximations and have to study so-called productive loans, especially of risk-takers, or enterprisers as Professor Fetter calls them, we shall find still other influences determining whether a person shall be a borrower or lender or both. At present we are only at the first approximation where it is assumed there is no risk and no such series of opportunities to vary the income stream as lie at the basis of so-called productive loans.

§5. Altering Income by Sale

But borrowing and lending are not the only ways in which one's income stream may be modified. Exactly the same result may, theoretically, be accomplished simply by buying and selling property; for, since property rights are merely rights to income streams, their exchange replaces one such stream by another of equal present value but differing in time shape, composition, or uncertainty. This method of modifying one's income stream, which we shall call the method of sale, really includes the former, or method of loans, for a loan contract is, as Böhm Bawerk has so well said, at bottom a sale, that is, it is the exchange of the right to present or immediately ensuing income for the right to future or more remote income. A borrower is simply a seller of a note of which the lender is the buyer. A man who buys a bond, for example, may be regarded indifferently as a lender or as a buyer of property.

The concept of a loan may therefore now be dispensed with by being merged in the concept of a sale. Every sale transfers property rights; that is, it transfers the title to income of some kind. By selling some property rights and buying others it is possible to transform one's income stream at will into any desired time shape. Thus, if a man buys an orchard, he is providing himself with future income in the form of apples. If, instead, he buys apples, he is providing himself with similar but more immediate income. If he buys securities, he is providing himself with future money, convertible, when received, into apples or other real income. Inasmuch as the productive life of a mine is shorter generally than that of a railway, if his security is a share in a mine, his income stream is less lasting than if the security is stock in a railway, though at first it should be larger, relatively to the sum paid for it.

Purchasing the right to remote enjoyable income, as was explained in Chapter I, is called investing; while purchasing more immediate enjoyable income is spending. These, however, are purely relative concepts; for remote and immediate are relative terms. Buying an automobile is investing as contrasted with spending the money for food and drink, but may be called spending as contrasted with investing in real estate. And yet the antithesis between spending money and investing is important; it is the antithesis between immediate and remote income. The adjustment between the two determines the time shape of one's income stream. Spending increases immediate real income but robs the future, whereas investing provides for the future to the detriment of the present. There is often misconception in reasoning about spending and investing. For example, Henry Ford's remark has been widely reported: "No successful boy ever saved any money. They spent it as fast as they got it for things to improve themselves." In this remark Mr. Ford drew no hard and fast line between spending for personal enjoyment and investment for improvement. And there is no hard and fast line. Spending merely means expending money primarily for more or less immediate enjoyment. Saving or investing is expending money for more or less deferred enjoyment. Consequently, much of what is called spending might legitimately be called investment. Even the money we spend for food, clothing and shelter is in a sense really partly invested, since our lives and capacity to work can be preserved only by means of these necessaries. Just so with a set of books, or any other durable good which increases the efficiency and hence the earning power of the purchaser; it is an example, not of spending for consumption merely, but of saving through investment. Mr. Ford cites the example of Thomas Edison as spending his early earnings as fast as he made them. But Edison did this, not for food and display, but for experimentation that resulted in time and labor saving inventions which have benefited everybody. His outlays were in a way investments.

Popular usage has devised many other terms and phrases in this field, most of which, like spending and investing, while containing meanings of importance, include also the alloy of misconception. Thus, the phrase "capital seeking investment" means that capitalists have property for which they desire, by exchange, to substitute other property, the income from which is more remote. It does not mean that there is any hard and fast line between invested and uninvested capital, much less does it mean that the inanimate capital has of itself any power to seek investment. Again, the phrase "saving capital out of income" means not spending—reserving money which would otherwise be spent for immediate enjoyable income in order to exchange it or invest it for remoter income; it does not mean the creation of new capital, though it may lead to that. Many needless controversies have centered about the phenomenon of saving chiefly because neither saving nor income was clearly defined.52

From what has been said it is clear that by buying and selling property an individual may change the conformation of his income stream precisely as though he were specifically lending or borrowing. Thus, suppose a man's original income stream is $1000 this year and $1500 next year, and suppose that he sells the title to this income stream, and, with the proceeds buys the title to another income stream yielding $1100 this year and $1395 next year. Although this man has not, nominally, borrowed $100 and repaid $105, he has done what amounts to the same thing; he has increased his income stream of this year by $100 and decreased that of next year by $105. The very same diagrams which were used before may equally well represent these operations. A man sells the income stream ABCD (Chart 5) and with the proceeds buys the stream EBD. The X' and X'' are, as before, $100 and $105, but now appear explicitly as differences in the value of two income streams, instead of appearing as direct loans and payments.

§6. Interest Ineradicable

Thus interest taking cannot be prevented by prohibiting loan contracts. To forbid the particular form of sale called a loan contract would leave possible other forms of sale, and, as was shown in Chapter I, the mere act of valuation of every property right involves an implicit rate of interest. If the prohibition left individuals free to deal in bonds, it is clear that they would still virtually be borrowing and lending, but under the names of selling and purchasing; and if bonds were tabooed, they could change to preferred stock. Indeed, as long as buying and selling of any kind were permitted, the virtual effect of lending and borrowing would be retained. The possessor of a forest of young trees, not being able to mortgage their future return and being in need of an income stream of a less deferred type than that receivable from the forest itself, could simply sell his forest and with the proceeds buy, say, a farm, with a uniform flow of income, or a mine with a decreasing one. On the other hand, the possessor of a capital which is depreciating, that is, which represents an income stream great now but steadily declining, and who is eager to have an increasing income, could sell his depreciating wealth and invest the proceeds in such instruments as the forest already mentioned.

It was in such a way, as for instance by rent purchase, that the medieval prohibitions of usury were rendered nugatory. Practically, the effect of such restrictive laws is little more than to hamper and make difficult the finer adjustments of the income stream, compelling would-be borrowers to sell wealth yielding distant returns instead of mortgaging them, and would-be lenders to buy such wealth instead of lending to the present owners. It is conceivable that explicit interest might disappear under such restrictions, but implicit interest would certainly remain. The young forest sold for $10,000 would bear this price, as now, because it is the discounted value of the estimated future income; and the price of the farm, $10,000, would be determined in like manner. The rate of discount in the two cases, the $10,000 forest and the $10,000 farm, must tend to be the same, because, by buying and selling, the various parties in the community would adjust their rates of preference to a common level—an implicit rate of interest thus lurking in every contract, though never specifically mentioned therein. Interest is too omnipresent a phenomenon to be eradicated by attacking any particular form of it; nor would any one undertake to eradicate it who perceived its substance as well as its form.

§7. "Marginal" Principle Is "Maximum" Principle

The fact that, through the loan market, the marginal rate of time preference for each individual is, by borrowing or lending, made equal to the rate of interest may be stated in another way, namely, that the total present desirability of, or want for, the individual's income stream is made a maximum. For, consider again the individual who modifies his original fixed income stream by borrowing until his rate of preference is brought into unison with the market rate of interest. His degree of impatience was at first, say, 10 per cent; that is, he was willing, in order to secure an addition of $100 to his present income, to sacrifice $110 of next year's income. But he needed to sacrifice only $105; that is, he was enabled to get his loan for less than he would have been willing to pay. He was therefore a gainer to the extent of the present desirability of, or present want for, $5 of next year's income. The second $100 borrowed was equivalent, in his present estimation, to $108 of next year's income, and the same reasoning shows that, as he pays only $105, he gains to the extent of the present desirability of $3 next year; that is, he adds this present desirability to the entire present total desirability of his income stream. In like manner, each successive increment of loans adds to the present total desirability of his income, so long as he is willing to pay more than $105 of next year's income for $100 of this year's income. But, as he proceeds, his gains and his eagerness diminish until they cease altogether. At, let us say, the fifth instalment of $100, he finds himself barely willing to pay $105; the present total desirability of his income is then a maximum, and any further loan would decrease it. A sixth $100, for instance, is worth in his present estimation less than $105 due next year, say $104, and since in the loan market he would have to sacrifice $105 next year to secure it, this would mean a loss of desirability to the extent of the desirability today of $1 due in one year. Thus, by borrowing up to the point where the rate of preference for present over future income is equal to the rate of interest, five per cent, he secures the greatest total desirability, or, so-called consumer's rent.53

Similar reasoning applies to the individual on the other side of the market, whose rate of preference is initially less than the market rate of interest. He also will bring his present net total desirability to a maximum by lending up to the point where his rate of preference corresponds to the rate of interest. At the beginning, $100 this year has to him the same present desirability as, say, $102 due one year hence, whereas in the market he may secure not $102 but $105. It is then clear that by lending $100 he gains the present desirability of $3 due one year hence. By lending each successive $100 he will add something to the total present desirability of his income, until his rate of preference for present over future income is raised to a level equal to that of the rate of interest, five per cent. Beyond that point he would lose by further lending.

§8. Market Equilibrium

We are now in a position to give a preliminary answer to the question, What determines the rate of interest? Thus far we have regarded the individual only, and have seen that he conforms his rate of income-impatience to the rate of interest. For him the rate of interest is a relatively fixed fact, since his own impatience and resulting action can affect it only infinitesimally. To him it is his degree of impatience which is the variable. In short, for him individually, the rate of interest is cause, and his lending and borrowing is the effect. For society as a whole, however, the order of cause and effect is reversed. This change is like the corresponding inversion of cause and effect in the theory of prices. Each individual regards the market price, say, of sugar, as fixed, and adjusts his marginal utility, or desirability, to it; whereas, for the entire group of persons forming the market, the adjustment is the other way around, the price of sugar conforming to its marginal desirability to the consumer.54 In the same way, while for the individual the rate of interest determines the degree of impatience, for society the degrees of impatience of the aggregate of individuals determine, or help to determine, the rate of interest. The rate of interest is equal to the degree of impatience upon which the whole community may concur in order that the market of loans may be exactly cleared.

To put the matter in figures: Suppose that at the outset the rate of interest is arbitrarily set very high, say, 20 per cent. There will be relatively few borrowers and many would-be lenders, so that the total extent to which would-be lenders are willing to reduce their income streams for the present year for the sake of a much larger future income will be, say, 100 million dollars; whereas, the extent to which would-be borrowers are willing to increase their income streams in the present at the high price of 20 per cent will be only, say, one million. Under such conditions the demand for loans is far short of the supply and the rate of interest will therefore go down. At an interest rate of 10 per cent the lenders may offer 50 millions, and the borrowers bid for 20 millions. There is still an excess of supply over demand, and interest must needs fall further. At 5 per cent we may suppose the market cleared, borrowers and lenders being willing to take or give respectively 30 millions. In like manner it can be shown that the rate would not fall below this, as in that case it would result in an excess of demand over supply and cause the rate to rise again.

Thus, the rate of interest registers in the market the common marginal rate of preference for present over future income, as determined by the supply and demand of present and future income. Those who, to start with, have a high degree of impatience, strive to acquire more present income at the cost of future income, and thus tend to raise the rate of interest. These are the borrowers, the spenders, the sellers of property yielding remote income, such as bonds and stocks. On the other hand, those who, to start with, have a low rate of preference, strive to acquire more future income at the cost of present income, and so tend to lower the rate of interest. Such are the lenders, the savers, the investors.

Not only will the mechanism just described result in a rate of interest which will clear the market for loans connecting the present with next year, but, applied to exchanges between the present and the more remote future, it will make similar clearings. While some individuals may wish to exchange this year's income for next year's, others wish to exchange this year's income for that of the year after next, or for a portion of several future years' incomes. The rates of interest for these various periods are so adjusted as to clear the market for each of the periods of time for which contracts are made.

§9. Four Principles

If we retain our original assumption that every man is initially endowed with a rigidly fixed or prescribed income stream which can be freely bought and sold and thereby redistributed in time, the foregoing discussion gives us a complete theory of the causes which determine the rate of interest, or rather, the rates of interest, there being, theoretically, a separate rate for each time period. These rates of interest would, under these circumstances, be fully determined by the following four principles, to which all the magnitudes in the problem of interest must conform:

THE TWO IMPATIENCE PRINCIPLES

A. Empirical Principle

The rate of time preference or degree of impatience of each individual depends upon his income stream.

B. Principle of Maximum Desirability

Through the alterations in the income streams produced by loans or sales, the marginal degrees of impatience for all individuals in the market are brought into equality with each other and with the market rate of interest.

This condition B is equivalent to another, namely, that each individual exchanges present against future income, or vice versa, at the market rate of interest up to the point of the maximum total desirability of the forms of income available to him.

THE TWO MARKET PRINCIPLES

A. Principle of Clearing the Market

The market rate of interest will be such as will just clear the market, that is, will make the loans and borrowings or, more generally expressed, purchases and sales of income equal for each period of time.

B. Principle of Repayment

All loans are repaid with interest, that is, the present value of the payments, reckoned at the time of contract, equals the present value of the repayments. More generally expressed, the plus and minus alterations or departures from a person's original income stream effected by buying and selling at two different points are such that the algebraic sum of their present values is zero.

Will these four sets of conditions determine the rate of interest? And why should there be so many conditions? Ought not one single condition to suffice?

These are really questions in mathematics. It is a fundamental principle that in order to solve an equation containing only one unknown quantity only one equation is necessary; and that to solve one containing two unknowns, two independent equations are needed; and so on, one additional equation for each additional unknown quantity introduced.

In the present problem we are trying to determine only one unknown, the rate of interest. But we can do so only by determining, at the same time, the other unknowns that are involved. To say that the rate of interest is equal to Smith's marginal rate of impatience is saying something, but not enough. It merely expresses one unknown, the rate of interest, in terms of another unknown, Smith's marginal rate; and two unknowns cannot be determined by one equation or condition. If we add that the rate of interest must also equal Jones' rate of impatience, while this statement gives us another equation it also adds another unknown and three unknowns cannot be determined by two equations; and so on. If we include Jones and everybody else in the market, we shall still be one equation short. This is equivalent to saying that the second set of conditions (Impatience Principle B) is not enough.

In a market comprising 1000 persons there will be, as our unknowns, not only the rate of interest, but 1000 rates of impatience, and the additions to or deductions from the income of these 1000 persons in each period of time. The rate of interest and these thousands of variables act and react on each other and the determination of each can be accomplished only with the determination of all the rest.

In Chapter XII this problem is stated in mathematical formulas such that the number of equations is exactly equal to the number of unknown quantities.

PART II, CHAPTER VI

SECOND APPROXIMATION TO THE THEORY OF INTEREST
Assuming Income Modifiable (1) by loans and (2) by other means

§1. The New Hypothesis

HITHERTO we have assumed:

• (1) perfect foresight, and
• (2) absence of any opportunity to alter income save by trading.

We now abandon the second of these hypotheses. Still assuming that all available income streams can be definitely foreseen, we now introduce the new hypothesis, much nearer actual life, that the income streams are not rigid, but are flexible, that is, that the owner of any item of capital-wealth or capital property, including, of course and especially, his own person, is not restricted to a sole use to which he may put it, but has open to his choice several possible or alternative uses, each of which will produce a separate optional income stream. He has, therefore, two kinds of choice: first, the choosing one from many optional income streams, and secondly, as under the first approximation, the choosing of the most desirable time shape of his income stream by exchanging present income against future.

The two sorts of choice are exercised concurrently in practice and each in consideration of the other. But, for purposes of exposition, we may take one at a time. Or rather, we may suppose the double choice made and then, in order to analyze it, we go back and consider each process separately, assuming the other constant. Let the varying process be the loan, that is, let us suppose one individual to have irrevocably made his choice from among options mutually available. This done, he is limited, as in the first hypothesis, to buying and selling or borrowing and lending as a means of changing the shape of that particular income stream. In this process he cannot change the present value, but in making his initial choice he had the privilege of selecting that option having the maximum present value.

For example, the owner of a piece of land may use it in any one of several different ways. He may, let us say, use it to grow crops, graze animals, plant forests, extract minerals, or to support buildings. Again, the owner of a building may use it, say, for office purposes, apartments, manufacturing, salesrooms, or a warehouse. Most raw materials, too, may be used for any one of a number of purposes. Iron may be wrought into steel rails, or into machinery, implements, tools, armor for ships, or girders for buildings. And so of tools and other implements; a derrick may be used for quarrying stone, building a house, or unloading a boat. A ship may be used to carry any sort of cargo, and sent over any one of numerous different routes. Hammers, saws, nails, and other tools may be used in almost numberless ways.

Perhaps the most adaptable of all instruments of wealth is man himself. He may be simply a passive enjoyer or "transformer"55 of the services of other wealth and as such derive his satisfactions in any one or more of several different ways, sensual, esthetic, intellectual, or spiritual. Or, he may also be an active producer, and, as such, perform work in any one or more of several different ways, physical or mental. Even the skilled laborer who is most specialized and restricted has many ways to turn. And each of these varieties includes numerous sub-varieties. If his work is physical, it may consist in anything from wielding a pick and shovel to the deft manipulation of the instruments employed in the jeweler's art. If his work is mental, he may be a bookkeeper, clerk, superintendent, manager, director, lawyer, physician, clergyman, editor, teacher, or scientist. Some of these options, of course, may be out of the question and, in each case, there will be only one best choice. That choice is what is now under discussion.

In consequence of such a range of choice, any given productive instrument, or any given set of productive instruments, including human beings, may produce any one of many different income streams. Men may work to produce cheap frame houses or durable stone ones; to equip a city with trolleys, elevated, or under-ground rapid transit; to secure an income stream which shall consist of the pleasures of the table, of the amusements of the theatre, of the gratification of social vanities, or of endless combinations of these groups, as well as of all others. Each individual must select one particular income stream out of a thousand possible income streams differing in size, composition, time shape, and uncertainty; but, in this chapter, the element of uncertainty is, as already stated, supposed absent, being reserved for the third approximation (Chapter IX).

As in the first approximation, a perfect market is assumed in which each individual is so insignificant a part that he acts as if the market rate of interest were fixed and merely has to decide how much at that rate he is willing to borrow or lend.

Because of the existence of a wide range of choice, the owner of a given capital has ample opportunity to modify the income stream he derives from it by changing the uses to which that capital is put. He is seldom so committed to a definite future program but that he can consider some alternative. It is on this principle that the cotton belt of the United States, by diversifying its crops and industries, has increased its real income. The production of these Southern States has recently risen with expanding industries, diversified agriculture, water power development, and improved highways. It was largely by changing the uses to which its income, natural resources, and technological equipment had been put that the South has entered a new era.

Under the first approximation, our first glimpse of any flexibility of income was by borrowing and lending. Next we introduced the process of buying or selling and noted that this really included as a special case borrowing and lending. It might be claimed here that, just as buying and selling virtually include borrowing and lending, so the substitution of one use of a person's capital for another use may be said to include buying and selling, and therefore also to include borrowing and lending. It is evidently quite possible to say that one method of utilizing capital is to sell it. In fact, a merchant regards himself as making use of his stock in trade only in the sense of selling it.

While we could thus extend the meaning of optional uses to include buying and selling (which in turn include borrowing and lending) it will better serve the purpose of our analysis not to do so.

There are two principal reasons for this. First, borrowing and lending, the narrower method of modifying income streams, cannot be applied to society as a whole, since there is no one outside to trade with; and yet society does have opportunities radically to change the character of its income stream by changing the employment of its capital. Secondly, when borrowing and lending, or ordinary buying and selling, are employed to modify an income stream, the present value of the original income stream and the present value of the modified income stream are the same, for each $100 added to this year's income has the same present value as the $100 with interest, returned out of next year's income, so that every loan adds and subtracts equal present values. But when an income stream is modified by a change in the use of capital yielding it, the present value of the alternative, as in the case of the South, may not, and, in general, will not, be the same as the present value of the original. This fact, that the present value is not changed by buying or selling (or, in particular, by borrowing or lending) but is changed by otherwise altering the use of one's capital, marks an important distinction between the two methods of altering one's income stream. The distinction and its importance are most clearly seen by a mathematical analysis such as that shown in Chapter XI and XIII.

§2. Optional Income Streams

The choice among all available optional income streams will fall on that one which has the maximum desirability or wantability.

We have seen in the preceding chapter that income streams may differ in size, time shape, composition and certainty. As among income streams of different sizes but similar in other respects, the most desirable will, of course, be the largest.

As among income streams of different composition but similar in other respects, the most desirable will be that in which, to the given individual, the marginal desirabilities of the different constituents are proportional to their several prices, in accordance with the fundamental principle of marginal desirability in the theory of prices.56

Finally, and principally, as among income streams differing in time shape alone, the most desirable is found in accordance with the principles which govern the rate of interest, and which are to be expounded in this book. It is, therefore, with income streams differing in time shape that we are here chiefly concerned.

In order definitely to illustrate income streams differing in time shape, let us begin by supposing only three. An individual is, let us say, possessed of a piece of land almost equally good for farming, lumbering, or mining. These terms are used merely to fix the reader's thought in concrete pictures. Logically, it would be better to designate the three optional supposititious income streams simply by the letters A, B, and C, for there is no pretense that the income streams closely resemble in more than a very general and sketchy way those of actual farming, lumbering, or mining; nor is it essential that the three products should differ in kind. Thus, the three streams might represent three different methods of producing the same product, one more roundabout or capitalistic than another. They are here given the concrete names of farming, lumbering, mining, merely for convenience in distinguishing and remembering the three types, not because these types are true to these names, nor because examples concerned with land comprise opportunities any more important than those concerned with commercial or industrial examples. The only essential point is that the three series of numbers representing the income streams A, B, and C are different.

Our imaginary land owner thus has the option of securing any one of these three different income streams. While they will, in the first instance, differ in composition—one income stream consisting in the production of crops, another in the production of lumber, and the third in the production of minerals—we may, for our present purpose, assume that these are all reduced to real income measured in terms of money. That is, we here assume that the prices and values of the crops, lumber, and minerals are given and determined in accordance with the principles which determine prices.57

Assuming, then, that the land owner finds predetermined prices and quantities of crops, lumber and minerals, with predetermined costs for obtaining them, he has before him simply the choice of three definite income streams, each expressible in terms of money, according as he uses his labor, land, and capital in one or the other of the following three ways:

(1) for farming purposes, which, let us say, will give him a regular and perpetual succession of crops and income equally valuable year after year, that is, with an income stream of the type AA' in Chart 14;

(2) for forestry purposes, with very slight returns for the first few decades, and larger returns in the future, as indicated by the curve BB';

(3) for mining purposes, in which case we shall suppose that the income is greatest for the early years and thereafter gradually decreases until the mine is exhausted; illustrated by Curve CC'.

The important question now before us is: What are the principles upon which the owner of the land chooses the best one among these three income streams, A, B, and C? This question is fundamental and typical in the second approximation.

The rate of interest is just as relevant to this initial choice of uses for maximum present value as to the subsequent choice for shape alone, for it is used in finding the present value; and when the rate changes, the relative present values of differently shaped streams may change about.

We shall suppose, as heretofore, that there is a uniform rate of interest in the community and that any individual is free either to borrow or to lend at that rate and up to any amount desired. Under this hypothesis the choice among the three available options will simply fall on that one which yields the maximum present value, reckoned at the market rate of interest.

Let us assume a market rate of interest at five per cent. To reckon the three respective present values, suppose the use of the land for mining purposes will yield an income stream, let us say, as follows: $2000 the first year, $1800 the second, $1600 the third, and so on, diminishing annually by $200 to the point of the mine's exhaustion. The present value of these ten sums, discounted at five per cent, is $9110. If the land is used for farming purposes and yields a net income of $450 a year perpetually, the present value at five per cent will be $9000. If, finally, the land is used for forestry purposes, we shall suppose it yields the following sums: zero for the first two years, $300 for the third, $400 for the fourth, $500 for the fifth, and $500 thereafter forever—then the value of the land, reckoning at 5 per cent, will be $8820.

Under these conditions the choice will evidently fall on the mining use, because, for mining purposes, the land is worth $9110, which is greater than $9000, its value for farming purposes, and than $8820, its value for forestry purposes.

The three options may be contrasted as to distribution in time as follows:

The particular income stream selected will tend to leave its impress on the time shape of the total income stream of the individual who owns it. For, as was seen in Chapter I, the total net, or final, income stream of any individual during any interval of time is simply the sum total of the items of income flowing during that interval from all the articles of property belonging to him. Hence, if one selects the mining use for his land, whereby the income stream gradually decreases, its tendency will be to produce a similarly decreasing trend in the total income stream enjoyed by the individual. This tendency may be counteracted, of course, by some opposing tendency, but will have full sway if the income from all other capital than the land remains the same in value and time shape. It is true that the direct income from the mine is not itself real income, but consists of services which, relatively to some other capital source, are disservices, thus constituting intermediate income or interactions. But those items are readily transformed, through a chain of credits and debits, into real, and then into enjoyment income. Thus the ore of the mine is exchanged for money, and the money spent for enjoyable services or for commodities which soon yield enjoyable services, so that the real income closely copies in time shape58 the original intermediate income from the mine.

§3. The Two Kinds of Choice

The possessor of the mine, however, is not compelled thus to copy in his real income the mine's fluctuations of physical or natural income. He may counteract any fluctuations in his whole net income which may be caused, in the first instance, by the choice of income C rather than B, or A. Or, if he prefers, he may further exaggerate those fluctuations. In fact he may make the time shape of his income follow any model he likes. He may do this as described under the first approximation, by either borrowing or lending in suitable amounts and at suitable times along his income stream; or, more generally, by buying and selling income streams or parts of income streams so as to fashion the time shape of his own final net enjoyable income to suit himself.

He may, for instance, so far as time shape is concerned, achieve an even flow of income such as he could get from the farm use of his land. But he will not on that account choose this farm use in preference to the mining use; for the mining use has the larger present value, and the undesirable time shape of its income stream, under our present hypothesis, can be very easily remedied. For instance, he may lend some of the proceeds of its earlier output and in later years be paid back with interest.

Of course, his loan at five per cent does not alter in the least the figure $9110, the discounted value at five per cent of all the ten items of income ($2000, $1800, $1600, $1400, $1200, $1000, $800, $600, $400, $200); it simply adds to the later of these ten figures and subtracts from the earlier ones. The present value of the additions is necessarily equal to the present value of the subtractions; for the additions are the repayments, while the subtractions are the loans, and the present value of any loan equals that of its repayment.

We may totally separate, therefore, in thought the two choices made by the land owner, namely, (1) the choice of C (mining) in preference to A and B on the ground of greater present value, and, (2) the choice of time shape. If, as just supposed for illustration, the second sort of choice is that of an even income stream, it will be at the rate of $455.50 a year perpetually. That is to say, the mine owner will lend at interest $1544.50 the first year (all but $455.50 out of his original mining income of $2000); in the second year he will lend $1344.50 (all but $455.50 out of his original $1800); and so on. When the ninth year is reached, he ceases to lend further, for the mine then yields only $400. Instead, he then ekes this out by $55.50 returned from the previous loans. Likewise, in the tenth year he ekes out the $200 from mining by $255.50 returned from loans. Thereafter he will get nothing further from mining; but his loans will have accumulated a sinking fund (of $9110) to take the place of the mine and from this fund he can annually derive a 5 per cent revenue of $455.50. Consequently, the net result of the double choice (mining use and even time shape) is to increase the perpetual income of $450 offered by farming to a perpetual income of $455.50. This new perpetual annuity has exactly the same time shape as that derived from the farming use, but is larger by $5.50 per annum.

Incidentally it may be observed that this mining income, thus evened out by financing into a uniform $455.50 per year, exceeds the uniform farming income of $450 in exactly the same ratio as the present value ($9110) of the mining income exceeds that ($9000) of the farming income.

The following table exhibits the operations in detail:

Or, instead of wanting a perpetual even flowing income, the land owner may prefer as his model the time shape of the forestry income. He will not, however, on that account, choose this forestry use in preference to the mining use. He will simply lend at interest from the items of mining income all of his $2000 the first year, leaving no income for that year; likewise, all of his $1800 the second; all but $310 the third; all but $413 the fourth and all but $516 the fifth, and every succeeding year until the ninth year. He will then turn around and use $116 from his loans just described to eke out his $400 and bring up his income in that year to $516. The tenth mining item, $200, will likewise be brought up to $516 after which he will depend entirely on his outside loans at five per cent, deriving therefrom exactly $516 every year.

The result will then be a series of income items exactly similar to the B, or forestry, series but each item magnified in the ratio of $9110 to $8820, the present values respectively of C and B.

The following table exhibits these operations:

Since, therefore, any time shape may be transformed into any other time shape, nobody need be deterred from selecting an income because of its time shape, but every one may choose an income exclusively on the basis of maximum present value. It will then happen that his income, as finally transformed, will be larger than it would have been if he had chosen some other use which afforded that same time shape.

All this is true under the assumption used throughout this chapter, namely, that after the most valuable option has been chosen, you can borrow and lend or buy and sell ad libitum and without risk. If this assumption is not true, if a person were cut off from a free loan market, the choice among optional income streams might or might not fall upon that one having the maximum present value, depending on the other circumstances involved, particularly his preferences as regards time shape.

Of course our assumption is a violent one, made in this second approximation, as in the first, in order to simplify the theory of interest. But already it must be evident that the principle involved has important practical applications. To a very considerable extent a modern business man, with access to loan markets, can choose from among the various options open to him on the basis of present value, and trust to loans or other financing to rectify any inconvenience in time shape.

The lines AB and A'B' in Chart 15 picture alternative income streams, of which the descending one, AB, has the larger present value. The choice will fall on AB, and if the individual prefers the time shape of A'B', he will then lend some of the early receipts from the income stream AB and receive back some of the latter, converting his income AB of undesirable shape into the income stream A''B'' which has the desired shape. This final income A''B'' combines the virtues of both the original alternative incomes AB and of A'B'; it possesses the superior shape of A'B' and the superior present value of AB. As compared with A'B' it has the same shape but a greater size.

In practice, of course, the two steps are usually made simultaneously, not successively. In fact, usually the borrowing or financing often precedes the choice of option, thus reversing the order of presentation here adopted for convenience of exposition. So it would be quite as true to say that the loan, with the choice of option it makes possible, is made to secure an increased income as it is to say that the loan is made to even up the distorted income given by the option chosen.

But were it not for the possibility here assumed of modifying the time shape of his income stream by borrowing and lending, or buying and selling, the land owner would not feel free to choose the one from among the optional income streams which possesed the highest present value. He might find it advantageous, or even necessary, to take one of the others, being scarcely able to live if his property offered only distant income. If his capital were all in the form of growing young forests, and he could not mortgage the future in some way, he would have to starve or give up some of his holdings. In actual life we find such people—people who are said to be "land poor." In fact, we are all somewhat hampered in the choice of options by difficulties and risks both in the choice of options and in the financing it requires.

But we see that, in such a fluid world of options as we are here assuming, the capitalist reaches his final income through the co-operation of two kinds of choice of incomes which, under our assumptions, may be considered and treated as entirely separate. To repeat, these two kinds of choice are: first, the choice from among many possible income streams of that particular income stream which has the highest present value, and, secondly, the choice among different possible modifications of this income stream by borrowing and lending or buying and selling. The first is a selection from among income streams of differing market values, and the second, a selection from among income streams of the same market value.

§4. Opportunity to Invest by Change of Use of Capital

Since this double choice results, when made, in a perfectly definite income stream, it might seem that the situation does not materially differ from the case of the rigid income stream discussed in the first approximation. But the two cases do differ materially, for under the present hypothesis (of optional income streams) the particular choice made by the individual depends upon what the rate of interest is. A change in that rate may shift the maximum present value to some other option, or alternative income stream, and that shift reacts on the rate of interest.

In the example cited, if the rate of interest should be 4½ per cent instead of 5 per cent, the order of choice would be changed. The present value of the land for A (farming) would be $10,000, for B (forestry), $9920, and for C (mining), $9280. The farming use, or A, would now be the best choice. Again, if the rate of interest should be 4 per cent instead of 4½ per cent, the present value of the use of the land for A, farming purposes, would be $11,250; for B, forestry purposes, $11,300; and for C, mining purposes, $9450. In this case, B, the forestry use, would be chosen.

Thus, it would pay best to employ the land for mining if the rate of interest were 5 per cent, for farming if it were 4½ per cent, and for forestry if it were 4 per cent.

The three options open to the owner of the land at these three different rates of interest may be summarized as follows:

Thus a change in the rate of interest results in a change in the relative attractiveness of different optional income stream opportunities. A high rate of interest will encourage investment in the quickly returning incomes, whereas a low rate of interest will encourage investment in incomes which yield distant returns. As the business man puts it, when interest is high, he can less afford to wait for a remote return because he will "lose so much interest." An investor will, therefore, make very different choices among the various options open to him, according as interest is at one rate or another.

Consequently, the existence of various options to use one's capital introduces a new variable into the problem of interest determination. For the individual, the rate of interest will determine the choice among his optional income streams, but, for society as a whole, the order of cause and effect is reversed—the rate of interest will be influenced by the range of options open to choice. If we live in a land covered with young forests or otherwise affording plenty of opportunities for distant income but affording few opportunities for immediate income (as was the case in the pioneer days in this country) the rate of interest will, other things being equal, be very much higher than in a land full of nearly worked out mines and oil fields or otherwise affording many opportunities for immediate but few opportunities for remote income.

We are thus coming in sight of a principle, applying to interest determination, new in our study, the principle of opportunity to invest, not simply by lending but by changing the use of one's capital. This new principle, largely physical or technical, is just as important as the psychical principle of human impatience. It is really old in the sense that, implicitly, it has been recognized in almost all theories of interest, and explicitly in those of Rae, Landry, Walras, and Pareto. To trace this new influence on interest is the special purpose of the second approximation.

§5. The Reasoning not "Circular"

At first sight it may appear to those not familiar with the mathematics of simultaneous equations and variables that the reasoning is circular; the rate of interest depends on individual rates of impatience; these rates of impatience depend on the time shapes of individual income streams; and the choice of these time shapes of income streams depends, as we have just seen, on the rate of interest itself.

It is perfectly true that, in this statement, the rate of interest depends in part on a chain of factors which finally depend in part on the rate of interest. Yet this chain is not the vicious circle it seems, for the last step in the circle is not the inverse of the first.

To distinguish between a true and a seeming example of a circular dependence we may cite simple problems in algebra or mental arithmetic. Suppose we wish to find the height of a father who is known to be three times as tall as his child. To solve this we need to know something more about these two heights. If we are told in addition that the child's height differs from his father's by twice itself, the problem is really circular and insoluble, for the additional condition is really reducible to the first, being merely a thinly veiled inversion of it. The problem essentially states (1) that the father's height is three times the child's and (2) that the child's is one-third of the father's—an obvious circle.

But if the dependence of the father's height on the child's is essentially different from—independent of—the dependence of the child's on its father's, there is no circle. Thus supposing, as before, that the father is three times as tall as the child, let us stipulate in addition that the child's height differs from the father's by four times as much as the child's less two feet. This may sound as circular as the first statement—the father's height is expressed in terms of the child's, and the child's is expressed in terms of the father's; but the second stipulation is not now reducible to the first. The heights are entirely determinate, that of the father being six feet and that of the child, two. The mere fact that both of these magnitudes, the father's height and the child's height, are specified each in terms of the other does not constitute a vicious circle. The general principle, as Cournot and other mathematical economists have often pointed out, is simply the well known algebraic principle of simultaneous equations. In order that the equations may determine the unknown quantities involved, there must be as many independent equations as there are unknown quantities, although any or all of these equations may contain all the unknowns. (The equations are independent if no one of them can be derived from another or the others.) Many an example of economic confusion and wrong reasoning could be avoided if this fundamental principle of mathematics were more generally applied.

This mathematical principle of determinateness applies in our present problem. Real examples of circular reasoning in the theory of interest are common enough, but the dependence, above stated, of interest on the range of options and the dependence of the choice among them on interest is not a case in point, for this last determining condition is not derivable from the others.59

For our present purpose we need only present the matter to the reader's imagination by a process of trial and error. To find the rate of interest on which the market will finally settle, let us try successively a number of different rates. First, let us suppose a rate of 5 per cent. This rate will determine the choice between options for each individual. The land owner formerly supposed will, as we have seen, choose C, the mining use, because the present value of the income so obtained ($9110) exceeds the present values of the rival uses. Every other individual in the market, in like manner, will select that particular use for his capital which will give him the maximum present worth. With these choices made, the different individuals will then enter the market of loans or sales, desiring to modify the time shapes of their income streams to suit their particular desires.

As a result of all these choices, the total amount which all the would-be lenders are willing to lend at 5 per cent out of this year's instalment of their chosen income stream will be perfectly definite, and likewise the total amount which all the would-be borrowers are willing to take. This we saw in the preceding chapter. In other words, the demand and supply of loans for the present year, at the given rate of interest, 5 per cent, will both be definite quantities. Should it happen that the supply of loans exceeds the demand, it would follow that 5 per cent could not be the correct solution of the rate of interest, for it would be too high to clear the market.

In that case, let us try again; suppose a rate of 4 per cent. Following the same reasoning as before, we now find that the land owner will select the forestry opportunity for his land because the present value ($11,300) of the income from forestry—now reckoned at 4 per cent—will exceed that of the two rival income possibilities. Other capitalists will likewise select their best option from among those available to them and on the basis of these income streams—not the same as before under 5 per cent. In a word, there will now be a different supply and demand. The land owner, for instance, instead of lending, may now borrow (or sell securities) to even up his income stream. Should it then happen that the demand and supply of loans, on the basis of 4 per cent, are still not equal, but that, this time, the demand exceeds the supply, it would be a proof that not 4 per cent is the true solution, but some higher rate. By again changing our trial rate—part way back toward 5 per cent, we may evidently reach some intermediate point, let us say 4½ per cent, at which rate not only will each individual choose the best use of his capital—that having the highest present worth—but also, at the same time, the demand and supply of loans engendered by all such choices will exactly clear the market, i.e., bids and offers at the given rate will be equal. Likewise, the same clearing will be worked out for next year and for all years.60

The introduction, therefore, of flexibility into our income stream still leaves the rate of interest entirely determinate, even though the income streams are now, in the second approximation, not fixed or rigid but subject to choice, and even though that choice will depend on the rate of interest itself.

§6. Summary

For the determination of the rate of interest we must now, therefore, in the second approximation, add two new principles to the four principles already given in the first approximation described in the previous chapter.

THE TWO INVESTMENT OPPORTUNITY PRINCIPLES

A. Empirical Principle

There exists, for each individual, a given specific set or list of optional income streams to choose from, differing in size and time shape (but without any uncertainty as to what will happen if any particular one is chosen).

B. Principle of Maximum Present Worth

Out of this list of options each individual will choose that particular income stream possessing the greatest present worth when calculated by means of the rate of interest as finally determined by these six conditions.

THE TWO IMPATIENCE PRINCIPLES

A. Empirical Principle

The degree of impatience, or rate of time preference, of any given individual depends upon his income stream as chosen by him and as modified by exchange.

B. Principle of Maximum Desirability

Each person, after or while first choosing the option of greatest present worth, will then modify it by exchange so as to convert it into that particular form most wanted by him.

This implies, as we have seen, that each person's degree of impatience, or rate of time preference, will at the margin, be brought to equality with the market rate of interest and, therefore, with the marginal preference rates of all the other persons.

THE TWO MARKET PRINCIPLES

A. Principle of Clearing the Market

The rate of interest must be such as will clear the market, that is, equalize supply and demand. That is, for every time interval, the additions to some individuals' incomes caused by borrowing or selling must balance the deductions from others caused by lending or buying.

B. Principle of Repayment

The loans must be equivalent in present worth to repayments, or, more generally, the additions to any individual's income, brought about by borrowing or selling, in some time intervals must be equivalent in present worth to the deductions from his income in other time intervals brought about by lending or buying.

Thus we see that the rate of interest is determined by two principles of investment opportunity as well as by two principles of impatience and by the two self-evident market principles.

More briefly stated, the rate of interest is determined so as (1) to make the most of opportunities to invest, (2) to make the best adjustment for impatience and (3) to clear the market and repay debts.

In short, the theory is thus one of investment opportunity and human impatience, as well as exchange.

But while we have reached the two chief theoretical foundations of our subject, we are still, of course, far from the real world. The real world is vastly more complex than the imaginary world described in this chapter. In particular, we still need to take account of risk. This we shall do in the third approximation.

PART II, CHAPTER VII

THE INVESTMENT OPPORTUNITY PRINCIPLES

§1. Eligible and Ineligible Options

THE essential point of the preceding chapter is that the possibility of more than one use of our resources affords opportunity to invest by substituting one such use for another. Whenever there is such a choice of alternatives, as for instance by changing from the "mining" to the "farming" use of one's land, as per Table 3, there is a differential sacrifice or investment of income during the earlier years for the sake of a differential return later. The fact that such alternative uses of labor, land, and capital exist, introduces on the scene the whole subject of "productivity".

Böhm-Bawerk was profoundly right when he wrote:

I have generally avoided the term productivity of capital because it may be used ambiguously to mean physical productivity, or value return, or return over costs; and because it suggests that capital produces income value instead of the reverse; and because it attributes the value of manufactured things to the cost of production, instead of to their discounted future services.

I prefer the term investment opportunity. It has some of the demerits as well as the merits belonging to any new term. It is unfamiliar and therefore requires precise definition. The concept of investment opportunity rests on that of an "option." An option is any possible income stream open to an individual by utilizing his resources, capital, labor, land, money, to produce or secure said income stream. An investment opportunity is the opportunity to shift from one such option, or optional income stream, to another.

It includes all possible opportunities to invest—those that can yield only negative returns upon the investment as well as those which are capable of yielding very large surpluses over the amount of the investment or cost.

The first (A) of the two investment opportunity principles specifies a given range of choice of optional income streams. Some of the optional income streams, however, would never be chosen, because none of their respective present values could possibly be the maximum. We have seen that the land, in our example, would be most profitably employed for farming, for mining, or for forestry, according to the rate of interest. But it would not be employed, let us say, for a quarry, no matter what might be the rate of interest.

The optional uses which are thus out of the question, whatever be the rate of interest, are called ineligible. The rest are the eligible options. We need to consider the eligible ones—any one of which might be made to have the maximum present value, given the right rate of interest to make it so.

§2. The Method of Comparative Advantage

The second (B) investment opportunity principle, that of maximum present value, is of great importance and has many aspects not always recognized as related to one another. Let us restate this maximum value principle in an alternative form, thus: one option will be chosen over another if its income possesses comparative advantages outweighing (in present value) its disadvantages.

To illustrate this alternative method of stating the same principle—which method might be called the method of comparative advantage—let us recur to the example of the land. We found that, when the rate of interest was 4 per cent, the owner would elect the forestry use, since this possessed the greatest present value. If we now compare, year by year, the income from the land when used for forestry purposes with the income which it might have yielded if used in one of the other ways, as for instance farming, we shall see that in some years there is an excess in favor of the forestry use, and in other years a deficiency, as shown in the table on the following page.

Here we see that, in the first four years, there are comparative disadvantages, a differential sacrifice, amounting in the four respective years to $450, $450, $150, $50. These are the disadvantages from the use of the land for forestry purposes as compared with its use for farming, but the disadvantages are offset later by advantages in return amounting to $50 each year perpetually. If prior to the first year listed above the owner has been using the land for farming purposes and was considering the advisability of changing over to forestry, he would think of the disadvantages or sacrifices of $450, $450, $150 and $50 as investments or costs and the advantages of $50 each year in perpetuity as returns on these investments or costs. And he could think of the proposal to substitute the forestry use for the farming use as an opportunity to invest the $450, $450, $150, and $50 for the sake of securing the return of $50 each year thereafter. If, now, we take the total present value, at 4 per cent, of the deficiencies, or investments, of $450, $450, $150, and $50, we shall obtain $1025, whereas the present value of the returns of $50 per annum beginning in five years and continuing in perpetuity will be $1069. Thus the present value (at 4 per cent) of the gains exceeds the present value of the sacrifices or costs by the difference between $1069 and $1025. As reckoned in present estimation, the gains of income outweigh the costs or sacrifices of income. We may say, therefore, that, the rate of interest being 4 per cent, forestry is preferable to farming because of a surplus of advantages over disadvantages reckoned in present value. Thus, the opportunity to invest by switching over from farming to forestry is, if money can be borrowed at 4 per cent, more than worth while.

But if the rate of interest were 4½ per cent, the comparison would be different. The present value of the sacrifices or costs would be $1016, and the present value of the gains or returns $932, showing a preponderance of the sacrifices or costs. That is, if the rate of interest is 4½ per cent, the cost from using the land for forestry rather than farming outweighs the returns. Therefore, when money is at 4½ per cent, the land would not be used for forestry purposes.

The general principle is, therefore, that among the various options open to the capitalist he chooses the most advantageous, or more fully expressed, the one which, compared with any other, offers advantages which in present value at the given rate of interest outweigh the disadvantages. But this is evidently merely another formulation of the original principle that the use chosen will be the one which has the maximum present value at the given rate of interest.

We may summarize the method of comparative advantage as follows: We are constantly confronted with the opportunity to choose one income stream rather than another. We inquire what difference it makes whether one or the other alternative is chosen. We find often it makes two kinds of differences, advantages and disadvantages. If we start with the option which has the more immediate advantages and ask whether it is or is not worth while to give up this option and adopt the other instead, we may call the proposal so to do an opportunity to invest, i.e., to incur certain disadvantages or, as they will hereafter be called, costs, for the sake of certain advantages or, as they will hereafter be called, returns. And we decide whether or not this investment opportunity is worth while by weighing the costs against the returns in terms of present worth, as reckoned by the rate of interest.

§3. The Concept of Rate of Return Over Cost

When we compare two optional income streams, and either may be preferable to the other according as one rate of interest or another obtains, the two options would stand on a par if the right intermediate rate were used for calculating the present values of the two options. That is, this equalizing rate is such that the present values of the two options would be equal, or what amounts to the same thing, it is such that, if that rate is used for discounting, the present value of the cost of choosing one option instead of the other would be equal to the present value of the return.

This hypothetical rate of interest which if used in calculating the present worth of the two options compared would equalize them or their differences (cost and return) may be called the rate of return over cost and hereafter this name will generally be employed. This new magnitude (or factor) in our study plays the central rôle on the investment opportunity side of interest theory.

Let us now apply this rate of return over cost to the case of the options already used for illustration.

We have seen that, in our land example, if the rate of interest is 4 per cent, the net advantage is in favor of the forestry use, and if the rate of interest is 4½ per cent, the net advantage is in favor of the farming use. It is evident then that at some intermediate rate of interest the comparative advantages of the two uses would be exactly equal. This intermediate rate is approximately 4.2 per cent, and this equalizing rate is the rate of return over cost.

But we may reduce the comparison to its simplest form if we change the figures in the example to the following:

In this case the equalizing rate, or the rate of return over cost, is evidently 10 per cent. At the cost of $100 there is a return of $110, or 10 per cent over the $100. At 10 per cent the present worth of the two will be equal; for the present worth of the return $110 due next year is, reckoning at 10 per cent, exactly $100 and the present value of the cost, $100, due immediately, is also $100.

The example just given, in which the cost ($100) is only one item and the return ($110) is also only one item received one year later, is the simplest possible example. But the same principle holds true however complicated may be the series of items constituting the costs and returns.

Perhaps the next simplest example is that in which one option shows in the present year a cost (of, say, $100) compared with the other but shows a return (of, say, $8) for every future year in perpetuity. Under these circumstances the equalizing rate (or the rate of return over cost) is 8 per cent.

Thus the expression "rate of return over cost" is applied to the comparative merits of two alternative income streams. I repeat that by cost is meant the comparative loss from one's income stream at first, caused by substituting one use of capital for another, and by return is meant the comparative gain which accrues usually later, by reason of this same substitution. The cost is literally the difference it makes today and the return is the difference it makes in the future—the first negative, the second positive.

It will be noted that this description is all inclusive. It applies to every possible cost and every possible return. The problem of the investor—and everyone is an investor in some degree and manner—is always to answer the question: "What difference does it make to my income stream whether I choose one way rather than another? What do I sacrifice and what do I gain?" If the cost comes first and the return comes later, he wants to know if the return exceeds the cost by enough to be worth while. The excess is his return over cost and the important magnitude is the rate per annum of this return over cost.

Usually this question, "What difference does it make?", is asked with reference to a proposed change from an old to a new layout of one's plans. Will a little more tilling of the soil bring a big or a little return, both the tilling and return in crops being translated at their market prices into money? Will a new harvesting machine at market prices make enough difference in the harvest to be worth while? Will a merger of two companies make a return in future profits sufficient to make the temporary costs involved in the merging process worth while? It will be seen, then, that the concept here used of investment opportunity is not contrary to ordinary ideas. It includes them. Every time a person considers what he calls an opportunity to invest, he weighs in his mind the differences in his expected income—the expected future additions against the more immediate subtractions. Even when the investment is not made in installments out of savings from current income, but is made in one lump sum, it must not be forgotten that this lump sum invested merely represents the sacrifice of some alternative income stream.

The rate of return over cost is not, of course, to be confused with the rate of interest which it helps to determine, any more than the rate of impatience is to be so confused.

§4. The Principle of Return over Cost

Now let us restate the forestry-farming-mining comparison in the land example of the preceding chapter in terms of the rate of return over cost.

If the actual market rate of interest is 4 per cent, a person using the land for farming, or thinking of so doing, would find forestry preferable. The change from farming to forestry would cost certain sacrifices of income in the first four years, as specified in Table 6, but would return certain net additions thereafter. The rate of return over cost which would be realized by choosing the forestry rather than the farming use is 4.2 per cent. He would be realizing 4.2 per cent, which is more than the market rate, 4 per cent.

If, however, the market rate of interest were 4.5 per cent, it would not pay to change from farming to forestry; for to do so would return only 4.2 per cent as compared with 4.5 per cent which he could get in the loan market. Our farmer would prefer to invest at 4.5 per cent by lending in the first four years $450, $450, $150, $50 rather than sacrifice these same amounts for 4.2 per cent by giving up farming for forestry. To induce him to make a change, the rate of return over cost must exceed the rate of interest.62

Thus, by employing the concept of a rate of return over cost, we may restate the investment opportunity principle of maximum present value, or the principle of comparative advantage, as the principle of greatest return over cost. So stated the principle is:

Out of all possible options open to a person that particular one is selected, the comparison of which with any other option affords a rate of return over cost equal to or greater than the rate of interest.

§5. Marginal Rate of Return Over Cost

Next let us apply this statement of principle to the case in which the range of choice is not confined to a few definite options, but extends to an infinite number varying by continuous gradations. This case is really more like the facts of life than the imaginary case of a few fixed options, such as the farming, mining, or forestry uses of land. In fact, each of these three uses is in actual life not merely a single use, as was assumed for simplicity, but a whole group of optional uses. Thus, the farmer may carry farming to any degree of intensity, and the same may be said of mining or lumbering. For each particular degree of intensity he will have a different income stream. He may, for instance, find it possible at the beginning of the scale of intensity to invest an extra $100 worth of his or other labor in the present in order that one year later he may have an income of $150 more than he would otherwise have. If the rate of interest is 4 per cent per annum, he would evidently prefer this course, for while his present income is diminished by $100 he would realize an increase of $150 in his income one year later, or $50 over cost, making a rate of return over cost of 50 per cent per annum, whereas the interest is only 4 per cent. If he invests another $100 in present cultivation, this will add to his income in a year's time something less than the $150, say $130, making a rate of return of 30 per cent. And so each successive choice compared with its predecessor follows the law of decreasing returns. A third $100 will add, let us say, $120 or $20 more than the cost. A fourth $100 may secure a return of an additional $10 a year over and above the cost; a fifth $100 may secure a return of an additional $8; a sixth $100 may bring $6; a seventh $100, $4.

Thus far, in the scale of intensity, each option yields 4 per cent or more, while the rate of interest is 4 per cent a year. The lure of a rate of return equal to or in excess of the interest rate will induce the farmer to incur the additional cost. But the next option, let us say, is to invest an eighth $100 for an additional $3 a year. Evidently, it will not be to the farmer's advantage to take this last step; he will stop at the previous step, at which he barely gets a 4 per cent return. As we saw in the preceding section, each successive investment opportunity is chosen as long as the rate of return over cost of that option compared with the previous one is greater than the rate of interest, and that use is rejected at which the rate of return over cost becomes less than the rate of interest. The intensiveness of his farming is thus determined by the rate of interest. In our example, he will stop at the seventh $100 which barely returns the equivalent of the rate of interest. We may say, then, that he chooses that degree of intensiveness at which the rate of return over cost is barely more than the rate of interest. This envisages a series of possible income streams arranged successively in order of intensiveness of the cultivation required for each. By substituting successively one of these income streams for the preceding we incur more cost but obtain more return. The rate of the return over the cost compared with the market rate of interest is our guide as to how far to go in the series. We thus reach the marginal rate of return over cost.

§6. The Illustration of Cutting a Forest

To vary the illustration from intensive agriculture to forestry, let us apply the option selection idea to cutting a forest. Let us consider as the first option the cutting of the forest at the end of nine years, when the income stream consists of the single-item, the production of 900 cords of wood (or $900 if wood is $1 a cord).63

The second option is holding the forest for another year of growth and cutting it at the end of ten years, to receive an income item of 1000 cords (or $1000, assuming an unchanging price of $1 a cord). The two alternatives may be put in precisely the same tabular form as the one previously employed for the case of forestry and farming as follows:

The last column shows that the ten-year plan, compared with the nine-year plan, involves a cost of 900 in the ninth year, but involves a return of 1000 in the tenth year. The rate of the return (100) over the cost (900) would thus be a little over 11 per cent. If the rate of interest in the market is 5 per cent, it would evidently pay to wait, that is, to postpone the cutting to the tenth year.

The next option would be to cut in the eleventh year, which, as compared with the previous or ten-year plan, would, let us say, cost 1000 in the tenth year and return 1050 in the eleventh year—in other words, give a rate of return over cost of 5 per cent. Evidently, then, it would be a matter of indifference whether the forest were cut in the tenth or eleventh year, inasmuch as the rate of return over cost would be exactly equal to the rate of interest.

Similar reasoning might show that the choice of the next option, that of cutting the forest in the twelfth year, would yield a return of say 21/1050 or 2 per cent. Inasmuch as 2 per cent is less than the rate of interest, this alternative would be rejected. Thus, equilibrium is found where the rate of return on cost equals 5 per cent, the rate of interest.

The case may be illustrated by Chart 16. Let AB represent the number of cords of wood on an acre of growing trees; let A' B' represent the amount of wood which may be expected at the end of five years; let A'' B'' represent what may be expected in ten years and so on for successive years until the forest reaches its maximum growth, MN, at the end of AM years. The percentage-slope, or rate of ascent,64 of the curve BN at any point, therefore, represents the rate of growth, at any time, of the forest. The value at present (at the point of time A) of the forest, in terms of cords of wood, will be represented, not by the height AB, but in a different manner, as follows: If from B' the discount curve65B' C' be drawn, the ordinate of which, at any time, will represent the discounted values of A' B' at that time, then AC' will represent the present value of A' B', i.e., of the amount of the wood if cut in five years. Similarly, AC'' will represent the present value of A'' B'', the wood if cut in ten years. We draw in like manner a number of discount curves until one is found, tT, which is tangent to the curve BN.At will then be the correct value of the young forest, and D will represent the time at which it should be cut. Clearly, At is quite different from AB, the amount of wood at the present time, and also from DT, the amount of wood at the time of cutting. At is the maximum present value out of all possible choices as to the time of cutting. If the forest is for some reason to be cut at once, its value will be only AB; if it is to be cut at A' its present value will be AC' if at A'', it will be AC''; if at D, it will be At.At is the maximum, for if the forest were cut at any other point of time on either side of T the discount curve passing through that point would evidently lie below the curve tT.

At the time A, then, the wood in the forest is only AB but, assuming proper foresting, the value of the forest in terms of wood is At; the rate of growth of the forest is the percentage-slope of BN at B, but the rate of interest is the percentage-slope (the same at all points) of tT.

At the point of tangency alone, namely T, are the rate of growth and rate of interest (both in terms of wood) identical, and to that extent at least there is truth in the thesis that the rate of interest is the rate of growth. This, however, is not the average rate of growth but the rate of growth at the time of cutting. This is the element of truth in the organic productivity theory of Henry George and Alexander Del Mar. These writers based their theories of interest on the productivity of those particular kinds of capital which reproduce themselves, and reached the conclusion that, in the last analysis, the rate of interest consists in the "average rate of growth of animals and plants."66 .

Evidently the theory would be substantially correct if "average" were replaced by "marginal." The example of cutting the forest illustrates the simplest theoretical case of marginal productivity as a true basis of the rate of interest.

But that this element of truth is insufficient of itself to afford a complete determination of the rate of interest is evident when we consider that the point at which the forest is to be cut itself depends, among other causes, upon the rate of interest! If the interest rate rises, the discount curves employed become steeper and the point of tangency T moves toward the left, that is, the forest will be cut earlier.

In no case, of course, is the time of cutting the time of maximum stumpage. To wait for that time would eat up too much interest. The theories of Del Mar and Henry George thus constitute a special case under the opportunity principles.

§7. Other Similar Illustrations

Both the preceding examples, one of intensive agriculture and the other of forest cutting, involve (1) an immediate cost and (2) a return one year later, thus reducing the marginal rate of return over cost to such simple calculations as (105 - 100) ÷ 100 = 5 per cent.

We may vary the illustration indefinitely and still preserve this elementary simplicity. A merchant has always before him an indefinite number of possible income-streams from which to choose. As in the case of the land cultivation and the forest cutting we may simplify his choice by supposing successive doses of costs of $100, each spent on more or better machinery, more or better workmen, more or better advertising, more or better supervision, and so forth, each $100 cost being immediate, and then supposing the returns to these successive doses of invested cost to come respectively one year later and to be respectively, say, $140, $130, $115, $106, $105, $104; so that the excess of return over the cost will be respectively $40, $30, $15, $6, $5, $4. Thus the rate of return over cost will be respectively 40, 30, 15, 6, 5, and 4 per cent. The enterpriser will incur the costs as long as the rate of return over these costs is greater than the market rate of interest. In this case, therefore, he will stop at 5 per cent if the market rate of interest is 5 per cent. Again we have ($105 - $100) ÷ $100 = 5 per cent.

In practice, however, we seldom, if ever, have such simplicity in calculating the rate of return over cost and there are innumerable other types of contrast between the successive income streams which may be at the same time under consideration by the investor.

§8. The Case of Perpetual Returns

Next in simplicity is the type in which $100 of immediate cost is incurred for the sake of a perpetual annuity of $5 a year. Let us suppose the individual possesses some swamp land in a primitive condition. He has a large range of choice as to the method of utilizing this land. He wants to make the most of his opportunities. One option is to allow the land to remain a swamp. Others occur if, by clearing and draining it, it is converted into crop-yielding land, the yield varying with the thoroughness with which the clearing and draining are accomplished. Let us suppose that, under the first option, he derives a perpetual net income of $50 a year, and let us suppose that, at an immediate cost of $100 in his labor or in payment for the labor of others for clearing and draining, he can secure an addition of $25 a year. That is, as between retaining these two options, the swamp undrained and draining it partially, the latter involves a $100 decrease of immediate income and thereafter an income of $75 a year, or an increase of $25 a year. In other words, at the cost of $100 he will obtain a return of 25 per cent per annum in perpetuity.

Evidently, if the rate of interest in the market is 5 per cent, or anything less than 25 per cent, it will pay him to make such an investment, borrowing at 5 per cent if he wishes the $100 required for the improvement. Next suppose that another $100 invested in improving the swamp would yield crop returns of $90, or $15 more than before. The investment of this second $100 yields 15 per cent, and is therefore also a lucrative one, when the rate of interest is only 5 per cent. A third $100 may increase the annual crop still further, say by $10, netting a return of 10 per cent over the cost. A fourth $100 invested will cause the annual crop to be increased by $5 giving a return of 5 per cent. A fifth $100 will cause the crop to increase by $3—a return of 3 per cent. Evidently it will pay the farmer to invest in draining and improving his swamp up to the fourth $100, but not to the fifth $100. Rather than invest this fifth $100 and receive thereon an annual income of $3 a year, he would prefer to invest $100 in the savings bank and receive 5 per cent a year.

In other words, the exact degree of intensity with which he will improve and cultivate his land is determined by the current rate of interest. Should the rate of interest in the market fall from the 5 per cent just assumed to 2 per cent, it would then pay him to invest the fifth $100. For, evidently, if need be, he could borrow $100 at 2 per cent and receive from his land a return of 3 per cent. As Rae has so clearly pointed out, in communities where the rate of interest is low, swamps will be more thoroughly improved, roads better made, dwellings more durably built, and all instruments developed to a higher degree of efficiency so as to yield a lower marginal return over cost than in a community where the rate of interest is high.

§9. The General Case

In general, the rate of return over cost has to be derived by more complicated methods. As already indicated, the rate of return over cost is always that rate which, employed in computing the present worth of all the costs and the present worth of all the returns, will make these two equal. Or, as a mathematician would prefer to put it, the rate which, employed in computing the present worth of the whole series of differences between the two income streams (some differences being positive and others negative) will make the total zero.

If the rate, so computed, were taken for every possible pair of income streams compared as to their advantages and disadvantages, it would authentically decide in each case which of the pair is to be preferred. That one which compared with the other shows a rate of return on sacrifice greater than the rate of interest would be preferred and the other rejected. By such preferences and rejections the individual would be led to a final margin of choice of the best option. This contrasted with its nearest rival would show a marginal rate of return over cost equal to the market rate of interest.

The problems of choosing when to cut a forest, of what length to make a production period, how far to push any industrial policy, to what degree of intensiveness to cultivate land, are all the same problem of choosing the best out of innumerable possible income streams, i.e., problems of making the best out of one's investment opportunities.

In each problem the rival income streams present differences as to size and shape. They can best be compared by means of diagrams. Charts 17 to 20 show typical ways in which the income streams may conceivably be subjected to slight variation. The unbroken line in each case indicates the income stream chosen, and the dotted line the next best opportunity, rejected on behalf of the unbroken line. Chart 17 may be taken as applying to the planting of a crop; Chart 18 to the draining of a swamp; Chart 19 to the cutting of a forest; and Chart 20 to the case of alternating costs and returns.

§10. Range of Choice Depends on Interest Rate

Up to this point one complication in the problem of interest has been kept in the background. Although this complication does not invalidate any of the principles which have been developed, it seemed advisable not to distract attention from the essential features of the theory by introducing it prematurely. The complication referred to is, after all, more intricate than important. It consists in the fact that not only, as we have seen, does the choice between different optional income streams depend upon the rate of interest, but also that even the range of choice depends upon that rate. If the rate of interest is changed, a change is produced not only in the present values of the income items but in the income items themselves.

The net income from any instrument or group of instruments of wealth is the difference between the total gross income and the outgo. But many of the elements, both of income and outgo, are materially dependent upon the rate of interest. This is especially true of those items of income and outgo which are not final but merely intermediate or interactions.67 In the case of interactions, a change in the rate of interest affects the income stream directly, because, as has been shown elsewhere,68 the valuation of an interaction (i.e., intermediate service) involves the discount process and is therefore dependent upon the rate of interest. Thus, the iron yielded by an iron mine has its value determined in part by the discounted value of the machinery to be made of it and therefore its value will be affected by a change in the rate by which this discount is reckoned.

For present purposes, it is only necessary to emphasize the bare fact that the range of choice between different income streams is somewhat dependent upon the rate of interest. If the modification due to this fact were introduced into the tables previously given for the three different uses of land, we should find that the income streams from using the land for farming, forestry, and mining would differ according to the rate of interest.

Thus, let us suppose, as before in Chapter VI, §2, that for a rate of interest of 5 per cent the three optional income streams are:

In our previous discussion, when we changed the rate of interest from the 5 per cent of the foregoing table to 4 per cent, we supposed the items in the foregoing table to remain unchanged. The only change we had then to deal with was the change in their present values. Now, however, we admit the possibility of a change in the table items themselves. If the rate of interest falls to 4 per cent, the product of forest, farm, and mine will be more nearly equal to the value of the ultimate services to which they lead. The value of lumber will be more nearly equal to the value of the houses it makes, and these to the value of the shelter they give; the value of wheat from a farm will be nearer the value of the bread it will make; and the value of ore from a mine will be nearer the value of the steel it will become, and this, in turn, more nearly equal to the values of those innumerable satisfactions which come about through the use of steel. These shiftings forward of the values of the intermediate income of forest, farm and mine toward the values of the ultimate satisfactions to which they lead, combined with possible readjustments in the values of these satisfactions themselves—the values of house shelter, bread consumption, etc.—will result in a change, say, in the items in the foregoing table, where we were assuming a 5 per cent rate of interest, to the following table wherein the rate is 4 per cent.

If, then, the rate is 5 per cent, the land owner will make the most of his opportunities by choosing that use among the three which, computing from the figures in the first table, has the greatest present value; while if the rate is 4 per cent, he will choose that which, computing from the figures in the second table, has the greatest present value. If, then, the rate is 5 per cent, he will choose mining, since, as we saw in Chapter VI, §4, the present values, when we compute at 5 per cent, are: forestry, $8820; farming, $9000; mining, $9110; but if the rate is 4 per cent, he will choose the highest from the present values at 4 per cent, computed from the second table. These present values now are: forestry, $13,520; farming, $12,500; mining, $10,100.

Whatever the final outcome of all the readjustments, it is evident that the introduction of the influence of the rate of interest on the range of choice does not in any material way affect the reasoning already given in regard to the determination of the rate of interest. Since the rate of interest will itself fix the range of choice, it will still be true that, once the range of choice is fixed for a given rate of interest, the individual will choose, as before, that use which has the maximum present value. On the basis of this choice he is then led to borrow or lend in order to modify his income stream so that his degree of impatience may harmonize with the rate of interest. If, upon an assumed rate of interest, the borrowing and lending for different individuals actually cancel one another—in other words, clear the market—then the rate of interest assumed is clearly the one which solves the problem of interest; otherwise the borrowing and lending will not be in equilibrium, and some other rate of interest must be selected. By successively postulating different rates of interest, and remembering that each rate carries with it its own range of options and its own set of present values of those options, we finally obtain that rate which will clear the market.

The rate which will clear the market, while drawing into equality with itself all marginal impatience rates and all marginal rates of return on cost, is the one which solves the problem of interest under the assumed conditions.

§11. The Investment Opportunity Principles Summarized

The chief results of the chain of reasoning which has been followed in this chapter are that the same principle of investment opportunity may now be stated in four ways as:

The Principle of Maximum Present Value.

The Principle of Comparative Advantage.

The Principle of Return over Cost.

The Same Principle when the Options Differ by Continuous Gradations.

Out of all options, that one is selected the differences of which from its nearest rival gives a rate of return over cost equal to the market rate of interest. Such a rate is called the marginal rate of return on cost.

In whichever of these aspects it is regarded, this is the principle of investment opportunity. However he reckons it, every one measures his opportunities to invest—to modify his income stream—in reference to the rate of interest by applying this principle.

We can scarcely exaggerate the importance of the concept of "rate of return over cost" and of its special variety "marginal rate of return over cost" as an element in our analysis of the conditions determining the rate of interest. It supplies, on the physical or technical or productivity side of the analysis, what the marginal rate of time preference supplies on the psychical side. The subject is, as has been seen, one which may be looked upon from many points of view, which may seem at first to be inconsistent yet which may be thoroughly coordinated under the foregoing generalizations.

§12. Interrelation of Human Impatience and Investment Opportunity

The rate of interest, then, is the resultant of three sets of principles of which the market principles are self-evident. The other two great sets of principles are the one comprising two principles of human impatience and the other comprising two principles of investment opportunity. The principles of impatience relate to subjective facts; those of investment opportunity, to objective facts. Our inner impatience urges us to hasten the coming of future income—to shift it toward the present. If incomes could be shifted at will, without shrinking in the process, they would be shifted much more than they are. But technical limitations prevent free shifting by penalizing haste and rewarding waiting. Thus Henry Ford might have continued making his Model T car. He would have thereby enjoyed a large immediate income but a gradually decreasing one. Instead, he resolved to place a better type of car on the market. To do so, he had to suspend the productive operations of his plant for a year, to scrap much of his old machinery and to provide a new installation at the cost of millions. The larger returns which he expected from the sale of the new car were only obtainable by the sacrifice of immediate income—by waiting.

Our outer opportunities urge us to postpone present income—to shift it toward the future, because it will expand in the process. Impatience is impatience to spend, while opportunity is opportunity to invest. The more we invest and postpone our gratification, the lower the investment opportunity rate becomes, but the greater the impatience rate; the more we spend and hasten our gratification, the lower the impatience rate becomes but the higher the opportunity rate.

If the pendulum swings too far toward the investment extreme and away from the spending extreme, it is brought back by the strengthening of impatience and the weakening of investment opportunity. Impatience is strengthened by growing wants, and opportunity is weakened because of the diminishing returns. If the pendulum swings too far toward the spending extreme and away from the investment extreme it is brought back by the weakening of impatience and the strengthening of opportunity for reasons opposite to those stated above.

Between these two extremes lies the equilibrium point which clears the market, and clears it at a rate of interest registering (in a perfect market) all impatience rates and all opportunity rates.

It is all a question of the time and amount of the series of items constituting real income. Shall we get income enjoyment now or later and how much? Shall we spend or invest?

PART II, CHAPTER VIII

DISCUSSION OF THE SECOND APPROXIMATION

§1. Opportunity Reduced to Lowest Terms

SINCE the second approximation contains the heart of the theory of interest, a further brief summary and discussion of the steps already taken will be helpful before proceeding to the third approximation.

Any opportunity to invest simply reduces itself to this: for a time there is more labor or less satisfaction than there would be in the absence of such opportunity, while there is expected later less labor or more satisfaction. The earlier item of labor or abstinence is less than the expected satisfaction or labor saving. This picture of temporary labor exerted, or abstinence from satisfactions which would otherwise be enjoyed, for the sake of later satisfaction or labor saving is the ultimate picture of cost and return.

When thus reduced to these lowest terms of labor and satisfaction, not only is our picture simplified, but with the simplification, we have rid it of a certain suspicion of begging the question of the interest problem. That is, as long as interactions, capital, and money were in the investment opportunity picture, interest was already implied in each of their valuations and there might remain a haunting fear that this new rate of return over cost as an interest-determining factor was simply involving us in a circle. The question might be asked: Is the rate of return a new influence? Is there really any important distinction between the rate realized on a bond, which is interest pure and simple, and the rate realized on any other investment? Are they not all simply interest, and is there anything else behind this interest besides human impatience? Is not the sum invested simply the discounted value of the return expected with due regard to the risk element, which has not yet been considered?

The answer, as should now be clear, is that the rate of return over cost really is a new element, not included in the first approximation, however mixed that element may be, in practice, with the elements considered earlier. When labor and satisfactions are concerned there is something more than exchange. The labor of planting a fruit tree is not the same thing as the discounted value of the fruit yielded by the tree, even though the value of the labor and the value of the fruit may be equal at a given time. The satisfaction from eating fruit is pleasure and the labor of planting it is pain, and these can be directly compared, despite the fact that in practice they are usually compared only indirectly in terms of their exchange equivalents.

Instinctively we feel the presence of this factor of rate of return over cost whenever we invest in a new enterprise. To invest in the original telephone enterprise, or in a railway under construction, seems somehow different from today buying telephone or railway securities. In the latter transactions we feel we are dealing with men—trading; in the former we feel we are dealing with Nature or our technical environment—exploiting. In fact, I came near selecting the term exploitation for a suitable catch word rather than investment opportunity to express the objective factor of a return over cost. Of course, even after the period of early exploitation is passed there are plenty of opportunities within the industry for variation in the rates of return over cost, but they are no longer so conspicuous.

Even when there is no exchange possible, as with Robinson Crusoe alone on his island, there will be dealings with Nature. Crusoe may plant trees or build a boat and balance his immediate labor against his future satisfactions without the presence of any exchange process. It would have been possible, of course, to have begun the presentation with Robinson Crusoe instead of ending with him. In that case, we should have first considered the primitive facts of labor exerted for the sake of future satisfaction, or their equivalent in berries. We could then bring in Man Friday, and proceed step by step to the complications of modern civilization. We should have seen how the primitive cost and return typified by labor and satisfaction became gradually hidden in a mass of exchanges until today we think of both in terms of money. The capitalist of today, instead of laboring for a future satisfaction, may simply abstain temporarily from a part of the satisfactions he could otherwise enjoy and, with the money which he would have spent for them, buy the labor to build a railway. The laborer is no longer the one who has to wait for the satisfactions to follow the completion of the railway. He is paid in advance and converts his pay into real wages very speedily, while the capitalist waits and receives the rewards for waiting.

In all these and the other manifold exchange relations the terms are partly set by the principles of discount in relation to impatience. But the primitive ingredients of labor and satisfaction, or their cost of living equivalents, with a time interval between, are never shuffled out of existence, however much they may be shuffled out of sight. They are ever present and exert their influence just as truly as they did with Robinson Crusoe.

In making the first of these two adjustments, the individual is not trading with other human beings, but is, as it were, trading with his environment—Nature and the Arts. That is why industry today maintains laboratories of research. These aim to improve products and service by scientific means, to develop new fields of application in by-products and materials, and to evolve new products and methods and so new investment opportunities. Trading with the environment is making the most of investment opportunity—of the future income returned per unit of present income sacrificed. Trading with mankind is making the most of impatience—of the preference for a unit of present income over a unit of future income.

When the individual sets out to trade with the environment he finds that the rate of return over cost varies with the extent to which he pushes this trading; he adjusts the trading so as to harmonize the marginal rate of return with the rate of interest. In his trading with other human beings, on the contrary, he finds the terms of the contract interest fixed, so far as any effort by him is concerned, but impatience varies with the extent to which he pushes this trading.

§2. Investment Opportunity Essential

Some economists, however, still seem to cling to the idea that there can be no objective determinant of the rate of interest. If subjective impatience, or time preference, is a true principle, they conclude that because of that fact all productivity principles must be false. But they overlook two important points. One is that, obviously and as a matter of practical fact, the technique of production does affect the rate of interest, and therefore cannot be ignored; the other, that their proposed solutions are indeterminate—i.e., they have more unknown quantities than determining conditions.

If, then, I am asked to which school I belong—subjective or objective, time preference or productivity—I answer "To both." So far as I have anything new to offer, in substance or manner of presentation, it is chiefly on the objective side.69

In my opinion minute differences of opinion as to the relative importance of human impatience and investment opportunity are of too little consequence to justify violent quarrels as to which of the two is the more fundamental, although I shall here and later, as occasion offers, note certain differences between them. The important point is that the two rates, that of marginal time preference and that of marginal return over cost, must be equal, granted continuity of variation, that is, variation by infinitesimal gradations. If, as Harry G. Brown,70 in a very interesting Robinson Crusoe phantasy, assumes as a theoretical possibility, the rate of return over cost is fixed immutably at 10 per cent, the rates of impatience must conform thereto and the rate of interest can only be 10 per cent. Later in this chapter an even simpler and more easily imagined case, while at the same time more startling in its conclusions, is presented in which the technical limitations impose a fixed rate of interest and of human impatience of zero per cent. There, investment opportunity dominates.

On the other hand, we could also imagine the converse case; we could assume, as a theoretical possibility, a society of persons having an obstinate constancy in their rates of impatience, all being 10 per cent. In such a case, the marginal rate of return over cost would be adjusted thereto.

A person's rate of impatience depends on the extent to which he modifies his income stream by loans or sales. It is evident that if loans can be used to any extent desired, impatience will vary continuously with them.

The rate of return over cost, on the other hand, depends on the extent to which a person modifies his income stream by altering the way in which he utilizes his capital resources. Such alteration, while partly continuous, is partly discontinuous, as when new machinery, buildings, personnel or systems are introduced.

It was to emphasize this distinction between impatience and opportunity that I chose to begin with the case of a supposedly rigid income stream, as in the first approximation, with no opportunity to substitute any other; then to proceed to the case of three optional uses of land (distinguished for convenience as farming, mining, forestry) affording opportunity to substitute for one of them either of the others and thus disclosing in such substitution two alternative rates of return over cost; and finally to reach the supposed case of an infinite variety of income streams differing from one another by infinitesimal gradations. Only in the last named case is the rate of return over cost as variable as the rate of impatience.

It should be noted that in the first approximation, where the income stream is fixed or rigid and there is no alternative income stream, there can be no comparative cost or return and therefore no rate of return over cost. But we cannot so easily imagine a similar disappearance of impatience. It would be quite impossible to have any exchange between present and future—any rate of interest—without the existence of time preference, as it would be quite impossible to have any exchange whatever without human wants. They are an omnipresent and necessary condition of all exchange and valuation.

§3. Options Differing in Time Shape Only

Options differ in three chief ways corresponding to the characteristics, already noted, of the income stream, namely, (1) in composition, (2) in risk, and (3) in size and time shape. Options which differ primarily in composition or the kind of services rendered are illustrated by the options of using a building as a dwelling, as a shop, or as a factory. Options which differ primarily in the probability or risk are exemplified by the use of a ship on a hazardous voyage or in safe river transportation. Options which differ in size and time shape of the income stream are illustrated by the innumerable uses of land and artificial capital to produce different kinds of goods (income) of different degrees of immediateness as to the satisfactions they render.

The third group of options (which differ in the size and time shape of the income stream) is the one which especially concerns us here. First, let us suppose only one degree of flexibility, permitting variation in the time when the income items arrive but no variation in their amounts. Let us suppose, then, that the income stream from any capital is fixed in aggregate amount, but that the times of receiving that income are controllable at will. This species of choice occurs approximately in the case of durable goods for consumption, which neither improve nor deteriorate with time. A stock of grain, for instance, may be used at almost any time, with little difference in the efficiency of the use and little cost except for storage. The same is true of coal, cloth, iron, and other durable raw materials, as well as, to some extent, of finished products such as tools and machinery, though usually deterioration from rust, or other injury by the elements, will set in if the use is too long deferred. Another simple example is a definite sum of money in a strong box which may be spent at any time, or times, desired. Thus a strong box containing $100,000 may be so used as to yield a real income of $100,000 for one year, or $10,000 a year for ten years, or $4,000 a year for twenty-five years.

Such options afforded by durable goods (as when to use them) are perhaps the simplest of all options. Since extreme cases are especially instructive, let us imagine a community in which the income from all capital is of the character just described. That is, we suppose the total quantity of income obtainable is absolutely fixed, but the times at which it can be obtained are absolutely optional. This community would then be endowed with a definite quantum of income as fixed as the quantity of money in a strong box. That is, every dollar of income sacrificed from one year's income would eke out any other income by that same amount, a dollar, no more and no less; conversely, every dollar of income enjoyed in one year would reduce indulgence elsewhere by exactly a dollar. The rate of interest would be reduced to zero.

§4. The Imaginary "Hard-Tack" Illustration

To fix our ideas, let us suppose these conditions to be realized on a desert island on which some sailors are shipwrecked and each left with a specified number of pounds of hard-tack and with no prospect of ever improving his lot. We shall suppose the use of this hard-tack to be the only real income open to these castaways, and that they have given up all hope of ever adding to it by accessions from outside or by cultivating the island which, for our hypothesis, must be barren. No change in their human nature need be assumed. We assume that they would react to the same income just as before the shipwreck. Merely their circumstances have changed. In consequence, the only possible variation of their income streams—consisting solely of the use of hard-tack—is that made possible by varying the time of its consumption. Suppose one of them has an initial stock of 100,000 pounds. He has the option of consuming his entire store during the first year, or of spreading its use over two or more years, but in any case he will eventually aggregate the same total income, measured in hard-tack, spread over the future, namely 100,000 pounds.

A little reflection will show that, in such a community, the rate of interest in terms of hard-tack would necessarily be zero! For, by hypothesis, the giving up of one pound of hard-tack out of present consumption can only result in an equal increase in future consumption. One pound next year can be obtained at the cost of exactly one pound this year. In other words, the rate of return over cost is zero. Since, as we have seen, this rate must equal the rates of preference, or impatience, and also the rate of interest, all these rates must be zero also.

This case is illustrated in Chart 21. One option is to consume the hard-tack at an even rate OA through the time OB. The total income will then be represented by the area OACB. Another option is to spread it over OB', double the above-mentioned time, and consume it at the rate of OA', half the rate first mentioned, so that the same total income will be represented by the area OA'C'B'. The choice of the second use rather than the first is at the cost of that part of the earlier income represented by the rectangle AD, and gives a return exactly equal in amount represented by the rectangle DB'. If the hard-tack is not consumed at a uniform rate, the alternative income streams will not be represented by rectangles, but by the irregular and equal areas OADB and OA'DB', shown in Chart 22. The substitution of the alternative OA'DB' for OADB increases immediate income by ADA' and decreases subsequent income by the exactly equal amount BDB'.

The conclusion, that the rate of interest, under such extreme conditions supposed in the hard-tack case, must be zero, is at first startling, but it is easy to convince ourselves of its correctness. It would be impossible for any would-be lender to obtain interest above zero on his loan for the only way in which a borrower could repay a loan would be to pay it out of his original stock of hard-tack. For assuming he had the impulse to borrow 100 pounds to consume today and pay back 105 pounds at the end of a year, he would instantly perceive that he could better consume the 100 pounds of his own hard-tack, thereby sacrificing next year not 105, but only 100 pounds out of his own stock. It is equally impossible that there should be a negative rate of interest. No one would lend 100 pounds of hard-tack today for 95 receivable a year later, when he had the option of simply storing away his 100 pounds today and taking it out, undiminished, a year later. Hence, exchanges of present for future hard-tack could not exist, except at par. There could be no premium or discount in such exchange.

Nor (to turn to the subjective side) could there be any rate of preference for present over future hard-tack. The sailors would so adjust the time shape of their respective income streams that any possible rate of preference for a present over a future allowance of hard-tack would disappear, and a pound of this year's hard-tack and a pound of next year's hard-tack would be equally balanced in present estimation. For, should a man prefer one rather than the other, he would transfer some of it from the unpreferred time to the preferred time, and this process would be continued, pound by pound, until his want for a pound of immediate hard-tack and his want for a pound of future hard-tack were brought into equilibrium. Thus, if through insufficient self-control, he prefers, however foolishly, to use up much of his store in the present and so to cut down his reserve for the future to a minimum, the very scantiness of the provision for the future will enhance his appreciation of its claims, and the very abundance of his provision for the present will diminish the urgency of his desire to indulge so freely in the present.

Provided each individual is free to apportion his share of the total stock of hard-tack between present use and future use as he pleases, and provided there is some hard-tack available for both uses, the present desire for a pound of each will necessarily be the same.

(Failure of such equilibrium of want could only occur when, as in starvation, the want for the present use was so intense as to outweigh the want for even the very last pound for future use, in which case there would be none whatever reserved for the future.)

All persons, however different in nature, would alike have a zero rate of impatience. They would differ simply in the way they distributed their income over present and future. The spendthrift and the miser would still spend and save respectively but both would value a unit of hard-tack today as the exact equivalent of one due a year hence. It is evident that some of the sailors, with a naturally keen appreciation of the future, would plan to consume their stores sparingly. Others would prefer generous rations, even with the full knowledge that starvation would thereby be brought nearer, but none of them would consume all of his stock immediately. They would, generally speaking, prefer to save out of such reckless waste at least something to satisfy the more urgent needs of the future.

In other words, a certain amount of saving (if such an operation can be called saving) would take place, without any interest at all. This conclusion coincides with conclusions expressed by Professor Carver in his Distribution of Wealth.71 It shows also that the preference for present over future goods of like kind and number is not, as some writers assume, a necessary attribute of human nature, but that it depends always on the relative provisioning of the present and future.

The foregoing imaginary hard-tack case is of great help, therefore, in emphasizing the essential rôle of the rate of return over cost. This simple example, of itself, demonstrates that no theory of interest is complete which ignores the rate of return over cost. In the example we have both elements, investment opportunity and impatience, although both are at the vanishing point, that is, the rate of return and the rate of impatience are both zero, the former, rate of return, being fixed at zero by the technical conditions of the particular environment on the desert island, and the impatience rate being forced thereby to be zero also. In this case opportunity (or the lack of it) rules impatience.

It would be possible, of course, to make this illustration somewhat more realistic by adding to our supposed supplies of hard-tack supplies of other foods, as well as of clothing and sundry other real income. But the value of the illustration is not in any realism which can be made out of it. Rather does the fact that conditions in real life do not permit such freedom of shifting real income in time (because of change in quantity or quality) reveal some of the reasons why the rate of interest is not zero.

§5. The Imaginary "Figs" Example

Not only may the rate of interest conceivably be zero; it may conceivably be negative. Suppose our sailors were left not with a stock of hard-tack, but with a stock of figs which, like the hard-tack, can be used at any time as desired, but which, unlike the hard-tack, will deteriorate. The deterioration will be, let us say, at a fixed and foreknown rate of 50 per cent per annum. In this case (assuming that there is no other option available, such as preserving the figs) the rate of interest in terms of figs would be necessarily minus 50 per cent per annum, as may be shown by the same reasoning that established the zero rate in the hard-tack case.

More generally, this would be true if there were a world in which the only provisioning of the future consisted in carrying over initial stocks of perishable food, clothing, and so forth and if every unit so carried over into the future were predestined to melt way each year by 50 per cent.

One reason why we do not encounter such cases, with negative rates of return over cost, negative rates of interest, and negative rates of time preference is that we have other income available for the future besides what can be carried over from present stocks. Future figs will come into being from fig trees and even existing stocks of figs and other perishables may be carried over for future use by canning, cold storage, preservation and similar processes. Yet we do, even in our real world, occasionally have cases such as of spoiling strawberries, where, the rate of interest reckoned in terms of the strawberries is occasionally negative.

We see, then, that there is no absolutely necessary reason inherent in the nature of man or things why the rate of interest in terms of any commodity standard should be positive rather than negative. The fact that we seldom see an example of zero or negative interest is because of the accident that we happen to live in an environment so entirely different from that of the ship-wrecked sailors.

§6. The Imaginary "Sheep" Example

The next example is more like that in our real world. In the real world our options are such that if present income is sacrificed for the sake of future income, the amount of future income secured thereby is greater than the present income sacrificed. That is, the income which we can extract from our environment is not, in the aggregate, a fixed quantum like a storehouse of hard-tack; still less is it like a storehouse of dwindling contents. On the contrary, Nature is, to a great extent, reproductive. Growing crops and animals often make it possible to endow the future more richly than the present. Man can obtain from the forest or the farm more by waiting than by premature cutting of trees or by exhausting the soil. In other words, Nature's productivity has a strong tendency to keep up the rate of interest. Nature offers man many opportunities for future abundance at trifling present cost. So also human technique and invention tend to produce big returns over cost.

It is difficult to imagine a precise and simple case in which the rate of return over cost is fixed as in the case of the hard-tack or the figs but, instead of being zero or negative, is positive, say 10 per cent, neither more nor less. The best example is the ingenious one worked out by Professor Harry G. Brown in which fruit trees are planted at the cost of 100 units of fruit and automatically produce 110 units of fruit a year later and then die.72 A simpler imaginary example, if we can forget certain obvious practical limitations, is that of the proverbial flock of sheep, which multiply in geometric progression affording alternately 100 units of mutton and wool today or 110 next year and ten per cent more each succeeding year. These examples symbolize a state of things in which it is always possible at the cost of 100 units out of this year's income to secure a return of 110 units next year, making a return over cost of 10 per cent. In such examples, just as in the hard-tack case with its zero per cent, or the fig case with its minus 50 per cent, the investment opportunity principles prescribe or dictate the rate of interest and the rate of time preference. These rates will in the present instance of the sheep all be 10 per cent.

We see then that, given the appropriate environment, the investment opportunity principle may dominate interest and force it to be zero, or minus 50 per cent, or plus 10 per cent, or any other figure. Under such conditions, the rate of impatience and the rate of interest will follow suit.

In actual life, however, any shoving of real income forward or backward in time can never be done without causing a variation in the rate of return over cost. The result is that the rate of impatience influences the rate of return quite as truly as the rate of return influences impatience.

§7. Opportunities as to Repairs, Renewals, Betterments

In the foregoing examples the options consisted of different employments of a particular instrument or set of instruments of capital which were assumed to retain their physical identities throughout the period of those employments. But now let us regard an instrument, or group of instruments, of capital as retaining only a sort of fictitious identity, through renewals or repairs, just as the proverbial jack-knife is said to be the same knife after its blade and then its handle have been replaced. This brings us to another large and important class of options; namely, the options of effecting, or not effecting, renewals and repairs, and the options of effecting them in any one of many different degrees. If the repairs are just sufficient for the up-keep they may be called renewals; if more than sufficient, or if involving improvement in quality, they may be called betterments. But it will be convenient to include in thought all alterations as to the form, position, or condition of an instrument or group of instruments affecting its stream of services. This will cover the whole subject of the production of reproducible goods.

This class of optional employments, when the employment involves sales from a stock, merges imperceptibly into the special case which we originally called the method of modifying an income stream by buying or selling. Thus, consider a merchant who buys and sells rugs. His stock of rugs is conveniently regarded as retaining its identity, although the particular rugs in it are continually changing. This stock yields its owner a net income equal to the difference between the gross income, consisting of the proceeds of sales, and the outgo, consisting chiefly of the cost of purchases, but including also cost of ware-housing, insurance, wages of salesmen, and so on.

If the merchant buys and sells equal amounts of rugs and at a uniform rate, his stock of rugs will remain constant and its net income to be credited to that stock will theoretically, that is, under our present assumption of a riskless world, be equal to the interest upon its value. It will be standard income.73 This income to be credited to his stock in trade is, of course, to be distinguished from that to be credited to his own efforts—his wages of super-intending (neither need be called profits in a riskless world).

But the owner has many other options than that of thus maintaining a constant stock of goods. He may choose to enlarge his business as fast as he makes money from it, in which case his net realized income will be zero for a time, because all return is "plowed back" into the business. His stock will increase and eventually his income will be larger. In this option, therefore, his income stream is not contant, but ascends from zero to some figure above the standard income which constituted the first option.

A third option is gradually to go out of business by buying less rugs than are sold, or none at all. In this case the realized income at first is very large, as it is relieved of the burden of purchases; but it declines gradually to zero.

Intermediate among these three options there are, of course, endless other options. The merchant thus has a very flexible income stream.

If the expenses and receipts for each rug bought and sold are the same, whichever option is chosen, and if the time of turnover is also the same, it will follow that all of the options possess the same present value and differ only in desirability. We should then be dealing with what we have called modifications of the income stream through buying and selling. The reason for placing optional employments of capital on a different footing from buying and selling is that the optional employments do not all possess the same present value. In actual fact, the rug merchant, and merchants in general, would not find that all the optional methods of proportioning sales and purchases of merchandise possessed equal present values. For one thing, if the rug merchant attempted to enlarge his business too fast he would find that his time of turnover would be lengthened, and if he reduced it too fast he would find that his selling expenses per unit of merchandise would be increased. There is, for each merchant, at any time, one particular line of business policy which is the best, namely, that which will yield him the income stream having the maximum present value. Since, therefore, the various methods of renewing one's capital usually yield income streams differing in present value, they may be properly classed as optional employments of such capital.

The propriety of such a classification becomes still more evident when, instead of mere renewals, we consider repairs and betterments, for it is clear that the income from a farm has a very different present value according as it is tilled or untilled, or tilled in different degrees of intensity, that the income from a house so neglected that a leak in the roof or a broken window pane results in injuring the interior is less valuable than the income it would yield if properly kept up, and that real estate may be underimproved or overimproved as compared with that degree of improvement which secures the best results.

In all cases the "best" results are secured when that particular series of renewals, repairs, or betterments is chosen which renders the present value of the prospective income stream the maximum. This, as we have seen, is tantamount to saying that the renewals, repairs, or betterments are carried up to the point at which the marginal rate of return over cost which they bring is equal to the rate of interest. The owner of an automobile, for instance, will replace a broken part and so prolong the life of his automobile. The first repair may cost him $10 and may save him $200. But such a twenty-fold return cannot be expected from every repair, and beyond a few such really necessary repairs, it soon becomes a question to what extent it is worth while to keep an automobile in repair. Repainting the body and regrinding the valves are both costly, and though, in such instances, the service of the automobile is increased in quantity and improved in quality, the return grows less and less as the owner strives after increased efficiency. Under our present hypothesis in which risk is disregarded, he will spend money on his automobile for repairs and renewals up to that point where the last increment of repairs will secure a return which will just cover the cost with interest. Beyond this he will not go.

In practice, of course, the choice between the various possible repairs, renewals, or betterments will involve some corresponding choice between possible employment of labor, land, and every agent of production. But I have tried here to isolate for study the services and disservices of a physical instrument subject to repairs, renewals, or betterments.

Another case of optional income streams is found in the choice between different methods of production, especially between different degrees of so-called capitalistic production. It is always open to the prospective house builder to build of stone, wood, or brick, to the prospective rail-road builder to use steel or iron rails, to the maker of roads to use macadam, asphalt, wood, cobble, brick, or cement, or to leave the earth unchanged except for a little rolling and hardening. The choice in all cases will depend theoretically on the principles which have been already explained.

To take another example, the mere services of a house which has a durability of 100 years will be equivalent to the services of two houses, each of which has a durability of 50 years, one built today and lasting 50 years, and the other built at the expiration of that period and lasting 50 years more; yet the one house may well be better than the two. The difference between the one and the two will not be in the services but in the cost of construction. The cost of constructing the 100-year house occurs in the present; that of the two successive 50-year houses occurs half in the present and half at the end of 50 years. In order that the more durable house may have any advantage as to cost, the excess of its cost over the cost of the less durable one must be less than the present value of the cost of replacing it 50 years later.

The choice between different instruments for effecting the same purpose may, of course, depend on their relative efficiency, that is, the rate of flow of income, or upon their relative durability, that is, the time of the flow. It is true, however, as John Rae has pointed out,74 that efficiency and durability usually go hand in hand. A house which will endure longer than another is usually more comfortable also; a tool which will cut better will usually wear out more slowly; a machine which does the fastest work will generally be the strongest and most durable.

The alternatives constantly presented to most business men are between policies which may be distinguished as temporary and permanent. The temporary policy involves the use of easily constructed instruments which soon wear out, and the permanent policy involves the construction at great cost of instruments of great durability. When one method of production requires a greater cost at first and yields a greater return afterward, it may be called, conformably to popular usage, the more capitalistic of the two. The word capitalistic refers to methods of employing capital which tend toward an ascending income stream. Although the term is not a happy one, it has a plausible justification in the fact that an ascending income stream means the accumulation of capital, or saving, and still more in the fact that only a capitalist can afford to choose a method of production which at first yields little or no income, or even costs some outgo. Capital involves command over income without which no one could subsist, or at any rate subsist with comfort. The capitalist, by using his capital, even to the extent of using up some of his accumulations, can supply himself with the immediate income necessary while he is waiting for returns on his new ventures. It is as a possessor of income that he is enabled to subsist while waiting. He is enabled to invest in an ascending, or slowly returning, income stream only by first having at command a quickly returning income stream. We may say, therefore, that a capitalistic method is a method resulting in an ascending income stream, and it is so called because it is open chiefly to those who have command of other—often descending—income streams, such persons being necessarily capitalists, that is, possessors of much rather than little capital.

§8. Opportunity to Change the Application of Labor

The best example of the choice between those uses of capital instruments affording immediate and those affording remote returns is found in the case of human capital, commonly called labor. Man is the most versatile of all forms of capital, and among the wide range of choices as to the disposition of his energies is the choice between using them for immediate or for remote returns. This choice usually carries with it a choice between corresponding uses of other instruments than man, such as land or machines. But the existence of optional employments of labor, however inextricably bound up with optional employments of other instruments, deserves separate mention here both because of its importance and because it usually supplies the basis for the optional employments of other forms of capital.

It is almost exclusively through varying the employment of labor that the income stream of society, as a whole, is capable of changing its time shape. The individual may modify the time shape of his particular income stream through exchange, but in this case some other person must modify his income stream in the opposite manner, and the two sorts of modifications, some plus and others minus, offset each other in the total of the world's income. On the other hand, if an income is modified in time shape merely through a change in the exertions of laborers, there is no such offset, and the total social income is actually modified thereby.

The labor of a community is exerted in numerous ways, some of which bring about enjoyable income quickly, others slowly. The labor of domestic servants is of the former variety. The cook's and waitress' efforts result in the enjoyment of food within a day. Within almost as short a time, the chambermaid and the laundress promote the enjoyment of house, furniture, and clothing. The baker, the grocer, the tailor are but one step behind the cook and laundress; their efforts mature in enjoyments within a few days or weeks. And so we may pass back to labor increasingly more remote from enjoyable income, until we reach the miner whose work comes to fruition years later, or the laborer on the Panama Canal or the vehicular tunnels, whose work was in the service of coming generations.

The proportions in which these various kinds of labor may be assorted vary greatly, and it is largely through varying this assortment that the income stream of the community changes its time shape. If there are at any time relatively few persons employed as cooks, bakers, and tailors, and relatively many employed as builders, miners, canal and tunnel diggers, there will tend to be less immediately enjoyable income and correspondingly more enjoyable income in later years. Thus, by withdrawing labor from one employment and transferring it to another, it is in the power of society to determine the character of its income stream in time shape, and also in size, composition, and uncertainty. This power is exerted through the "enterpriser," to use Professor Fetter's term, according to the enterpriser's estimate of what return will come from each particular employment taken in connection with the cost involved and the ruling rate of interest.

§9. Fluctuations in Interest Rates Self-Corrective

Since the choice, for an individual, among different options, depends on the rate of interest in the manner described in Chapter VI, it is clear that a low rate favors the choice of the more ascending income streams, but also that the choice of such income streams reacts to raise the rate of interest. If, on the contrary, the rate is high, the opposite of both these propositions holds true; the high rate favors the choice of the less ascending income streams, but that choice reacts to lower the rate of interest.

Thus, if we apply these principles to repairs, renewals, and betterments, it is evident that the lower the rate of interest, the better can the owner of an automobile afford to keep it in repair, and the better can the owner of a railroad keep up its efficiency, and the same applies to all other instruments. But it is equally clear that the very attempt to improve the efficiency of instruments tends, in turn, to increase the rate of interest, for every repair means a reduction in present income for the sake of future—a shifting forward in time of the income stream—and this will cause a rise in the rate of interest. Thus, it follows that any fall in the rate of interest will tend to bring its own correction.

Again, it is evident that a choice of the more durable instruments, as compared with those less durable, will be favored by a low rate of interest, and a choice of short-lived instruments will be favored by a high rate of interest. If the rate of interest should fall, there would be a greater tendency to build stone houses as compared with wooden ones. The present value of the prospective services and disservices of stone houses as compared with wooden houses would be increased, for although stone houses are more expensive at the start, they endure longer, and their extra future uses, which constitute their advantage, will have a higher present value if the rate of interest is low than if it is high. We find, therefore, as John Rae has so well pointed out, that where the rate of interest is low, instruments are substantial and durable, and where the rate of interest is high they are unsubstantial and perishable.

We see, then, that the existence of numerous options has a regulative effect. Beyond the margin of choice there always lie untouched options ready to be exploited the instant the rate of interest falls. Among these, as Cassel75 has pointed out, are waterworks of various kinds. Not only works of stupendous size but hundreds of less conspicuous improvements are subjects of possible investment as soon as the rate of interest falls low enough to make the return upon cost equal to the rate of interest. The same is true of the improving, dredging, and deepening of harbors and rivers, the use of dikes and jetties, the construction of irrigation works for arid lands, and Boulder Dam projects.

There is still room for much improvement in our railway systems by making them more efficient and more durable, by making the roads straighter, the roadbeds more secure, the rolling stock heavier, the bridges larger and stronger, by further electrifications, and similar improvements. In a new country where the rate of interest is high, the cheapest and most primitive form of railway is first constructed. Very often it is a narrow-gauge road with many curves, costing little to construct, though much to operate. Later, when the rate of interest falls, or the traffic so increases that the rate of return on sacrifice is greater, the broad-gauge comes into use and the curves are eliminated. This is the kind of change which has been proceeding in this country with great rapidity during recent years. There is a transition from relatively small first cost and large running expenses to precisely the opposite type of plant, in which the cost is almost all initial and the expense of operation relatively insignificant.

§10. Wide Opportunities Stabilize Interest

The existence of a wide variety of available income streams, then, acts as a sort of governor or balance wheel which tends to check any excessive changes in the rate of interest. Interest cannot fall or rise unduly; any such fluctuation corrects itself through the choice of appropriate income streams.

We see here a reason why interest does not suffer very violent fluctuations. It is not only true that natural processes are regular enough to prevent sudden and great changes in the income stream; it is also true that man constantly aims to prevent such changes. Man is not the slave of Nature; to some extent he is her master. He has many ways to turn. He possesses, within limits, the power to flex his income stream to suit himself. For society as a whole, the flexibility is due to the adaptability and versatility of capital—especially human capital commonly called labor; for the individual, the flexibility is greater still, since he possesses a two-fold freedom. He is not only free to choose from among innumerable different employments of capital, but he is free to choose from among different ways of exchanging with other individuals. This power to exchange is the power to trade incomes; for under whatever form an exchange takes place, at bottom what is exchanged is income and income only.

PART II, CHAPTER IX

THIRD APPROXIMATION TO THE THEORY OF INTEREST
Assuming Income Uncertain

§1. More than One Rate of Interest

THE great shortcoming of the first and second approximations, from the standpoint of real life, is the complete ruling out of uncertainty. This exclusion of the risk element was made in order to make the exposition simpler and to focus the reader's attention on the factors most relevant to the theory of interest. But in real life the most conspicuous characteristic of the future is in its uncertainty. Consequently, the introduction of the element of chance, or risk, will at once endow our hypothetical picture with the aspect of reality. The foundation for our study of risk in relation to interest has already been laid in Chapter IV where the relation of risk to time preference was noted.

One consequence of changing our assumption as to the certainty of future events is to compel the abandonment of the idea of a single rate of interest. Instead of a single rate of interest, representing the rate of exchange between this year and next year, we now find a great variety of so-called interest rates. These rates vary because of risk, nature of security, services in addition to the loan itself, lack of free competition among lenders or borrowers, length of time the loan has to run, and other causes which most economists term economic friction. The very definition of loan interest as one implying no risk must now be modified so as to imply some risk that the loan may not be repaid in full according to the contract. Practically all of them are varieties of risk. Even in loans which theoretically are assumed to be riskless, there is always some risk. Modern corporate finance makes no pretence that risk is completely absent, but merely concerns itself with providing a more or less safe margin of protection varying with each specific case.

Furthermore, for our present purposes, contract or explicit interest is too narrow a concept. We now include not only the implicit interest realized by the investor who buys a bond, but the implicit interest realized by the investor who buys preferred stock. We may even include the rates realized on common stock, real estate, or anything else. Thus extended, the concept of interest becomes somewhat vague. And yet, if we exclude exceptional cases, there tend to emerge, at any time, several fairly definite market rates of interest according to the character of the security.

We find quoted rates on call loans, four months prime commercial paper, prime bankers' acceptances, first mortgages, second mortgages, as well as rates given by savings banks, rates allowed on active checking accounts, pawn shop rates, Morris Plan bank rates, rates realized on government bonds, railroad bonds, on other bonds, whether mortgage, debenture, or income bonds (all of which bond rates vary according to the character and credit of the issuer as well as in accordance with other circumstances), rates realized on preferred stock, and sometimes even the rates realized on common stocks. Wherever there is a sufficiently definite rate per cent per annum to be quoted as an expression of the current market, whether the quotation be in print or a verbal quotation in a broker's or banker's office, it seems proper to call it in a broad sense a rate of interest. Even when confined to such market rates, and excluding exceptional or individual rates, the rate of interest ceases to be the ideal, imaginary, single-valued magnitude hitherto assumed and takes on the myriad forms which we find in actual business transactions.

As indicated, this profuse variety is brought about chiefly by the introduction of risks of various sorts. The rate on call money is affected by the chance of the loan being "called" by the lender, or the sudden reduction of the total of such loans outstanding and the raising of the rate for those remaining. The rate on a loan-shark's loan is high because of the risk of non-payment by the borrower; the rate on a debenture and the rate on a second preferred stock of a moribund corporation are affected by the risk of inadequate corporate assets in event of liquidation; the rate on a government bond of a nation at war is affected by the chance of that nation's defeat; the rate of dividends on common stock is affected by the risks of the business; and so on in an infinite number of different cases.

§2. Relations Between the Various Rates

No very satisfactory theoretical treatment of the general relations between interest and risk has yet been worked out. But for practical purposes, a good usage is to limit the term "interest" to fairly safe loans and staple or standard market quotations and to designate by some other term, such as dividends or profits, the other less certain and less standardized rates. Another usage is to reckon as net profits or net losses the difference between these less standardized rates and a normal rate of interest so far as this can be expressed in figures. Thus a man who has invested $100,000 in common stock and is getting an income of $15,000 may think of $5,000 of this, or 5 per cent, as a fair interest on his investment and the remaining $10,000, or 10 per cent, as net profit. But we do not need here to enter into such discussions, especially in so far as they are only verbal. All that is here needed is to show briefly how risk modifies the theoretically perfect determination of the interest rate thus far made.

The rate in every loan contract is adjusted according to the degree of security given. Thus, security or guarantee may be furnished by a simple endorsement of reputable persons, in which case the degree of security will be the greater the larger the number of endorsers and the higher the credit which they possess, or it may be by the deposit of collateral securities. Thus the very name security has come to mean the properties themselves rather than their safety.

If we pass from explicit interest, or the rate of interest involved in a loan contract, to implicit interest, or the rate involved in purchases and sales of property in general, we see again that the greater the risk, the higher the basis on which a security will sell. A gilt-edge security may sell on a 3 per cent basis, when a less known or less salable security may sell only on a 6, or even on a 9 per cent basis.76

The period of time a loan or bond runs is also an important factor as regards risk.77 There is a see-saw between the rates on short term and long term loans. That is, if the short term rate is greatly above the long term, it is likely to fall, or if greatly below, to rise. The long term rates thus set a rough norm for the short term rates, which are much more variable. When the future is regarded as safer than usual, loan contracts tend to be longer in time than otherwise. In a stable country like the United States, railway and government securities are thus often drawn for half a century or more. There is also a variability according to the degree of liquidity. A call loan which may be recalled on a few hours' notice has a very different relation to risk than does a mortgage, for instance. The call rate is usually lower than time rates because money on call is a little like money on deposit, or ready money. It is ready, or nearly ready, for use whenever occasion demands. This readiness or convenience takes the place of some of the interest. On the other hand, a sudden shortage of funds in the call loan market may send the call rates far above time rates and keep them there until the slow working forces release "time-money" and transfer it to the call loan market. Thus the call loan rates are very volatile and mobile in both directions.

The element of risk will affect also the value and basis of the collateral securities. Their availability for collateral will increase their salability and enhance their price. On the other hand, when, as in times of crisis, the collateral has to be sold, it often happens that for purposes of liquidation it is sold at a sacrifice.

§3. Limitations on Loans

The necessity of having to offer collateral will affect not only the rate which a man has to pay, but the amount he can borrow. It will limit therefore the extent to which he can modify his income stream by this means. Consequently it will not be possible, as assumed in the first two approximations, for a man to modify his income stream at will; its possible modification will be limited by the fear of the borrower that he may not be able to repay and the greater fear of the lender that he may not be repaid—because the borrower's credit may not prove good. In consequence of this limitation upon his borrowing power, the borrower may not succeed in modifying his income stream sufficiently to bring his rate of preference for present over future income down to agreement with the rate or rates of interest ruling in the market; and for like reasons he may not succeed in bringing the rate of return over cost into conformity with any rate of interest.

One feature of these limitations on borrowing may here be noted. The ability and willingness to borrow depend not only on the amount of capital which the would-be borrower possesses, but also on the form in which that capital happens to exist. Some securities are readily accepted as collateral, and accepted as collateral at a high percentage of their market value, whereas others will pass with difficulty and only at a low percentage of that value. The drift, especially during the last generation, toward the corporate form of business has had a striking effect in increasing the power and readiness to borrow. Whereas formerly many businesses were conducted as partnerships and on a small scale, numerous stocks and bonds have now been substituted for the old rights of partnership and other less negotiable forms of security. Similarly the small local companies, the stock of which was held almost exclusively by one family or group of friends, have been merged into large nationally known companies, the securities of which are widely marketable. This increase in size of business units, although it tends to decrease their number, has resulted in a rapid growth of the number of securities listed on the stock exchanges. The possessors of these securities have far wider opportunities to make use of collateral, and the tendency to borrow has received a decided impulse.

Where, on the other hand, the security needed is not available in the convenient form of engraved certificates, there is often considerable difficulty in negotiating a loan. A poor man may see what he believes to be an investment opportunity to make millions by exploiting an invention of his own, and he may be right. This option would have a much higher present value than the one he actually chooses, if only he could borrow the money needed to exploit it. But, being poor and hence without adequate collateral or other guarantees, he cannot get the loan. His choice of income stream, therefore, although the maximum open to him, is quite different from what it would be if he had that collateral or guarantee. If he goes into the enterprise at all he must choose a stopping point far short of what he would choose were he a large capitalist. This means that his marginal rate of return over cost will be higher than the market rate of interest, just as his rate of impatience will be higher than the market rate of interest. The last $100 he ventures to put in may promise a yield of 25 per cent as compared with a rate of interest of 5 per cent. Yet he does not go further into debt because he cannot. Supposing a definite limit of possible debt, all he can do toward further investing must be out of his own income, obtained by abstinence. But this possibility is also limited. He cannot cut his income down to zero, or he would starve. He can however cut it "to the quick", stopping at the point where his impatience has risen to meet the rate of return over cost which in turn will tend to fall with each additional dollar invested.

The story is told of the inventor of rubber making a last desperate—and, fortunately, successful—sacrifice in his experiments in which he resorted to burning up his furniture because he could not get funds with which to buy fuel.

Many such cases exist—cases of limitation on loans—which prevent a person's degree of impatience and his rate of return over cost from reaching the level of the rate of interest. But there is another part of the picture. The poor man who cannot borrow enough to exploit his invention can often find substitutes for loans and lenders. He may associate himself with others in a joint stock company and get the required capital partly from loans, by selling bonds secured by mortgage, partly by selling debentures on a higher interest basis, partly by selling preferred stock on a still higher basis, and partly by selling common stock. That is, the risks are recognized and pooled. One result may be to bring both his estimated rate of return over cost and his rate of impatience more nearly into harmony with these various rates of interest when due account has been taken of the various risks involved.

§4. Risk and Small Loans

Where the borrowing takes place in pawn shops, the rate of interest is usually very high, not so much because of the inadequacy of the security as because of its inconvenient form. The pawnbroker will need to charge a high rate of interest, if it is to be called interest, partly because he needs storage room for the security he accepts, partly because he needs special clerks and experts to appraise the articles deposited, and partly because, in many cases, when not redeemed, he has to make an effort to find markets in which to sell them. He is, moreover, able to secure these high rates partly because pawnbroking is in bad odor, so that those who go into the business find a relative monopoly, and partly because of the fact that the customers usually have, either from poverty or from personal peculiarity, a relatively high preference for present over future income. While the effect of their accommodation at the pawn shop is to reduce their impatience to some extent, it will not reduce it to the general level in the community, because these persons do not have access to the loan market in which the ordinary business man deals. To them, undoubtedly, the fact that they cannot borrow except at high, or usurious, rates is often a great hardship, but it has one beneficent effect, that is, the discouraging of the improvident from getting unwisely into debt.

One of the very greatest needs has always been to sift out the relatively safe and sane from the relatively risky and reckless loans of the poor in order to encourage the one and discourage the other. When this has been more fully accomplished, the scandal of the loan shark will be largely a thing of the past. A loan which, to the shortsighted or weak willed borrower, seems to be a blessing, but which is really sure to prove a curse, ought certainly to be discouraged no matter what may be the rate of interest. The Russell Sage Foundation has studied the loan shark problem intensively and as a result has formulated a model small loans act which has been adopted by the legislatures in a large number of our States. This model act recognizes the greater risk and trouble involved in small loans for short periods, by permitting a maximum rate per month of 3½ per cent.

Only in the present generation has the age-long curse of the loan shark been met by constructive measures on a large scale. These are based on the simple principle that a man's friends and neighbors possess the necessary knowledge whereby to distinguish between a safe and unsafe extension of credit to him. The Morris Plan banks are founded on that principle. More effective are the Credit Unions founded by Edward Filene and others in America somewhat on the models of the Raiffeisen and other plans in Europe. Labor banks are rendering a similar service. These are enabling the poor to make effective use of personal character as a substitute for collateral security and are thereby greatly reducing the rate of interest on the loans of the poor. In 1928 one large bank in Wall Street instituted a similar system for loans without collateral to salaried employees. These devices and others are doing much to solve the problem of accommodating the reliable man of small means with loans at rates comparable with those ruling in the markets for the well-to-do.

§5. Salability as a Safeguard

When a security, because it is well known, or for any other reason, has a high degree of salability, that is, can be sold on short notice without risk of great sacrifice, its price will be higher than less favored securities, and the rate it yields will therefore be low. Salability is a safeguard against contingencies which may make quick selling advisable. In other words, in a world of chance and sudden changes, quick salability, or liquidity, is a great advantage. For this reason, the rate of interest on individual mortgages will be higher than the rate of interest on more marketable securities. It is, in general, advantageous to have stock listed on the stock exchange, for, being thus widely known, should the necessity to sell arise, such a stock will find a more ready market.

The most salable of all properties is, of course, money; and as Karl Menger pointed out, it is precisely this salability which makes it money. The convenience of surely being able, without any previous preparation, to dispose of it for any exchange, in other words, its liquidity, is itself a sufficient return upon the capital which a man seems to keep idle in money form. This liquidity of our cash balance takes the place of any rate of interest in the ordinary sense of the word. A man who keeps an average cash balance of $100, rather than put his money in a savings bank to yield him $5 a year, does so because of its liquidity. Its readiness for use at a moment's notice is, to him, worth at least $5 a year. There is a certain experienced buyer and seller of forests, in Michigan, who makes a practice of keeping a ready cash balance in banks of several million dollars in order better to be able to compete with other forest purchasers by having available spot cash to offer some forest owner who, becoming forest-poor, wishes to sell. Forests are extremely non-liquid while cash balances are extremely liquid.

§6. General Income Risks

Even when there is no risk (humanly speaking) in the loan itself, the rate realized on it is affected by risk in other connections. The uncertainty of life itself casts a shadow on every business transaction into which time enters. Uncertainty of human life increases the rate of preference for present over future income for many people,78 although for those with loved dependents it may decrease impatience. Consequently the rate of interest, even on the safest loans, will, in general, be raised by the existence of such life risks. The sailor or soldier who looks forward to a short or precarious existence will be less likely to make permanent investments, or, if he should make them, is less likely to pay a high price for them. Only a low price, that is, a high rate of interest, will induce him to invest for long ahead.

When the risk relates, however, not to the individual's duration of life, but to his income stream, the effect upon the rate of interest will depend upon which portions of the income stream are most subject to risk. If the immediately ensuing income is insecure, whereas the remoter income is sure, the rate of preference for an additional sure dollar immediately over an additional sure dollar in the remoter period will, as was shown in Chapter IV, tend to be high, and consequently the effect of such a risk of immediate income upon the rate of interest will be to raise it. A risky immediate income acts on interest like a small immediate income.

But if, as is ordinarily the case, the risk applies more especially to the remoter income than to the immediate, the effect is the exact opposite, namely, to lower the rate of interest on a safe loan. The risky remote income acts as the equivalent of a small remote income. This example is, perhaps, the most usual case. If a man regards the income for the next few years as sure, but is in doubt as to its continuance into the more remote future, he will be more keenly alive to the needs of that future, and will consequently have a less keen preference for the present. He will then be willing, even at a very low rate of interest, to invest, out of his present assured income, something to eke out with certainty the uncertain income of the future. The effect of risk in this case, therefore, is to lower the rate of interest on safe loans, though at the same time, as already explained, it will raise the rate of interest on unsafe loans. Consequently, in times of great social unrest and danger, making the future risky, we witness the anomalous combination of high rates where inadequate security is given coexistent with low rates on investments regarded as perfectly safe. When an investor cannot find many investments into which he may put his money without risk of losing it, he will pay a high price—i.e., accept a low rate of return—for the few which are open to him. It has been noted in times of revolution that some capitalists have preferred to forego the chance of all interest and merely to hoard their capital in money form, even paying for storage charges, a payment which amounts to a negative rate of interest. During the World War some investors in the warring countries sought safekeeping for their funds in neutral countries.

§7. Securities Classified as to Risk

When risk thus operates to lower the rate of interest on safe investments and to raise the rate on unsafe investments, there immediately arises a tendency to differentiate two classes of securities and two classes of investors—precarious securities and adventurous investors on the one hand, and safe securities and conservative investors on the other. Some risk is inevitable in every business, but is regarded by most people as a burden; hence the few who are able and willing to assume this burden tend to become a separate class. When enterprises came to be organized in corporate form, this classification of investors was recognized by dividing the securities into stocks and bonds, the stockholder being the person who assumes the risk and, theoretically at least, guaranteeing that the bondholder shall be free of all risk. Which person shall fall into the class of risk-takers and which not is determined by their relative coefficients of caution,79 as well as by the relative degree of risk which an enterprise would involve for the various individuals concerned. The same enterprise may be perilous for one and comparatively safe for another because of superior knowledge on the part of the latter, and the same degree of risk may repel one individual more than another, owing to differences in temperament or, most important of all, to differences in amount of available capital.80

This shifting of risk from those on whom it bears heavily to those who can more easily assume it discloses another motive for borrowing and lending besides those which were discussed in a previous chapter. Borrowing or lending in corporate finance usually indicates not simply a difference in time shape as between two income streams, but also a difference of risk. The object of lending which was emphasized in earlier chapters, before the risk element was introduced into the discussion, was to alter the time shape of the income stream, the borrower desiring to increase his present income and decrease his future, and the lender desiring, on the contrary, to decrease his present income and add to his future. But the ordinary stockholder and bondholder do not differ in this way so much as they do in respect to risk. They are both investors, and the positions, in which they stand as to the effect of their investment on the time shape of their income, are really very similar. But the stockholder has a risk attached to his income stream from which the bondholder seeks to be free. It is this difference in risk which is the primary reason for the distinction between stockholders and bondholders. The bondholder gives up his chance of a high income for the assurance, or imagined assurance, of a steady income. The stockholder gives up assurance for the chance of bigger gains.

The existence of this risk, tending as we have seen to raise the rate of interest on unsafe loans and lower that on safe loans, has, as its effect, the lowering of the price of stocks and the raising of the price of bonds from what would have been their respective prices had the risk in question been absent.

In the last few years, however, this disparity has been decreased from both ends. The public have come to believe that they have paid too dearly for the supposed safety of bonds and that stocks have been too cheap. Studies of various writers, especially Edgar Smith81 and Kenneth Van Strum82 have shown that in the long run stocks yield more than bonds. Economists have pointed out that the safety of bonds is largely illusory83 since every bondholder runs the risk of a fall in the purchasing power of money and this risk does not attach to the same degree to common stock, while the risks that do attach to them may be reduced, or insured against, by diversification. The principle of insurance84 of any kind is by pooling those risks virtually to reduce them. This raises the value of the aggregate capital subject in detail to these risks.

It is in this way that investment trusts and investment counsel tend to diminish the risk to the common stock investor. This new movement has created a new demand for such stocks and raised their prices; at the same time it has tended to decrease the demand for, and to lower the price of, bonds.

Again, speculation in grain, for example by setting aside a certain class of persons to assume the risks of trade, has the effect of reducing these risks by putting them in the hands of those who have most knowledge, for, as we have seen, risk varies inversely with knowledge. In this way, the whole plane of business is put more nearly on a uniform basis so far as the rate of interest is concerned.

Risk is especially conspicuous in the financing of new inventions or discoveries where past experience is a poor guide. When new inventions are made, uncertainty is introduced, speculation follows, and then comes great wealth or great ruin according to the success or failure of the ventures. The history of gold and silver discoveries, of the invention of rubber, of steel, and of electrical appliances is filled with tales of wrecked fortunes, by the side of which stand the stories of the fortunes of those few who drew the lucky cards, and who are among today's multi-millionaires.

The rates of interest are always based upon expectation, however little this hope may later be justified by realization. Man makes his guess of the future and stakes his action upon it. In his guess he discounts everything he can foresee or estimate, even future inventions and their effects. In an estimate which I saw in print of the value of a copper mine, allowance was made for future inventions which might reasonably be expected. In the same way, too, the buyer of machinery allows not simply for its depreciation through physical wear, but for its obsolescence. New investments in steam railroads are today made with due regard to the possibility that the road may, within a few years, be run by electricity, or that it will be injured by competition of bus lines or helped by terminal connections with them.

It may easily happen that, in a country consisting of overly sanguine persons, or during a boom period when business men are overhopeful, the rate of interest will be out of line with what actual events, as later developed, would justify. It seems likely that, in ordinary communities, realization justifies the average expectation. But in an individual case this is not always true; otherwise there would be no such thing as risk. Risk is synonymous with uncertainty—lack of knowledge. Our present behavior can only be affected by the expected future,—not the future as it will turn out but the future as it appears to us beforehand through the veil of the unknown.

§8. Effect of Risk on the Six Principles

We see, then, that the element of risk introduces disturbances into those determining conditions which were expressed in previous chapters as explaining the rate of interest. To summarize these disturbances, we may now apply the risk factor to each of the six conditions which were originally stated as determining interest. We shall find that its effects are as follows:

THE TWO PRINCIPLES AS TO INVESTMENT OPPORTUNITY

A. Empirical Principle

The condition that each individual has a given range of choice still holds true, but these choices are no longer confined to absolutely certain optional income streams, but now include options with risk. That is to say, each individual finds open to his choice a given set of options (and opportunities to shift options, that is, opportunities to invest) which options differ in size, time shape, composition and risk.

B. Principle of Maximum Present Value

When risk was left out of account, it was stated that from among a number of different options the individual would select that one which has the maximum present value—in other words, that one which, compared with its nearest neighbors, possesses a rate of return over cost equal to the rate of time preference, and therefore to the rate of interest.

When the risk element is introduced, it may still be said that the maximum present value is selected, but in translating future uncertain income into present cash value, use must now be made of the probability and caution factors.

But when we try to express this principle of maximum present value in its alternative form in terms of the marginal rate of return over cost, we must qualify this expression to: the marginal rate of anticipated return over cost.

Three consequences follow. First, that the rate of return over cost which will actually be realized may turn out to be widely different from that originally anticipated. Second, there is in the market not simply one single anticipation; there are many, each with a different degree of risk allowed for in it. Third, the need of security may be such as to limit also the choice of options.

THE TWO PRINCIPLES AS TO IMPATIENCE

A. Empirical Principle

The rate of time preference depends upon the character of the income stream, but it must now take into account the fact that both the immediate and the future (especially the future) portions of that stream are subject to risk. There are many rates of time preference, or impatience, according to the risks involved. But they all depend on the character of the expected and possible income stream of each individual—its size, shape, composition and especially the degree of uncertainty attaching to various parts of it as well as the degree of uncertainty of life of the recipient.

B. The Principle of Maximum Desirability

It is still true, of course, that the individual decides on the option most wanted. But, in a world of uncertainty there are two features not present in a world of certainty. One (which however does not affect the formulation of the principle) is that what is now desired may prove disappointing. That is, though it seems, when chosen, the most desirable course, it may not prove the most desirable in the sense of deserving, in view of later developments, to be desired. The other new feature is that the most desired income stream is no longer necessarily synonymous with that which harmonizes the rate of preference with the rate of interest.

Rates of time preference in any one market tend toward equality by the practice of borrowing and lending, and more generally, that of buying and selling, but this equality is no longer, in all cases, attainable, because of limitations on the freedom to modify the income stream at will, limitations growing out of the existence of the element of risk and consequent limitations on the borrowing power.

THE TWO MARKET PRINCIPLES

A. Principle of Clearing the Market

In the first two approximations, where the element of risk was considered absent, it was shown that the aggregate modification of the income streams of all individuals for every period of time was zero. What was borrowed equaled what was lent, or what was added by sale was equal to what was subtracted by purchase. The same principle still applies, for what one person pays, another person must receive. The only difference is that, in a world of chance, the actual payments may be quite different from those originally anticipated and agreed upon, that is, will often be defaulted, in whole or in part.

B. Principle of Repayment

In the former approximations, the total present value of the prospective modifications of one's income stream was zero, that is, the present value of the loans equaled the present value of the borrowings, or the present value of the additions and subtractions caused by buying and selling balanced each other. In our present discussion, in which future income is recognized as uncertain, this principle still holds true, but only in the sense that the present market values balance at the moment when the future loans or other modifications are planned and decided upon. The fact of risk means that later there may be a wide discrepancy between the actual realization and the original expectation. In liquidation there may be default or bankruptcy. When the case is not one of a loan contract, but relates merely to the difference in income streams of two kinds of property bought and sold, the discrepancy between what was expected and what is actually realized may be still wider. Only viewed in the present is the estimated value of the future return still the equivalent of the estimated cost.

We thus see that, instead of the series of simple equalities which we found to hold true in the vacuum case, so to speak, where risk was absent, we have only a tendency toward equalities, interfered with by the limitations of the loan market, and which, therefore, result in a series of inequalities. Rates of interest, rates of preference, and rates of return over cost are only ideally, not really, equal.

We conclude by summarizing in the accompanying table the interest-determining conditions not simply for the third approximation but for all three of our three successive approximations (distinguished by the numerals 1, 2, 3).

In this summary tabulation the "Principles as to Investment Opportunity" are formally inserted, under the first approximation, in order to complete the correspondence with the other two approximations, but of course they merely re-express the hypothesis under which the first approximation was made. They are therefore bracketed, since only the remaining four conditions are of real significance for the first approximation.

The first and second approximations were, of course, merely preparatory to the third, which alone corresponds to the actual world of facts. Yet the other two approximations are of even greater importance than the third from the point of view of theoretical analysis. They tell us what would happen under their respective hypotheses. Both these hypotheses are simpler than reality; hence they lend themselves better to formal analysis and mathematical expression.

Moreover, to know what would happen under these hypothetical conditions enables us better to understand what does happen under actual conditions, just as the knowledge that a projectile would follow a parabola if it were in a vacuum enables the student of practical gunnery better to understand the actual behavior of his bullets or shells. In fact, no scientific law is a perfect statement of what does happen, but only what would happen if certain conditions existed which never do actually exist.85 Science consists of the formulation of conditional truths, not of historical facts, though by successive approximations, the conditions assumed may be made nearly to coincide with reality.86

The second approximation gives a clear cut theory applicable to the clear cut hypotheses on which it is based. The third approximation cannot avoid some degree of vagueness.

[29.][29] Or ophelimity, utility, wantability, or the want for one more unit. See The Nature of Capital and Income, Chapter III; also my articles, Is 'Utility' the Most Suitable Term for the Concept It Is Used to Denote? American Economic Review, June, 1918, pp. 335-337; and A Statistical Method for Measuring "Marginal Utility" and Testing the Justice of a Progressive Income Tax. Economic Essays Contributed in Honor of John Bates Clark, pp. 157-193.

[30.][30] To be more specific, we obtain the rate of time preference for a present dollar over a dollar one year hence by the following process:

• (a) take the present want for one more present dollar; and
• (b) the present want for one more dollar due one year hence; and then
• (c) subtract (b) from (a); and finally
• (d) measure the result (c) as a percentage of (b).

[31.][31] See The Nature of Capital and Income, Chapter X.

[32.][32] It is true, of course, that, in determining economic equilibrium, every variable theoretically affects every other, and the rate of interest, as one variable, must therefore be assumed to affect indirectly the price of everything else by affecting its supply and demand.

[33.][33] For a statement of the theory of valuation in general, see Walras, Éléments d'Économie Politique Pure; Pareto, Cours d'Économie Politique; also, Manuel d'Économie Politique.

[34.][34] Cf. Landry, L'Intérêt du Capital, Chapter X, § 149, pp. 311-315; §150, pp. 315-317.

[35.][35] Böhm-Bawerk, The Positive Theory of Capital, p. 249.

[36.][36] For a theoretical discussion of marginal want as a function of various factors, see my Mathematical Investigations in the Theory of Value and Prices. For a mathematical formulation of impatience as a function of successive installments of income, see Appendix to this chapter, §7. See also Pareto, Manuel d'Économie Politique, p. 546 et seq.

[37.][37]Cf. Rae, Sociological Theory of Capital, p. 54; Böhm-Bawerk, The Positive Theory of Capital, Book V, Chapter III.

[38.][38] To be exact, however, we should observe that lack of foresight may either increase or decrease time preference. Although most persons who lack foresight err by failing to give due weight to the importance of future needs, or, what amounts to the same thing, by estimating over-confidently the provision existing for such future needs, cases are to be found in which the opposite error is committed; that is, the individual exaggerates the needs of the future or underestimates the provision likely to be available for them. Such people stint themselves needlessly, even impairing health by insufficient food in their efforts to save for the dreaded future. Their lack of foresight in this case errs in under-estimating instead of overestimating future income and so makes them too patient instead of too impatient. But in order not to complicate the text, only the former and more common error will be hereafter referred to when lack of foresight is mentioned. The reader may, in each such case, readily add the possibility of the contrary error.

[39.][39] Rae, Sociological Theory of Capital, p. 54.

[40.][40] Rae, The Sociological Theory of Capital, pp. 53-54.

[41.][41] See Rae, The Sociological Theory of Capital, p. 97.

[42.][42] Tarde, G. Social Laws. English translation, New York, Macmillan and Co., 1899. Also Les Louis de l'Imitation. Paris, Germer Baillière et C., 1895.

[43.][43] The Psychology of Socialism. English translation. London, T. Fisher Unwin, 1899. Also The Crowd.

[44.][44] Social and Ethical Interpretations in Mental Development. New York, Macmillan and Co., 1906.

[45.][45] Bagehot, Walter. Physics and Politics. New York, D. Appleton and Co., 1873, Chapter III.

[46.][46] See The Sociological Theory of Capital, Appendix, Article 1, pp. 245-276.

[47.][47] See The Nature of Capital and Income, Chapter XIV.

[48.][48] One of the few defects in Rae's analysis of interest, or at any rate of his statement of it, is his emphasis on the accumulation of capital. Since this accumulation is merely in anticipation of future income, the emphasis belongs on the latter.

[49.][49] One consequence of this assumption (to secure which the assumption was really made) is that the capitalized value of each person's income at a given rate of interest will be unchangeable. He is, so to speak, on a definite allowance, and any trading, as by borrowing, or mortgaging the future, cannot make him richer or poorer. It can only shift his income in time (with interest). The theoretical significance of this constancy will appear in the second approximation.

[50.][50] The above-mentioned 10 per cent and 8 per cent rates of time preference are not rates actually experienced by him; they merely mean the rates of preference which he would have experienced had his income not been transformed to the time shape corresponding to 5 per cent. As in the general theory of prices, this marginal rate, 5 per cent, being once established, applies indifferently to all his valuations of present and future income. Every comparative estimate of present and future which he actually makes may be said to be "on the margin" of his income stream as actually determined.

[51.][51] This is the case mentioned by Carver (The Distribution of Wealth, pp. 232-236), when he remarks that a man with $100 in his pocket would not think of spending it all on a dinner today, but would save at least some of it for tomorrow. Whether these conformations of the income stream resulting in zero or negative preference may ever actually be reached so that the market rate of interest itself may be zero or negative is another question.

[52.][52] Thus, by saving, some writers understand that capital necessarily increases, and hence the income stream is made to ascend; others, like Carver (loc. cit., p. 232), apply the term broadly enough to include the case where a descending income is simply rendered less descending. The latter view harmonizes with that here presented. Saving is simply postponing enjoyable income.

[53.][53] We do not here need to argue as to the zero or starting point from which we measure net total desirability. The crest of a hill is the highest point whether the height is measured above sea level or from the center of the earth.

[54.][54] See my Mathematical Investigations in the Theory of Value and Prices.

[55.][55] See Chapter I, or The Nature of Capital and Income, Chapter X.

[56.][56] See my Mathematical Investigations in the Theory of Value and Prices.

[57.][57] It is, of course, realized that the principles of price determination involve interest just as the principles determining interest involve prices. A complete picture of economic equilibrium includes every possible variable, each acting and reacting on the others. Theoretically we cannot determine the price of bread by itself and then go on to determine, each separately, other prices, including the rate of interest. Theoretically any analysis of one part of the economic organism must include an analysis of the whole, so that a complete interest theory would have to include also price theory, wage theory and, in fact, all other economic theory.

But it is convenient to isolate a particular element by assuming the other elements to have been determined. So this book is a monograph, restricted, so far as may be, to the theory of interest, and excluding price-theory, wage theory and all other economic theory. Afterward it will be easy to dovetail together this interest theory, which assumes prices predetermined, with price theory which assumes interest predetermined, thus reaching a synthesis in which the previously assumed constants become variables. But all the principles remain valid.

[58.][58] See The Nature of Capital and Income, Chapters VIII, IX, XVII.

[59.][59] That this is the case under our present hypothesis is shown fully in Chapter XIII.

[60.][60] The details of such a multiform equilibrium are given in mathematical terms in Chapter XIII.

[61.][61] Positive Theory of Capital, p. 277, footnote.

[62.][62] In case the advantages (returns) precede the disadvantages (costs), as is the case when the merits of the mining use are compared with those of the farming use, the proposition must be reversed, as follows: The earlier advantage will be chosen only in case the rate of future costs over present returns is less than the rate of interest. In such a case it would be more convenient, in comparing the two options, to regard them in the reverse order, that is, to consider the advantages of the farming use over the mining use, so that the disadvantages may come first, i.e., the investment precede the returns. As long as the costs always precede the returns, we need only to consider whether or not the rate of return over cost exceeds the rate of interest.

[63.][63] Inasmuch as we assume that the income from the forest is all to accrue at one time—the time of cutting—instead of being distributed over a long period, the income stream becomes a single jet and might here better be called income item.

[64.][64] The Nature of Capital and Income, pp. 221-222.

[65.][65] The Nature of Capital and Income, Chapter XIII.

[66.][66] Del Mar, Alexander. Science of Money. New York, Macmillan & Co., 1896; George, Henry. Progress and Poverty. New York, Sterling Publishing Co., 1879. For a general criticism of this theory see Lowry, The Basis of Interest, American Academy of Political and Social Science, March, 1893, pp. 53-76

[67.][67] See Chapter I or The Nature of Capital and Income, Chapters VII, VIII, IX, and X.

[68.][68] Ibid., p. 317.

[69.][69] A somewhat similar treatment is that of Professor Harry G. Brown, Economic Science and the Common Welfare. Mathematical treatments substantially in harmony with mine are those of Walras and Pareto referred to in Appendix to Chapter XIII.

[70.][70] H. G. Brown, Economic Science and the Common Welfare, pp. 137-145.

[71.][71] p. 232. See also Carver, T. N. The Place of Abstinence in the Theory of Interest, Quarterly Journal of Economics, Oct., 1893, pp. 40-61.

[72.][72] Brown, Economic Science and the Common Welfare, pp. 137-147.

[73.][73] See The Nature of Capital and Income, Chapter XIV, No. 4.

[74.][74] Rae, The Sociological Theory of Capital, p. 47.

[75.][75] The Nature and Necessity of Interest, p. 122.

[76.][76] For a more complete treatment of the relation of risk to the interest yield of securities, see The Nature of Capital and Income, Chapter XVI.

[77.][77] Even in the first and second approximations the rate of interest for different periods would not necessarily be the same.

[78.][78] See Carver, The Distribution of Wealth, p. 256, and Cassel, A Theory of Social Economy, pp. 246-247.

[79.][79] See The Nature of Capital and Income, Chapter XVI, §6.

[80.][80] Ibid., Appendix to Chapter XVI, p. 409.

[81.][81] Smith, Edgar L. Common Stocks as Long Term Investments. New York, The Macmillan Company, 1924.

[82.][82] Van Strum, Kenneth, Investing In Purchasing Power. Boston, Barron's, 1925.

[83.][83] See The Money Illusion. Also When Are Gilt-Edged Bonds Safe? Magazine of Wall Street, Apr. 25, 1925.

[84.][84] See The Nature of Capital and Income, Chapter XVI.

[85.][85] See the writer's Economics as a Science, Proceedings of the American Association for Advancement of Science, Vol. LVI, 1907.

[86.][86] See Appendix to Chapter IX, No. 1.