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The Theory of Interest; Fisher, Irving
34 paragraphs found.
Part I, Chapter 1

In this indirect way, past costs can determine present values temporarily and until the prices of goods available are brought into conformity with the present costs of production through the operation of supply and demand. For example, the cost of producing woolen cloth declined very sharply after the close of the World War, but the price did not decline for many months because the new cloth made at less expense was not sufficient to meet the demand, hence the price remained above the new costs of production for a time. Again, the cost of making shoes advanced rapidly during the early years of the twentieth century, but the price of shoes did not advance pari passu with increased costs, because the supply of more cheaply made shoes was still large and for a time controlled the market price. In the same indirect way, many other influences affect the value of the services of any good, especially any alternative to those services. But none of these considerations affects the principle that the value of the good itself is the discounted value of the value (however determined) of its future services.


The student should also try to forget all former notions concerning the so-called supply and demand of capital as the causes of interest. Since capital is merely the translation of future expected income into present cash value, whatever supply and demand we have to deal with are rather the supply and demand of future income.

Part I, Chapter 3

This premium, that is, the terms of exchange of this year's income and next year's, may be said to depend, in brief, on the relative supply and demand of those two portions of the income stream; and this statement may be interpreted as including almost the entire impatience and investment opportunity theory of this book. But, like many brief statements, this supply and demand statement is crude and inadequate. Crude and inadequate notions beset this subject and some of them are so common and treacherous that it seems worth while, before proceeding with further analysis, to examine these notions in order to avoid falling into their pitfalls.


To say that the rate of interest is fixed by supply and demand is merely to state, not to solve the problem. *23 Every competitive price is fixed by supply and demand. The real problem is to analyze the particular supply and demand forces operative in determining the rate of interest.


Enough has already been said to show that an increase in the quantity of money in circulation tends to raise the price level and consequently to depreciate the value of the money unit. This depreciation in turn tends to increase the rate of interest. Yet, there is a very persistent belief that an increase or decrease in the quantity of money in circulation causes a decrease or increase in the rate of interest. This fallacy seems to be based on a confused interpretation of the general observation that the rate of interest generally rises or falls with a decrease or increase in the reserve ratio of banks. While it is true that if new money first finds its way from the mint into the banks, it tends to lower the rate of interest, this effect is temporary. The maladjustment between the money in banks and in circulation is soon corrected as the demand for loans overtakes the supply. As far as the total supply of money is concerned, if this is doubled in amount and prices are thereby, in the end, doubled too, there is double the money to lend, but borrowers will require double the amount of money. At the doubled prices they will need twice the money to make the same purchases. The demand is doubled along with the supply and the interest rate remains as before.

In Chapters XI and XII supply and demand curves will be derived from the principles of impatience and opportunity. It will also be shown that impatience is not to be associated with demand to the exclusion of supply, nor opportunity with supply rather than demand, nor vice versa.
Part II, Chapter 4

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.


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.

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.
Part II, Chapter 5

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.

Part II, Chapter 6

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 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.

Part III, Chapter 10

Expressing the problem with the aid of the graphic method, the determination of the rate of interest may be reduced to a simple problem of geometry, just as the problem of price may be shown by supply and demand curves.


This statement will be clear if we ask ourselves what would happen were we to suppose the "fixed" market rate to have been fixed too high, or too low. If we imagine the market rate to be very high, say 25 per cent, then, the bulk of individuals would try to lend and few would want to borrow. The aggregate of loans thus offered would exceed the demand and the interest rate would fall. Conversely, if the rate were too low, demand would exceed supply and the rate would rise. Since the total sums actually lent must equal, in the aggregate, those borrowed, the horizontal displacements of all the Q's in one direction must equal that of all the other Q's in the other direction. Some Q's, those of borrowers, are to the right of the corresponding P's. Others are at the left. As a group, they are neither. The average Q has the same longitude as the average P. The same is true as to latitude. In short, the geometric "center of gravity" of all the Q's must coincide with that of all the P's, in order that the loan market may be cleared.


These charts do, for the ideas they illustrate, what supply and demand curves do for the ideas illustrated by them.

§17. Relation to Supply and Demand


Some students familiar with demand and supply curves as applied to the loan market may feel that they can get their bearings better if the exact relation is shown between these and the "map" here used. Therefore, it seems worth while here to bridge the gap between these two sorts of representations just as, at the outset, the gap was bridged between the map and pictures of the income stream earlier in this book. We may readily and completely derive the curves of demand and supply from the map and the constructions which have been drawn on it.


Of course, at any given slope near the slope of the market rate, some individuals will have a right, and others a left, displacement, and at the market rate itself the two displacements are equal in the aggregate. This is true where the supply and demand curves intersect.


Evidently the map gives us the same relationships as the ordinary supply and demand curves and much more. The supply and demand curves, for instance, give us only the displacements, or differences in income position, as between P and Q, while the map gives the whole income position of both points. And while we can reconstruct, as above, the demand and supply curve from our map, we cannot reconstruct our map from the supply and demand curves.

Part III, Chapter 11

§11. Relation to Supply and Demand Curves


In §17 of Chapter X it was shown how supply and demand curves can be derived from the M line and the Wlines depicted in Chart 34. Supply and demand curves can equally well be derived from the M line, the O line and the W lines shown in Chart 38. A series of positions of PQ, with different slopes, gives us all the material needed, each slope giving a rate of interest and each horizontal spread between P and Q being the demand for loans (if Q is east of P) or supply of loans (if Q is west of P). The only difference is that P is not now fixed as in the first approximation, but shifts as PQ has different slopes.


It will be noted that the Opportunity line which embodies the technical or production elements in the problem has no more relation to the supply than to the demand, although this runs counter to the common notions that productivity rules one side of the market and time preference the other.


It will also be noted that the map gives us vastly more light on the analysis of interest than do the mere supply and demand curves. But even the map fails to give a complete picture because, in particular, it shows only two years. The truth seems to be that no complete visualization of this difficult problem is possible. The only complete symbolization which seems to be possible is in terms of mathematical formulas as in the next two chapters.

Part IV, Chapter 15

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 ofinterest, 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.

Part IV, Chapter 16

Because of these inventions, introducing economies which revolutionized industry, common stocks on the American exchanges have advanced in 1928 and 1929, so that the dividend yields of dividend paying stocks were lower than the interest yields of high grade bonds. As an example of the eagerness of the investing public to finance newly-evolving industries, the Daniel Guggenheim Fund for the Promotion of Aeronautics announced that it was no longer necessary to grant equipment loans to air-transport companies, because, it stated, the "investment public is now ready to supply the capital for enterprises of this kind." By the close of the third decade of the twentieth century America had already shot ahead of Europe in commercial aviation, and was operating more than eighteen thousand miles of airways, of which eight thousand miles were lighted for night travel. The New York Trust Company in its reports took note that airplane production for 1928 was about five times that of 1927, and that demand for almost every type of aviation market was rapidly expanding.

Part IV, Chapter 20

To the criticism that the consumption concept of income when used as the foundation of interest theory presents but a partial analysis of the supply and demand factors which are operative in determining interest rates, I make this reply: Interest rates are not a resultant of the supply of, and demand for, either capital goods or of capital values—sometimes conceived of as a loanable fund or funds, except as these signify the supply of and demand for income. An investment of capital, so called, is nothing more nor less than the sacrifice of income in anticipation of other, larger, and later income. It is a case of flexing the income stream, reducing it in the present or early future and increasing it in the remoter future. The income stream, so fundamental in the interest problem, includes incomes from all sources. It includes the value of the services of land, machines, buildings, and all other income-producing agents. Upon the value of these services, discounted at the prevailing rate of interest, the valuation of said land, machinery, buildings, and so on depends. What is properly called funds is this valuation of the income stream or portions of it. It should be evident that the approach to the problem of interest through the income stream and the supply of and demand for income gives to the problem the broadest possible basis.


But, although it is true, it is objected, that under the supply and demand analysis, an increase in the supply of a single commodity will lower its value, the same does not follow when applied to all goods. "Exchange values and prices are relations among goods. Increase the supply of one good and the ratio at which it exchanges for others or for money will change to its disadvantage. If, however, you increase at the same time the supplies of all goods, including gold, the standard money material, you affect simultaneously both sides of all ratios of exchange and consequently the ratios should remain substantially as before. It is just such an increase of goods of all sorts and descriptions that is denoted by Böhm-Bawerk's phrase, 'the technical superiority of present over future goods', or by the more familiar phrase 'the productivity of capital'. Admitting the physical-productivity of capital (and Fisher does not question it), the value-productivity of capital or, more accurately, an increase in the total value product as a consequence of the assistance which capital renders to production seems to me to follow as a logically necessary consequence.... Since there is nothing in the assumption that the productivity of all instruments is doubled that involves any serious change in the expense of producing the instruments, the productivity theorist certainly would claim that under these conditions there must be, if not a doubling, certainly a very substantial increase in the rate of interest." *91


I do not assume, except temporarily in the first approximation, that "income streams, like mountain brooks, gush spontaneously from nature's hillsides", and this is temporarily assumed, precisely as physicists temporarily assume a vacuum in studying falling bodies, or, to take a better but still imperfect analogy, precisely as, in treating supply and demand, we first assume a fixed supply before introducing the supply schedule or supply curve. This assumption gives place in the second approximation and the third approximation to the more complicated conditions of the actual world. My method of exposition is here, as usual, to take one step at a time, which means to introduce one set of variables at a time. All other things, for the time being, are assumed to remain equal. I realize that this is not the only method and that it may not be the best one, but it is at least a legitimate method.

Part IV, Chapter 21

But the more fundamental theory of interest presupposes a stable purchasing power of money so that the real and nominal rates coincide. In that case the rate is theoretically determined by six sets of equations or conditions: the two Opportunity Principles; the two Impatience Principles; and the two Market Principles. The last pair may be said to cover prima facie supply and demand.


The other two pairs represent the two sets of forces, one objective and the other subjective, behind supply and demand. The subjective pair expresses the influence of human impatience or time preference.

Appendix to Chapter XX

FRIDAY, DAVID. Factors which Determine the Future of the Rate of Interest: Economic Principles of Supply and Demand. Trust Companies, Vol. XXIII, July, 1921, pp. 9-12.