The Theory of Interest

Fisher, Irving
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New York: The Macmillan Co.
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§1. Interest Rates and Values of Goods


HAVING completed the exposition of the theory of the causation and determination of the rate of interest which is most acceptable to me, it now remains to show how this theory fits into a complete system of economic theory and what results must flow from its acceptance.


Interest plays a central rôle in the theory of value and prices and in the theory of distribution. The rate of interest is fundamental and indispensable in the determination of the value (or prices) of wealth, property, and services.


As was shown in Chapter I, the price of any good is equal to the discounted value of its expected future service, including disservices as negative services. If the value of these services remains the same, a rise or fall in the rate of interest will consequently cause a fall or rise respectively in the value of all the wealth or property. The extent of this fall or rise will be the greater the further into the future the services of wealth extend. Thus, land values from which services are expected to accrue uniformly and indefinitely will be practically doubled if the rate of interest is halved, or halved if the rate of interest is doubled. The value of dwellings and other goods of definitely limited durability will fall less than half if interest rates double, and will rise to less than double if interest is halved. Fluctuations in the value of furniture will be even less extensive, clothing still less, and very perishable commodities like fruit will not be sensibly affected in price by a variation in the rate of interest. In all the foregoing cases it is, of course, assumed that the expected services remain unchanged.

§2. Interest Rates and Values of Services


As to the influence of the rate of interest on the price of services, we first observe that services may be either final or intermediate.*1 The value of a dinner about to be eaten involves no time of waiting and so no discount or interest. Nor does the irksomeness of labor about to be undertaken involve discount to the laborer. Both the dinner or its enjoyment and the labor are final items of income, the one positive and the other negative. The value of intermediate services ("interactions") is derived from the succeeding future services to which they lead. For instance, the value to a farmer of the services of his land in affording pasture for sheep will depend upon the discounted value of the services of the flock in producing wool. If he rents the land, he will calculate what he can afford to pay for it on the basis of the value of the wool which he would expect to obtain from his flock. In like manner, the value of the wool output to the woolen manufacturer is in turn influenced by the discounted value of the output of woolen cloth to which it contributes. In the next stage the value of the production of woolen cloth will depend upon the discounted value of the woolen clothing to which that cloth contributes. Finally, the value of the last named will depend upon the expected real income which the clothing will bring to those who wear it, in other words, upon the use or "wear" of the clothes.


Thus the final services, consisting of the use of the clothes, will have an influence on the value of all the anterior services of tailoring, manufacturing cloth, producing wool, and pasturing sheep, while each of these anterior services, when discounted, will give the value of the respective capitals which yield them, namely, the clothes, cloth, wool, sheep, and pasture land. The values, not only of all articles of wealth, but also of all intermediate services which they render, are dependent upon the values of final enjoyable uses. Capital values and values of final uses are linked by the rate of interest. A rise or fall in the rate of interest will be felt most by the links most distant from these final services. A change in the rate of interest will tend to affect but slightly the price of making clothing, but it will tend to affect considerably the price of pasturing sheep.


The theory of prices, so far as it can be separated into parts, includes: (1) explanation of the prices of final services on which the prices of anterior interactions depend; (2) explanation of the prices of intermediate interactions, as dependent, through the rate of interest, on the final services; (3) explanation of the prices of capital instruments as dependent, through the rate of interest, upon the prices of their final services. The first study, which seeks merely to determine the laws regulating the price of final services, is independent of the rate of interest.*2


The second and third problems, which seek to show the dependence on final services of the intermediate services and of the capital which bears them, involve the rate of interest. Under this second study will fall, as a special case, the study of the determination of economic rent, the rent both of land and of other instruments of wealth. The rent of a pasture consists of the value of the services of pasturing. This value, in accordance with the principles expounded in Chapter I, is dependent through the rate of interest upon the discounted value of the future final services to which the pasturing contributes. It is clear, then, that the rent of the land is partly dependent upon the rate of interest, and that the same dependence applies to the rent of any other instrument.

§3. Interest Rates and Wages


Similar considerations apply to the determination of the rate of wages. From the standpoint of the employer, the payment of wages to a workman supposedly represents the value of his services. These services are interactions, or intermediate services, leading ultimately to some future enjoyable service. Thus the shepherd, hired by the farmer to tend the sheep in the pasture, renders services the value of which to the farmer is estimated in precisely the same way as the value of the services of the land which the farmer hires.


Consequently, if interest varies, wages will vary. Thus, if the land is used for farming, the wages paid for planting crops will be gauged in the estimate by the farmer by discounting the value of the expected crops and will vary somewhat according to whether the discounting is at 5 per cent or at 4 per cent. In like manner the workers engaged in bridge building are presumed to be paid the discounted value of the ultimate benefits which will be yielded by the bridge. The wages of those engaged in making locomotives normally represent the discounted value of the completed locomotives, and hence, as the value of a completed locomotive is in turn the discounted value of its expected service, their wages represent the discounted value of the ultimate benefits in the series.*3 In all these cases, the rate of wages is the discounted value of some future product, and therefore tends to decrease as interest increases. But the effects in the different lines will be very unequal.


Wages of domestic servants and those engaged in putting the finishing touches on enjoyable goods will have their wages affected comparatively little by the rate of interest. On the other hand, for laborers who are engaged in work requiring much time the element of discount applied to their wages is a considerably more important factor. If a tree planter is paid $1 because this is the discounted value at 5 per cent of the $2 which the tree will be worth when matured in fifteen years, it is clear that a change in the rate of interest to 4 per cent will tend materially to increase the value of such work. Supposing the value of the matured tree still to remain at $2, the value of the services of planting it would be not one dollar but $1.15. On the other hand, for laborers engaged in a bakery or other industry in which the final satisfactions mature early, the wages are more nearly equal to the value of these products. If they produce final services worth $1, due, let us say, in one year, their wages would be 95 cents when the interest rate is 5 per cent and 96 cents if interest falls to 4 per cent.


It is clear, nevertheless, that such unequal effects coming from a reduction in the rate of interest, as an increase from $1 to $1.15 in one industry and from 95 cents to 96 cents in another, could not remain permanently. Labor will tend to shift from the lower paid to the higher paid occupations until equality of wages for workers of the same skill is re-established. In the end, therefore, the change in the rate of interest from 5 per cent to 4 per cent would effect a redistribution in the values of intermediate items of income and in final items of income.


Evidently then, the effect of a change in the rate of interest on the value of interactions will naturally be the more pronounced in a country where lengthy processes are usually employed than in one where the shorter ones are common. If, for instance, laborers in a given country are engaged largely in building elaborate works, such as the Panama Canal, or in digging tunnels and constructing other great engineering works, or in planting forests and otherwise investing for the sake of remote returns, a fall in the rate of interest will produce a considerable rise in wages, whereas, in a country where such lengthy processes are unknown and workmen are chiefly employed in tilling the ground and performing personal services, a change in the rate of interest will hardly affect wages or the values of other preparatory services at all.


What has been said, however, applies only to wages from the standpoint of the employer. The rate of wages is dependent upon supply as well as upon demand, that is, upon the willingness of the workman to offer his services, as well as upon the desire of the employer to secure them. From the standpoint of the laborer, wages constitute an incentive to exertion or labor. This exertion is a final disservice, or negative item of income, and its valuation by the laborer is not directly affected by the rate of interest, as are other services which are not final but intermediate. It is a great mistake to treat the subject of wages, as many authors do, exclusively from the employer's standpoint. The purpose here is not to undertake to outline a complete theory of wages, but merely to show why a complete wage theory must take cognizance of interest and must explain how the interest rate affects some wage rates and not others.

§4. Interest and Functional Distribution


In the theory of distribution interest must be assigned a quite different and much more important rôle than economists thus far have given to it. In classical economics the nature of interest and its place in distribution were not clearly understood. Distribution has been erroneously defined as the division of the income of society into "interest, rent, wages, and profits." Rent and interest are merely two ways of measuring the same income; rent, as the yield per acre or other physical unit, and interest as the same yield expressed as a per cent of capital value. The value of the capital is derived from the income which it yields by capitalizing it at the prevailing rate of interest. To reverse this process by multiplying the capital value by the rate of interest gives the original income, as long as the capital value remains stationary. It is not really a complex product of two factors, but, on the contrary, is the single original factor, namely, income, from which we started. As explained in previous chapters, it is this income which affords the basis for the determination of the rate of interest, and through the rate of interest, of capital value.


The final enjoyable income of society is the ultimate and basic fact from which all values are derived and toward which all economic action is bent. All of this income is derived from capital wealth, if land and man are included in that term, or if not, from capital and man, or capital, land, and man, according to the terminology adopted. This income may all be capitalized, and hence all income (excluding capital gain) may be viewed as interest upon the capital value thus found.


Viewed as above outlined interest is not a part, but the whole, of income (except for capital gain). It includes what is called rent and profits and even wages, for the income of the workman may be capitalized quite as truly as the income of land or machinery. Thus, instead of having interest, rent, wages, and profits as mutually exclusive portions of social income, interest may be regarded as including all four. If we prefer to exclude profits, the reason is because of the element of risk and not because profits are not discountable just as truly as rent and wages. The error of the classical economists and of their modern followers in regarding interest, rent, wages and profits as separate but coördinate incomes is partly due to the failure to perceive that, whereas all income is produced from capital wealth, capital value can emerge only from man's psychic evaluation and capitalization of that income in advance of its occurrence.


Another oversight closely associated with the last stated fallacy is that in which rent and wages are conceived as determined independently of the rate of interest, whereas we have just seen that the rate of interest enters as a vital element into the determination of both. The great defect in the theories propounded by the classical economists lay in their inability to conceive of a general equilibrium and the mutual dependence of sacrifice and enjoyment.


In discussing the theory of distribution, we shall, therefore, abandon the classical point of view entirely. The classical concepts of distribution are quite inappropriate to explain the every day facts of life and the economic structure. The phrase distribution of wealth, as understood by the ordinary man, implies the problem of the relative wealth of individuals, the problem of the rich and the poor. But the separation of the aggregate income into four abstract magnitudes, even if correctly done, has little to do with the question of how much income the different individuals in society receive.

Only on condition that society was composed of four independent and mutually exclusive groups, laborers, landlords, enterprisers, and capitalists, would the fourfold division of the classical economists be even partially adequate to explain the actual distribution of income. In fact, the four classes all overlap. The enterpriser is almost invariably a genuine capitalist and usually also performs labor; the capitalist is frequently a landlord and laborer, and even the typical laborer is today often a small capitalist and sometimes a landlord. It is true that a century ago in England the lines of social classification corresponded roughly to the abstract divisions proposed at that time by the classical economists. But this fact is of little significance except as explaining historically the origin of the classical theory of distribution.*4

§5. Interest and Personal Distribution


The main problem of distribution, as I see it, is concerned with the determination and explanation of the amounts and values of capitals and incomes possessed by different individuals in society. It is astonishing how little economists have contributed to resolving the problems of distribution so conceived. A statistical beginning was made by Professor Pareto in his presentation of interesting "curves of distribution of income."*5 For the United States, Professor W. I. King *6 and the National Bureau of Economic Research *7, and for England, Sir Josiah Stamp *8 have made and analyzed important statistical compilations on the amount and distribution of income and capital wealth by income groups and social classes. On the theory of distribution, especially the rôle of interest in distribution, John Rae seems to have contributed more than any other writer*9. He showed in a vivid way that persons who had naturally what we have called in this book a low rate of impatience or preference for present over future income tended to accumulate savings, whereas those who had the opposite trait tended to spend their incomes and even their capitals.


In previous chapters it is shown that the rates of preference among different individuals are equalized by borrowing and lending or, what amounts to the same thing, by buying and selling. An individual whose rate of preference for present enjoyment is unduly high will contrive to modify his income stream by increasing it in the present at the expense of the future. The effects upon incomes may be traced to capital by applying the principles explained in The Nature of Capital and Income, Chapter XIV.


If a modification of the income stream is such as to make the rate of realized income relative to capital value exceed the standard rate of income returns, capital will be depleted to the extent of the excess, and the individual, group, or class, under consideration will grow poorer. This condition may be brought about either by borrowing immediate income and paying future income, or by selling instruments whose returns extend far into the future and buying those which yield more immediate returns. Individuals of the type of Rip Van Winkle, if in possession of land and other durable instruments, will either sell or mortgage them in order to secure the means for obtaining enjoyable services more rapidly. The effect will be upon society as a whole that those individuals who have an abnormally low estimate of the future and its needs will gradually part with the more durable instruments, and that these will tend to gravitate into the hands of those who have the opposite trait.


By this transfer an inequality in the distribution of capital is gradually effected, and this inequality once achieved tends to perpetuate itself. The poorer a man grows the more keen is his appreciation of present goods likely to become. When once the spendthrift is on the downward road, he is likely to continue in the same direction. When he has succeeded in losing all his capital except his own person, the process usually comes to an end, because civilized societies in self-protection frown upon chattel slavery and involuntary servitude. Many examples, however, of forced labor and even slavery still survive. The negro farmers of the Southern States, the Mexican peons, the peasants of Russia until recently, the forced labor and slavery in many tropical colonies, such as Java,*10 the Congo, and other African countries, are examples in point.


Reversely, when an individual has saved a considerable capital, his rate of preference for the present diminishes still further, and accumulation becomes still easier. Hence, in many countries the rich and poor come to be widely and permanently separated, the former to constitute an hereditary aristocracy of wealth and the latter, a helpless proletariat.


This progressive sifting, by which the spenders grow poorer and the savers richer, would go on even if, as assumed in our first and second approximations, there were no risk element. But it goes on far faster when as in actual life there is risk. While savings unaided by luck will ultimately enrich the saver, the process is slow as compared with the rapid enrichment which comes from the good fortune of those few who assume risks and then happen to guess right. Likewise, while millions of people lose their small properties by thriftlessness, the more rapid impoverishment comes from guessing wrong. This will often turn a rich man into a poor man within a few years and sometimes within a few days.


It should also be noted, especially when the element of uncertainty is taken into account, that borrowing may be the means of gaining great wealth quite as well as of losing it. The business borrower who borrows in order to invest always hopes to gain and often succeeds beyond his expectations.


The rates of return over cost in various investment opportunities play an important rôle in both. Henry Ford and others grew rich not so much because of thrift as because they took advantage of unusual investment opportunities, in which the rates of return over cost proved to be many times the market rate of interest.


Besides thrift and luck, with their opposites, there is another factor closely associated with the process of accumulation or dissipation. This is habit. It has been noted that a person's rate of preference for present over future income, given a certain income stream, will be high or low according to the past habits of the individual. If he has been accustomed to simple and inexpensive ways, he finds it fairly easy to save and ultimately to accumulate a little property. The habits of thrift being transmitted to the next generation, by imitation or by heredity or both, result in still further accumulation. The foundations of some of the world's greatest fortunes have been based upon thrift.


Reversely, if a man has been brought up in the lap of luxury, he will have a keener desire for present enjoyment than if he had been accustomed to the simple living of the poor. The children of the rich, who have been accustomed to luxurious living and who have inherited only a fraction of their parents' means, may spend beyond their means and thus start the process of the dissipation of their family fortune. In the next generation this retrograde movement is likely to gather headway and to continue until, with the gradual subdivision of the fortune and the reluctance of the successive generations to curtail their expenses, the third or fourth generation may come to actual poverty.


The accumulation and dissipation of wealth do sometimes occur in cycles. Thrift, ability, industry and good fortune enable a few individuals to rise to wealth from the ranks of the poor. A few thousand dollars accumulated under favorable circumstances may grow to several millions in the next generation or two. Then the unfavorable effects of luxury begin, and the cycle of poverty and wealth begins anew. The old adage, "From shirt sleeves to shirt sleeves in four generations," has some basis in fact. This cyclical movement is more likely to occur in countries like the United States, where, owing to the rapidly changing conditions, there is more chance either to rise or fall in the economic scale. Wherever, as in the older countries of Europe, conditions have become fixed and less subject to changes of any kind, incomes and wealth are likely to remain relatively unchanged in the same families, generation after generation. This tendency is strengthened in England, where the customs of inheritance have helped to keep large fortunes intact in the hands of the eldest son.


We are not concerned here with creating a complete theory of personal distribution and its changes. This would include the effects of many factors other than thrift. But here we are interested simply in the rôle of interest and thrift in distribution.

§6. The Loan Market Is a Highway for Re-Distribution


We see, then, that the existence of a market rate of interest to which the individual adjusts his rate of impatience supplies an easy highway for the movement of his fortune in one direction or the other. If an individual has spendthrift tendencies, their indulgence is facilitated by access to a loan market; and reversely, if he desires to save, he may do so the more easily if there is a market for savings. In like manner, the business man may, by recourse to loans, either lose or gain. The inequality of the distribution of capital is thus fundamentally caused in large part by exchanging present for future income. A rate of interest is simply a market price for such exchange. If all individuals were hermits, it would be much more difficult either to accumulate or to dissipate fortunes, and the distribution of wealth would therefore be much more even.


It is true, as the socialist maintains, that inequality is due to social arrangements, but these arrangements are not, as he assumes, primarily such as take away the chance to rise in the economic scale; they are, on the contrary, arrangements which facilitate both rising and falling, according to the choices made by the individual. The improvident sink like lead to the bottom. Once there, they or their children find difficulty in rising. Accumulation is usually a slow process, and especially slow because the great numbers of the poor competing against each other reduce the values of their services to so low a point that the initial saving becomes almost impossible. While it is true that waste begets poverty, it is equally true that poverty begets waste. Whole communities and peoples, for example, the Chinese and Indians, are steeped in misery not because of any inherent extravagance, but because they are so poor they must use up all they produce, leaving no margin of savings for bettering their methods of production. Occasionally a Rockefeller, a Carnegie, or a Ford rises from near the bottom and ascends to the top. But the great masses, once they get near the bottom, are likely to remain there. Their high rates of impatience manifested through generations have brought many if not most of them to poverty. A labor leader once said to me that few labor men have any acquisitive instinct. They are a self-selected group of those impatient by nature or habit or both. They tend to spend rather than to save. The great need and opportunity for education in thrift is manifest.


This is not the place to answer the many questions which arise in such an inquiry, such as, what is the effect of change in the rate of interest in stimulating or discouraging the accumulation or dissipation of capital?*11 What is the effect on the poor of the luxurious habits of the rich? Nor are we concerned with the other factors which influence the distribution of wealth but which do not involve the rate of interest. We are at present content merely to prepare the way for their answer by indicating the nature of the problem and the relation of the theory of interest to it.

Notes for this chapter

See Chapter I; also The Nature of Capital and Income, Chapter IX.
See my Mathematical Investigations in the Theory of Value and Prices. New Haven, Yale University Press, 1926.
This is, of course, highly theoretical; it assumes a competitive market free from legal and other restrictions.
See Cannan, Edwin, Theories of Production and Distribution. London, P. S. King & Son, 1903.
Pareto, Cours d'Êconomie Politique, Vol. II, Book III.
King, W. I., The Wealth and Income of the People of the United State, New York, The Macmillan Co., 1915.
Mitchell, W. C., King, W. I., Macaulay, F. R., Knauth, O. W., Income in the United States. New York, National Bureau of Economic Research, Inc., 1922.

Knauth, O. W., Distribution of Income by States in 1919. New York, Harcourt, Brace & Co., 1922.

Leven, Maurice, and King, W. I., Income in the Various States; Its Sources and Distribution, 1919, 1920, and 1921. New York, National Bureau of Economic Research, Inc., 1925.

Stamp, Sir Josiah, Wealth and Taxable Capacity. London, P. S. King & Son, Ltd., 1922. Also, British Incomes and Property. London, P. S. King & Son, 1916.
Rae, The Sociological Theory of Capital, Chapter XIII.
See Day, Clive. The Dutch in Java. New York, The Macmillan Co., 1904, Chapter X.
See Gonner, Interest and Savings.

Part IV, Chapter 16

End of Notes

21 of 34

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