Part II: First Approximation

PART II. FIRST ApPROXIMATION CHAPTER V. ApPRECIATION AND INTEREST CHAPTER VI. TIMEPREFERENCE CHAPTER VII. FIRST ApPROXIMATION TO THE THEORY OF INTEREST (ASSUMING INCOME RIGID) CHAPTER V APPRECIATION AND INTEREST § 1 IN the four preceding chapters we have criticised those theories of interest which enjoy the greatest currency in present economic and business circles. Inasmuch as we .have found radical defects in all of them, our best course now is to formulatede novo what seems to us to be the cor rect theory. At the outset we need to note an oversight common to all the theories reviewed. In none of them is any account taken of the fact that the number expressing the rate of interest depends upon the monetary standard .of value in terms of which that rate of interest is expressed. To say that the rate of interest is 4 per cent. means 1 that the quantity of this year's goods which is worth $100 is equivalent to the quantity of next year's goods which is worth $104. In this statement we observe that the (( goods" which are considered are expressed not in their own special units, - pounds, bushels, yards, etc., -Jl"!:!,~",.!E:,,~~!~~ .2[.J~....,§,t~!!g~:rg~ ...Q,f."i"Y~!!!~; Th~,,··standard ... of..,..~alue... ch.Qs,en...Ia ~~p.~~~~ey. This money, the $100 and $104, is nomiO>nally'" exchanged; but actually it merely measures the "goods" which are exchanged. 'W:4~!!.-..~ !!!tt~l~:rl<l~,'~()O ~~i~.y~~~,J:rl()~ger t() .obtain _$lQ~o :next .yeftr, he is .really /~~cri~ciJJ.~n?t on~ 1J.undred dollars in mOI).ey,.])\It ()Il~ ht¥!'dr~<I~doIl~tS'. ,worth of goodssll~h as .. foo~l, cI9thing, .. bOQk~1 ()r .. pleas"tlr~t:rip~, .in . order .. tQ ()lJt.3,iIl.Il~~~_ ye3,~J:l0t 0:rl~ h~d.r~CJ. ,. ~~g.,. JQ!lr.dQJlar~ .. m}Jl()p.~y, .. J)~~_.():rl~..~~dr~gaIl9.

fOllr dollars' ..worth ofothergoo-ds."y41Qp._l!_~_4~,~!~~~. 1 See Glossary at end of this volume; also the writer's The Nature 0/ Capital and Income (Chap. XI), the nomenclature of which book is followed in the present work. 77 78 THE RATE OF INTEREST [CHAP. V Yet the fact that both sets of goods are measured in money introduces a monetary factor into the problem of interest. Interest.? being a premium in the exchange between the money·valuesof this year's and next year's goods, is there foritl,iot wholly an affair of goods. but is partly one of money. The relation of the rate of interest to goods will form the subject of subsequent chapters. The present chapter is devoted to a study of the relation which subsists between the rate of interest and the monetary standard in terms of which it is expressed. The monetary standard affects the rate of interest in so far as there is a chan e in the value of that standard in re erence to other standards. Could it always be as sumed that the monetary standard was invariable in value with reference to all goods, the rate of interest reckoned in money would be the same as though it were reckoned in terms of the goods themselves. But if money and goods are to change with reference to each other - in other words, if the money standard U appreciates" or "depreciates"

- the number expressing the rate of interest will be affected. § 2 The influence of monetary appreciation or depreciation on the rate of interest will be different according to whether or not that appreciation or depreciation is foreseen. ...If it., -is not foreseen, the appreciation of money necessarily in jures the debtor, because, the purchasing power of money being increased, the principal of his debt, when due, repre sents a larger quantum of goods than was anticipated when the debt was contracted. But if the appreciation is fore seen, any increased burden in the" principal" may be offset by a reduction in the rate of interest. This fact, strangely enough, has seldom been recognized. The assumption has been tacitly made that contracting parties are power less to forestall gains or losses due to an upward or down ward movement of the monetary standard. Yet no reason SEC. 2] APPRECIATION AND INTEREST 79 has been given to show that it is any more difficult to make allowance for a change in the unit of value than for a change in any other unit. If the unit of length were changed, and its change were foreknown, it is clear that contracts would be modified accordingly. Suppose, for instance, that a yard were defined (as possibly it once was) as the length of the king's girdle, and suppose the king to be a child.

Everybody would then know that the " yard" would probably increase with the king's age, and a merchant who should agree to deliver one thousand "yards" ten years hence would make his terms correspond to his ex pectations. It would be strange if, in some similar way, an escape could not be found from the effects of changes in the monetary yardstick, provided these changes were known in advance. To offset a foreseen appreciation, itl would only be necessary that the rate of interest be cor-,J' respondingly lower, and to offset a foreseen depreciation,f that it be correspondingly higher.1 <J If a debt is contracted optionally in either of two stand ards and one of them is expected to change with reference to the other, the rate of interest will by no means be the same in both. A few years ago, during the uncertainty as to the adoption or rejection of "free silver," a syndicate offered the United States government the alternative of some $65,000,000 of bonds on a 3 per cent. basis in gold, or on a 31 per cent. basis in "coin." Everyone knew that the additional i per cent. in the latter alternative was due to the mere possibility that It coin" might not continue at full gold value, but sink to the level of silver. If the alternative had been between repayment in gold and a not merely possible but actual-repayment in silver, the additional interest would obviously have exceeded t per cent.

• 1 For the history of the theory of appreciation and interest, see 4\ppendix to Chap. V, § 1.

80 THE RATE OF INTEREST § 3 [CHAP. V The relation between the rate of interest and the rate of a foreseen appreciation or depreciation of money may be readily illustrated. In order to illustrate the theory, we may imagine two specified standards of value diverging from each other, in either of which loan contracts may be expressed. Let the two standards be ...gg.l9:_,.~l:!d ... _w;b.~at, and let a bushel of wheat be first worth $1. If the two st'andards'did not diverge, that is, if the .price of wheat in terms of gold held good till next year, it is clear that the rate of interest in a gold contract and a wheat contract would be the same; if it were 4 per cent. in gold, it would be 4 per cent. in wheat also. This may be expressed as follows:If to-day 100 dollars is the equivalent of 100 bu. @ $1 per bu., then next year 104 dollars is the equivalent of 104 bu. @ $1 per bu. But let us suppose that the price of wheat rises from $1 to $1.01. We then readily see that: Whereas to-day 100dollars is the equivalent of 100bu. @ $1 per bu., next year 104 x 1.01 dollars is the equivalent of 104 bu. @ $1.01 per bu.

If we calculate out the 104 x $1.01, we shall obtain $105.04 as the Sllm which next year should be repaid in gold to be equivalent to 104bu. payable in wheat. In other words, if 4 per cent. is the interest in the wheat standard, its equiva... lent is 51 ~ 0 per cent. in the gold standard; or, again, if the rate of interest in wheat is 4 per cent., an appreciation of wheat of 1 per cent. is exactly offset by a rise of lIto per cent. in the rate of interest in gold. It is thus a matter of indifference whether, under our supposed circumstances, a man who borrows $1000 expresses his contract in gold and agrees to pay 5 T!O per cent. interest or translates the same contract into terms of wheat, borrowing the value of SEC. 4] APPRECIATION AND INTEREST 81 1000 bushels and agreeing to pay 4 per cent. interest. By the first form of contract he pays back $1000 of gold prin cipal and $50.40 of gold interest; by the second, he pays back the value of 1000 bu. as principal and of 40 bu. as interest. At the end of a year his debt by the one reckoning is $1050.40, by the other, 1040 bu., and these are equivalent.

It is to be noted that we have been regarding gold or wheat as standards of value and not as media of exchange. In either contract the actual liquidation need not be made eit~~r in actual gold or wheat. The speculator who sells wheat "short" comes very close to using., wheat as a standard,but not as a medium. The relative change in'the two 'standards may be spoken of either as an ~P.£~~!~~_!.Q!!..~.gt.JY4~~t_"I~I~!!Y~!r,,,.~.~.",,,.g~!?, ~~~~~,~~"-9:~E~~~~~.~~~2g'HQf",gQ!~l,,"~~!~~!Y~!~,;,,~2",Wg~"~~. We are not compelled to inquire which is the '~..~2~~.~~~~~'.~~~~g~; If we use the first of these two modes of expression, we may . say that since C?ge ~~s:ll~~~?-~Ilg~§iIlvft!~~J~?~~l~()~l.Q,!., ~h~~tJ;!~~..~p~r,~.Qiit'e.di",per·,-cent. ;'"if';~ ~se the second mode of expression, we may say a gold dollar has fallen in its wheat value from one bushel to t-S-.q. of a bushel, and has therefore depreciated by 1fT or .991 fT per cent.!

§ 4 In our numerical example, the ~EJ2r~~i~ti~~~~ll?e~,~~~~.) of one standard relatively to the other, and likewise the de-: preciation (.99T~T per cent.) of the latter standard relatively to the former, are not quite so great as the difference (11 60 per cent.) in the rate of interest. This slight disparity must always exist so long as the rate of interest is reckoned annually or discontinuously. But the shorter the period of "compounding," the less the disparity; that is, the more 1 For the general formula connecting the rates of interest in any two diverging standards, see Appendix to Chap. V, § 2. G 82 THE RATE OF INTEREST [CHAP. V nearly equal are the two magnitudes: (1) the rate of divergence between the two standards, whether measured as appreciation or depreciation, and (2) the difference between the rates of interest in the two standards. When the rates are" reckoned continuously," the disparity dis appears altogether. 1 § 5 Having established the truth and generality 2 of the principle connecting the rates of interest in two standards and the appreciation of one of them relatively to the other, we next inquire what limits, if any, are imposed on the three magnitudes; namely, the two rates of interest in the respective standards and the rate of relative apprecia tion between the standards. From what has been said it might seem that, when the appreciation is sufficiently rapid, the rate of interest in the upward-moving standard, in order to equalize the burden, would have to be zero or even negative. For instance, if the rate of interest in gold is 4 per cent., and if wheat appreciates relatively to gold at 4 per cent. also, the rate of interest in wheat, i{perfectly adjusted, would have to sink to zero! But we know that zero or negative interest is practically impossible. Wheat would be hoarded, and this action would effectually pre Vent the rate of interest in terms of wheat from passing below the zero mark. But this very limitalliw on t.he possible rate of interest carries with it a limitation ~ 1 For the mathematical demonstration of this proposition, see Appendix to Chap. V, § 3. For the significance of "continuous"

reckoning, see The Nature 01 Capital and Income, Chap. XII; also Chap. XIII and Appendix. We have here an example of the fact there observed that, considered mathematically, the analytical rela tions connected with the rate of interest are simplest when that rate is reckoned continuously. Since, however, the rate of interest reck oned continuously is so rarely used in practice, we shall adhere, in the remainder of our discussion, to the system of annual reckoning. 2 For mathematical proofs, numerical illustrations, and formulre . see Appendix to Chap. V, §§ 4 to 9 inclusive.

SEC. 5] APPRECIATION AND INTEREST 83 possible rate of appr~ja,tjon. If interest on money, for instance, were 4 per cent., it would be impossible for wheat to have a foreknown appreciation of 10 per cent. per an num relatively to money; for it would immediately be bought and held for the rise. It would therefore rise a1 Q!.tce to the discounted value of its future expected value, and its succeedin ns~ ~ouId not exceed the ra.te.o~ inter-J( est.1 In other words, If Interest IS per cent., It IS Impos sible that wheat should be worth $1 to-day and $1.10 next year foreknown to-day. For, under these circumstances, holding for a rise would give a sure return of 10 per cent. The lowest price of present wheat possible would be the Sl.10 discounted at 4 per cent., or about $1.06. At this figure the rate of interest in gold is 4 per cent., but in wheat it is zero per cent. We should have:To-day $106 equivalent to 100 bu. @ $1.06 per bushel.

Next year $110 equivalent to 100 bu~ @ $1.10 per bushel. and the two alternative forms of contract would be: for $106 this year $110 are returned next year, or (about) 4 per cent., and 19r 100 bu. this year 100 bu. are returned next year, or zero per cent. Every case of holding wheat or land or other wealth for a rise may be, in fact, regarded as a case of zero interest in terms of these articles as standards of value. The same principle which prevents the rate of interest in wheat or land from being negative also prevents a negative interest in money. A lender, rather than ex change $101 to-day for $100 next year, would hoard his $101. It is important to emphasize the .fact that the limits imposed on the rates of interest and appreciation come from theJ?,~~~~~,~~i~~.?~ ~?~r~i,~~~?Il~)T)!~Pl1()llt19~S. Jf_ money were '3, perisha15lecommodity,' like fruit the limit_-'"'W";""·~~··~<'·"-,;,;"" ..,;~" ..."",_,",~",,,v"Ac;'_'''_''.'V'''''''''",N."",,,~...,,~,,,,,l,,•.,-.;,,<,,,-,,;,,,.,0'"%~.'.';_''''''''''''' ~~~~~~1?~~dliiTo'~the r~~~~~..,,,=~!..,_,..,~~g.~~.!!,~".,,,,,~~~~~!~.!~,~,.

f;,l";~""'f;':~.''>\!i.!:i:(;;i:t;'''....:-~4f,i.~:.'-:,...#''''~;~>t~r'~'',...1'':'';''-%'''';''''.i,''J;1i:"_,_.";,4C·-~__ -" 1 See The Nature oj Capital and Income I on the rate of rise of U dis count curves," Chap. XIII.

84 THE RATE OF INTEREST [CHAP. V One can imagine a loan based on strawberries or peaclles, contracted in summer and payable in winter, with negative interest. 1 Or, again, we may define a "dollar" as consist ing of a constantly increasing number of grains of gold, the weight of which is to double yearly. Such "dollars" cannot be hoarded without necessarily becoming fewer with time, and if interest in the old fixed-weight dollars is 5 per cent., it will be minus 47! per cent. in the new dollars of increasing weight; for he who borrows $100 (2580 grains) to-day will need to pay back only $52.50 (2709 grains) one year hence. § 6 The relation existing between interest and apprecia-j' tion implies, then, that the "rate of interest" is always' relative to the standard in which it is expressed. The fact that interest in money is high, say 15 per cent., may merely indicate that general prices are expected to rise at the rate of 10 per cent., and that the rate of interest in terms of goods is not high, but only 4! per cent.

We thus need to distinguish between interest in terms of money and interest in terms of goods. The first thought suggested by this fact is that the rate of interest in money is "nominal," and that in goods" real." But this distinc tion is not sufficient, for no two forms of goods maintain, ~:r are expected to maintain, a constant price ratio tow ard each other. There are therefore iust as many rates of interest in goods as there are forms of goods diverging in. value. . Is there,. then, no absolute standard of value, as utility, in terms of which "real" interest should be expressed? To this we reply that any absolute standard is absolute only for a particular indiviclua1.2 The fact that a dollar 1 Cf. Bohm-Bawerk, The Positive Theory of Capital, pp. 252, 297; Landry, L'Interet du Capital, p. 49. 2 Marshall, Principles of Economics, Vol. I, 3d ed. New York (Macmillan), 1895, p. 198, and Royal Commission on Depression of SEC. 6] APPRECIATION AND INTEREST 85 is a smaller unit to a millionaire than to a poor laborer ' has a~ its consequence that, as the millionaire grows poorer his dollar grows larger, while as the laborer grows richer his dollar grows smaller. On account of such changes in personal fortunes, the dollar will be constantly' appreciat ing and depreciating in different degrees among different men and classes. But if the dollar appreciates in terms of absolute utility in the eyes of one man, and depreciates.

in a correspondingstandard of utility in the eyes of another, the rates of interest in the men's" absolute" standards must be different in the two cases; for the rates of in terest to both persons in terms of objective units, such as money, must by the operation8 ot the market be the same. If, in the gold standard, $100 to-day is equivalent to $104 due one year hence, both for him who is growing richer and for him who is growingpoorer, the rates in terms of ab solute utility will be different for the two men. Thus, sup pose that the dollar to-day is worth to each man one'unit of utility, but that one year hence, to the man who is growing richer, the dollar will be worth slightly less -let us say, -r\\of one unit of utility. Consequently,when he considers $100 to-day as equivalent to $104 due next year, he is' virtually contrasting in his mind 100 units of utility to-day with 104 x .99, or about 103 units of utility next year. His rate of interest, therefore, in terms of absolute utility, is 3 per cent. Similar .calculations for the man whose for-' tunes were declining, and to whom the marginal utility of the dollar was increasing 1 per cent. per annum, would show that whereas $100 to-day is equivalent in his esti mation to $104 next year, 100 units of present utility are equivalent to about 105 units of next year's utility. To him, therefore, the rate of interest in the absolute standard would be 5 per cent.

Trade, 1886, p. 423; the writer's "Mathematical Investigations in the Theory of Value and Prices," Transaction8 01 the Connecticut Academy, New Haven, 1892, pp. 11-23,86-89; A. C. Pigou, "Some Remarks on Utility," Economic Journal, March, 1903, p. 60.

86 THE RATE OF INTEREST [CHAP. V From this explanation it is very evident that if we seek to postulate an absolute standard of value in which the rates of interest are to be reckoned, we cannot fix one which will be uniform for all the individuals in the market. Supply and demand operate only to make objective rates equal. Hereafter we shall confine ourselves to a study of objective interest; and since the objective standard usually employed is money, the rate of interest, unless otherwise specified, will be taken in this book to mean the rate of interest in terms of the money standard. As was observed at the beginning of this chapter, it makes a great difference whether the relative divergence of the different standards is or is not known in advance. In actual fact it usually happens that future appreciation or depreciation is neither entirely foreseen nor entirely unforeseen. An intermediate condition is usually main tained. When prices are rising, the rate of interest is usually high, but not as high as it should be to compensate for the rise; and when prices are falling, the rate of interest is usually low, but not as low as it should be to compensate for the fall. The facts as they are actually found in the market will be given in Chapter XIV.

CHAPTER VI TIMEPREFERENCE §1 IN the last chapter we saw that the number expressing the rate of interest depends on the standard of value in which present and future goods are expressed. We saw how 'the rate of interest in one standard is to be derived from the rate of interest in any other standard. It is clear that'this translation of the rate of interest from one standard to another does not constitute a com plete determination of the rate 0/ interest in any standard whatever; for it assumes that the rate in some one standard is already known, and merely enables us on the basis of this known rate to calculate the rates in other standards. The case is similar to the conversion of temperature from the Fahrenheit system into the Centigrade or the Reaumur, which clearly does not determine temperature itself; or, to the conversion of the price of cotton in dollars into its price in shillings or francs, which does not determine the price.of cotton itself. ' The relation which has been shown between appreciation (or depreciation) and interest therefore solves merely the problem of translating the rate of interest from one standard into another; but the problem of determining 'the rate of interest is still left untouched. This problem - the problem of determining the rate of interest - now demands attention.

In our theory we shall find a place for each of the partial truths which we have found in the foregoing review of the productivity, cost, and agio theories. Our presentation may, in fact, be classified as a form of the agio theory, differ ing from Bohm-Bawerk's version chiefly by the omission of 87 88 THE RATE OF INTEREST [CHAP. VI the "technical advantage of present over future goods," and from agio theories in general by the explicit introduc tion of the income-concept. The income-concept plays the central role. The theory of interest bears a close resemblance to the theory of prices, of which, in fact, it might be regarded as a part; for, as was shown in The Nature of Capital and J} Income, Chap. XII, the !!1te of interest expresses ~ prk.e J..n 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 on a psychological or sub jective element, - their comparative marginal utility, so in the theory of interest the rate of interest, or the pre mium in the exchange between present and future goods, is based on a subjective prototype; namely, the preference for present over future goods.

This "time-reference" is the central fact in the theory of interest. 1 I t IS what ae calls the "effective desire for accumulation," and very nearly what B6hm-Bawerk c~lls the" perspective undervaluation of the future." 2 It is the (percentage) excess of the present desirability 8 of present goods over the present desirability of an equal amount of future goods. 1 Cf. Bullock, Introduction to the Study of Economics (Silver, Bur dett & Company), 1900, p. 390; Fetter, Economics, New York (Century Co.), 1904, p. 135. 2 At least, as applied to objective goods. Bohm-Bawerk applies it to subjective pleasures, which he translates into objective goods at a ratio depending on the" relative provision for present and future needs." As we have seen in § 6 of the preceding chapter, it is possible to translate the rate of interest (and, it might have been added, the rate of preference) from an objective to a subjective standard, or vice versa, provided we know the rate at which the two standards are diverging. We prefer to base our reasoning in this book on rates of preference and rates of interest expressed in terms of an objective, monetary standard. As we have seen, the rate of preference ex pre.ssed in terms of subjective standards will be different for different individuals.

3 Or "ophelimity," or "utility." See The Nature oj Oapital and Income, Chap. III.

SEC. 2] TIMEPREFERENCE § 2 89 But 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.1 It is true that present machines are preferred to future machines; present houses to future houses; land possessed to-day 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 (whether capital-wealthor capital-property)is pre ferred to future capital, this preference is really a prefer ence for the income of the first capital as compared with. the income of the second. The reason we would choose a present fruit tree rather than a similar tree available in ten years is that the fruit production of the first will occur earlier than that of 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 begin six months earlier in one ca~e than in the other. In short, capital wealth available early is preferred to· capital-wealth of like kind available at a more remote time, because the income of the former is available earlier than the income of the latter. For the same reason, early capi.tal-property is preferred to late capital-property of the same description.

$or proJi,.ertyis merely a claim to future incomei. and the earlier the property is acquired, the earlier will the in come accrue, of the right to which the property consists. Thus, all timepreference resolves itself into the prefer-\ ence for early income over late income. Moreover, the preference for present income over future income resolves itself into the preference for present final income over future final income. The income from an article of capital which 1 For definitions of these terms, see Glossary.

90 THE RATE OF INTEREST [CHAP. VI consists Inerelyof an "interaction" 1 or "preparatory ser vice" 2 is desired for the sake of the final income to which that interaction paves the way. We prefer present bread baking to future bread baking because the enjoyment of the resulting bread is available earlier in the one case than in the other. Present weaving is preferred to future weaving, because the earlier the weaving takes place the sooner will the cloth be manufactured, and the sooner will the clothing made from it be worn by the consumer. "When, as is usually the case, exchange intervenes be tween the weaving and the use of the clothes, the goal in the process is somewhat obscured by the fact that the manufacturer feels his preference for present weaving over future weaving, not because the clothes will be more early available, but because he will be enabled to sell the cloth earlier. To him, early sales are more advantageous than deferred sales, because the earlier the money is received the earlier can he spend it for his own personal uses,-the shel ter and the comforts of various kinds constituting his real income. It is not he, but his customers, those who buy the cloth he manufactures, that base their preference for present cloth over future cloth on the earlier availability of the clothes which can be made from it. But in both cases the mind's eye is fixed on some ultimate enjoyable income to which the interaction in question is a mere preparatory step. We thus see that all preference for present over future goods resolves itself, in the last analysis, into a preference for early enjoyable income over late enioyable income. This simple proposition would have received attention before had there been at hand a clear-cut con cept of income.

§ 3 In The Nature 01 Capital and Income 3 it was shown that income ultimately consists of the stream of conscious 1 See Glossary. 2 See The Nature of Capital and Income, Chap. IX. 3 Chap. X.

SEC. 3] TIMEPREFERENCE 91 ness. Or, if we prefer to stqp just short of this subjective income, we may say that income consists of the objective services which.impinge upon our persons and are on the point of producing the subjective effects on consciousness. In short, the income-stream consists of nourishment, cloth ing, shelter, amusements, the gratification of vanity, and other miscellaneous items. It is this income-stream upon which attention now centers. Henceforth, instead of speaking vaguely and loosely of the preference for present "goods" over future "goods," we shall speak of the prefer ence for present enjoyableincome over future enjoyablein come. "Present" and "future" are, of course, used in a comparative sense only; -in a more accurate statement we should substitute U early" and U deferred." It should be noted that the preference for present over future goods, when thus reduced to its lowest terms, rids the values of the contrasted present and future goods of the interest element. When any other goods than enjoy able income are considered, their values already imply a rate of interest. When we say that interest is the premium on the value of a present house over that of a future house, we are apt to forget that the value of each house is itself based on a rate of interest. We have seen 1 that the price of a house is the discounted value of its future income. In the process of discounting there lurks a rate of interest.

The value of houses will rise Of fall as the rate of interest falls or rises. Hence, when we compare the values of present and future houses, both terms of the comparison involve the rate of interest. If, therefore, we undertake to make the rate of interest depend on the relative preference for present over future houses, we are making it depend on two elements, in each of which it already enters. The same is true of all ~apital, and also of those items of income which we have called interactions; for the value of an interaction is the discounted value of the ultimate income 1 See supra, Chap. II, and The Nature 01 Capital and Income, Chap. XIII.

92 THE RATE OF INTEREST [CHAP. VI to which that interaction leads. We could not rest satisfied in the statement that interest is the premium on the value of present tree-planting over that of future tree planting; for the value of each tree-planting itself depends on the rate at which the future income from the tree is discounted. But when present ultimate income is com pared with future ultimate income, the case is different, for the value of ultimate income involves no interest what ever. We see, therefore, that the reduction of the problem of interest to a comparative value of present and future enjoyable income avoids the difficulty of making interest depend on magnitudes which themselves depend directly on interest. § 4 Having seen that timepreference is really a preference for early enjoyable income compared with remote enjoy able income, we next note that this preference depends on the entire future income-stream, that is, the amount of 'I income and the manner in which it is distributed in time.

l It depends on the relative abundance of the early and k remote incomes - or what we may call the time-shape of "..: '. the income-stream. If future income is particularly abundant, its possessor would evidently be willing to sacrifice a large amount of it for the sake of a relatively small amount of present income.1 Thus, in winter, the possessor of a strawberry patch might be willing to sell two boxes of strawberries, due in six months, for one available to-day, while in strawberry season he might, on the contrary, be 1 It is noteworthy that, though lacking any definite theory of income, those writers who have made the most successful analysis. of the rate of interest have, in substance, made it depend, to some extent, at least, on income. Thus Bohm-Bawerk, as has been observed, gives as one of the "three circumstances" affecting the "preference for present goods" the It relative provision for present and future"; and Landry virtually states the same relation, on p. 55 of L' Inter~t du Oapital.

willing to give up two boxes of his then abundant crop for the right to one bqx in the succeeding winter. It is, therefore, not necessary here to distinguish, as Bohm-Bawerk does, between the principles which lead to the existence of interest and those which regulate the rate of interest; for to determine the. rate of interest will include the determination of whether the rate must necessarily always be greater than zero. As a matter of fact, the rate I may theoretically be negative, ,as in the case just mentioned . 1 of strawberries in strawberry season, or in the case cited bycJ:t w-t ~ ! Bohm-Bawerk himself, of ice in winter. The reason such vVvt ~,a negative interest is not actually encountered in the market.~""t"'" ,I is that perishable articles such as ice and strawberries are I ~~ never used as standards of value. We express our rates ~ ~ of interest in money,.even if our contracts relate to ~ . , I strawberries or ice. But money possesses durability, and may be hoarded without loss. This explains why the rate of interest in terms of money can never be negative.1 The proposition that the preference of any individual for present over future income depends upon his pro spective enjoyable income corresponds to the proposition in the theory of prices, that the marginal utility of any article depends upon the quantity of that article; both proposi tions are fundamental in their respective spheres.

When it is said that the timepreference of an individual depends on his enjoyable income,.it is meant that the rate of preference for, say, $100 worth of this year's enjoyable income over $100 worth of next year's enjoyable income depends upon the entire character of the individual's in come-stream. An income-stream is made up of a large nllmber of different elements, some of which contribute to nourish ment, others to shelter, others to amusement, etc. In a conlplete enumeration of these elements, we should need to distinguish the use of each different kind of food, the 1 See Supra, Chap. V, §5. SEC. 4] TIMEPREFERENCE 93 94 THE RATE OF INTEREST [CHAP. VI gratification of every variety of human want. Each of these constitutes a particular filament of the income stream, extending from the present out into the indefinite future and varying at different points of time in respect to size and probability of attainment. A man's rate of I timepreference, therefore, depends on the size and prob ability at various moments of the entire collection of income-elements. For the graphic representation, how- ~ ever, of size and distribution in time, it is simpler to lump together these innumerable elements of income, expressed in terms of money. We may say, therefore, that an indi vidual's timepreference depends on the following four elements:1. On the size of the income-stream.

2. On its distributionin time,-according as it accrues evenly or unevenly, and if unevenly, according to the periods at which it is expected to be relatively abun dant and the periods at which relatively scarce. 3. On the compositionof the income-stream,-what part consists of nourishment, what part clothing, what part shelter, etc. 4. On the probabilityof the income-stream and its con stituent elements. We shall consider these in order. § 5 Our first step, then, is to show how a person's time preference depends on the size of his income. In general, it may be said that the smaller the income the higher is\ " the preference for present over future income. It is truet ~~', that a small income implies a keen appreciation of future~: wants as well as of immediate wants. Poverty bears down heavily on all parts of a man's life, both that Wllich is imSEC. 6] TIMEPREFERENCE 95 mediate and that which is remote. But it enhances the utility of immediate income ·even more than of future in come. This result is p..!!'rtly ration~ because of the im portance, by supplying present needs, of keeping up the continuity of life and the ability to cope with the future; "

and OO:,!t1lirratio~l, because th~ pressure of present needs ~ blinds one to the needs of the future. As to the rational side, it is clear that present income is absolutely indispen sable, not only for the present, but even as a precondition to the attainment of future income. "A man must live." Anyone who values his life would prefer to. rob the future for the benefitof the present, so far, at least, as to keep life going. If one has only one loaf of bread he would not preserve it for next year; for if he did he would starve in the meantime. A single break in the thread of life suffices to cut off all the future. And not only is a certain mini mum of present income necessary to prevent starvation, but the nearer this minimum is approached the more precious does present income appear, .relatively to future income. As to the irrational side, the effect of poverty is oftenI' to relax foresight and selfcontrol and tempt one to "trust · to luck" for the future, if only the all-absorbing clamor of present necessitiesis satisfied.

We see, then, that a low income tends to produce a high timepreference, partly from lack of foresight and selfcon trol, and part1y from the thought that ~rovision for the. ~resent is necessary both for itself ~nd for the future as well. § 6 We come next to the influence upon timepreference of the distribution of income in time - the time-shall!of the income-stream. The concept of the time-shape of one's income-stream is fundamental in the following chapters. Four different type.s.. of timE(=Sha.pemsM be distinguished: 96 THE RATE OF INTEREST [CHAP. VI uniform income, as represented in Figure 2; 1 increasing income (Fig. 3) ; decreasing income (Fig. 4) ; and fluctuating FIG. 2. income (Fig. 5). The effect of possessing an iucreasing in ~s to make the preference for present over future FIG. 3. income higher than otherwise, for it means that present income is relatively scarce and future income abundant.

FIG. 4. A man who is now enjoying an income of only $1000 a year, but expects in ten years to be enjoying one of $10,000 a year, will prize a dollar to-day far more than a dollar due ten years hence. He may, in fact, borrow 1 In these curves, time is represented horizontally and rate of flow of income vertically, as in The Nature 01 Capital and Income, Chap. XIII.

SEC. 6] TIMEPREFERENCE 97 money to eke out this year's income, and make repayment, 1ft!~by sacrificing from the more abundant income ten years t later. Reversely, a .radually decreasing income, making, ( . as it does, present income re a Ively abundant and future income scarce, tends to reduce the preference for present as compared with future income. A man who has a salary of $10,00Q at present, but expects to retire in a few years on half pay, will not have a very high preference " for present in'come over future. He will want save . from his present abundance to provide for coming needs. TIle extent of t4ese effects will of course vary greatly with different individuals. Corresponding to a given ascenclFIG. 5. ing income, one individual may have a preference of 10 per cent., and another only 4 per cent. What we need here to emphasize is merely that, given a descending instead of an ascending income, both of these individuals would experience a reduction of time~preference, -the first, say, to-S per cent. and the second, say, to 2 per cent..

If we consider the combined effect on timepreference of . both the size and time-shape of income, we shall observe / that those with ~mall inco!llilli.J1r~ much more sensitive to , time-shaBe in their feeling of timepreference than ar~ tliOSe with large incomes. For a poor man, a very Sligh~. stinting of the present suffices to enhance enormously his ' preference for present over future income; and reversely, i a very slight increase in his present income will suffice to J H 98 THE RATE OF INTEREST [CHAP. VI enormously lessen that preference. A rich man, on the other hand, requires a relatively large variation in the '. comparative amounts of this year's and next year's in come to suffer any material change of timepreference. It is clear that the dependence of timepreference on time-shape of income is practically identical with what B6hm-Bawerk calls the "first circumstance" making for the superiority of present over future goods: 1 "The first great cause of difference in value between present and future goods consists in the different circumstances of want and provision in present and future. • •• If a person is badly in want of certain goods, or of goods in general, while he has reason to hope that, at a future period, he will be better off, he will always value a given quantity of immediately available goods at a higher figure than the same quantity of future goods."

§ 7 We come next to the influence of the composition of the income-stream on the timepreference of its possessor. An income worth $5000 may, for one individual, comprise 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-element in their incomes than those of another. These differences will have an influence in one direction or the other upon the timepreference. Diminution of anyone constituent of income would have an effect upon the timepreference similar to the effect of diminution of income in general. A decrease of the food element would be felt especially, both because this element usually forms a considerable part of income and because it is a prime necessity. Were we to pursue the subject in detail, we should need to resolve a person's income into the elements of which it is composed, -nourishment, shelter, clothing, and other gratifications. As we have seen, the income-stream is a complex magnitude consisting of a large number of sepal The Poaitive Theory of Capital, p. 249.

SEc.B] TIMEPREFERENCE 99 rate filaments, one for each separate constituent. Any individual's rate of preference depends on this complex magnitude in its entirety. Theoretically a change in any of these individual partial income-streams will in fluence the rate of preference. A bread famine, a large wheat crop, the outlook for the fuel supply, electric light service, shoes, or diamonds, all should be taken into ac count ina statement designed fully to cover the influence of the income-stream upon timepreference. It is not necessary to formulate the concept of "com position" .of an income-stream in such a way as to divorce it from the concepts of size and time-shape; for the com position of an income-streamis included in a statement of the size and time-shape of each filament of which that income-strearrl consists. We content ourselves by con... sidering all these· elements of income lumped together in a single sum of money value. We need not here concern.

ourselves with the principles which govern the valuation I of the sum. These principles constitute the theory of. Uft~ I prices, not of interest; and these prices, as we have I,..{.. ~~ already observed, being prices of final or enjoyable 1;. ~ I '6 i elements of income, do not, like the prices of capital ~:- '04. 1 or of interac~ions, emba:rrass us by dire.ct dependence on ~~~ the ;ate of Interest WhIch we a:e ~eking to solve. As- ~A ,J-, ~ Burning,then, the elements of which Incomes are composed ~vy ! to be adjusted according to the principles which regulate · ! prices, we shall hereafter· usually treat an income-stream as a homogeneous quantum expressible in terms of gold or some other monetary standard. Our task is therefore reduced to answering the question: Enjoyable incomesbeing expressed in terms of money, what determines the rate of interest in terms of this same money? § 8 We come finally to the element of risk. . Income, being future,is alwayssubjectto some uncertainty, and this un100 THE RATE OF INTEREST [CHAP. VI J ; certainty must naturally have an influence on the rate of I timepreference of the possessor. We have seen that time \'preference is the preference for $1 certain added to immediate income over $1, also certain, added to income one year hence. The influence of risk on timepreference therefore means the influence of uncertainties in the anticipated income of an individual upon his relative valuation of present and future small increments of in come, both increments being certain. The manner in which risk operates upon timepreference will differ accord ing to the particular periods in the future to which the risk applies. If the possessor of income regards the income of the immediate future as fairly well assured, but fears the loss of income in more remote periods, he may be aroused to a high appreciation of the needs of that rell10tefuture and save from his present certainabundance in order to provide for the later possible scarcity. Income in which this sort of risk exists tends, therefore, to produce a low rate of timepreference for income which is immediate and cer tain as compared with income which is remote and uncer tain. In actual fact, such a type is not uncommon. The remote future is usually less known than the immediate future. This means that the risk connected with distant income is greater than that connected with income near at hand. The chance of disease, accident, disability, or death is always to be reckoned with, but under ordinary circumstances is greater in the remote future than in the immediate future. Consequently there is usually a ten dency toward a low timepreference. This tendency is expressed in the phrase to "lay up for a rainy day."

But the influence of risk is not always in the direction of lowering timepreference. Sometimes the relative un certainty is reversed, and immediate income is subject to higher risk than remote income. Such is the case in war or other temporary threat of misfortune. Such is also the case when an individual is assured a permanent position with a salary after a certain time, but in the meanSEC. 8] TIMEPREFERENCE 101 time 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 may, instead of applying especially to remote periods or espe cially to immediate periods, apply to all alike. Such a con~ dition largely explains why salaries and wages are lowe than the average earnings of those who work for themselves. Those who choose salaries rather than profits are willing to accept a low income in order to get rid of a precarious, one. Since a risky income, if the risk applies evenly to all parts of the income-stream, is nearly equivalent to a low income, and .since a low income, as we have seen, tends to create a high timepreference, risk, if u~iformly distributed in time, must tend ~o raise timepreference.

We see, then, that risk tends in some cases to increaseI' and in others to decrease the rate of timepreference. But,i there is a common principle in all these cases. Whether the result is a high or a low timepreference, the primary fact is that the risk of losingthe incomein a particular period of time operates as a virtual impoverishment of the income in that period, and hence increases the estimation in which it is held. If that period is a remote one, the risk to which it is subject makes for a high appreciation of re mote income; if the period is the immediate future, the risk makes for a high appreciation of immediate income; if the risk is in all periods of time, it acts as a virtual de crease·of income all along the line. There are, however, anomalous individuals in whom caution is.absent or perverted. Upon these, risk will have quite the opposite effects. Some persons, who see great speculative chances in the remote future, may treat that future as though it were especially well-endowed,and there fore be willing to sacrifice a large amount of their "great expectations" in the future for the sake of a relatively small addition to their present income. In other words, they will have a high timepreference. The same individ uals, if receiving an income which is risky for all periods 102 THE RATE OF INTEREST [CHAP. VI of time alike, might have, as a result, a low instead of a high timepreference.

The income to which risk applies may be either the in come from articles of capital external to man, or the income from man himself. In the latter case the risk of losing the income is the risk of death or invalidism. This risk the uncertainty as to human life and health - differs somewhat from the uncertainty of income dependent on objective capital; for the cessation of life not only produces a cessation of income from the human machine, but a ces sation of the enjoyment of all income whatsoever. For persons who have children whose future welfare they have at heart, this consideration loses much of its force. A man with wife and children is willing to pay a high insurance premium in order that they may continue to enjoy an income after his death, while an unmarried man, or a man who cares only for self-indulgence and wishes to "make the day and the journey alike," will not try to con tinue the income after his death. Uncertainty of life in the latter case is especially calculated to produce a high degree of timepreference. Sailors offer a good example. They are natural spendthrifts, and when they have money use it lavishly. The risk of shipwreck is constantly before them, and their motto is, "A short life and a merry one."

The effect of risk, therefore, is manifold, according to the degree and range of application of risk to various periods of time; according to the cautious or incautious character of the individual; according to whether or not the risk in question applies to human life, and if so, according to whether or not the individual's interest in the future ex tends beyond his own lifetime. The manner in which these tendencies operate upon the rate of interest will be discussed in Chapter XI. § 9 The proposition that the preference for present over future income depends upon the income, its size, timeSEC. 9] TIMEPREFERENCE 103 shape, composition, 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 utility of 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 timepreference on income is of most importance, for timepreference is a preference for income.

It is in the same way that the dependence of the marginal utility of bread on the quantity of bread is more important than its dependence on the quantity of some other com modity, such as Qutter. As to the dependence of this time preference for income on other factors than that income, these otherfactorsmay convenientlybe regardedas affect ing the" form of the function" whichexpresses its depend ence on income. In this light may be considered the influence of "the personal equation." It is clear that the rate of timepreference which corresponds to a specific income-stream will not be the same for everybody. One man may have a timepreference of 5 per cent. and another 10 per cent., although both have the same income. The difference will be due to the personal characteristics of the individuals. These characteristics are chiefly five in number: 1 (1) foresight, (2) selfcontrol, (3) habit, (4) ex pectation of life, (5) interest in the lives of other persons.

We shall take these up in order. (1) First, as to foresight. Generally speaking, the greater the foresight, the less the rate of time-reference ~ vice versa.2 In the case 0 prImItive races and uninstructed 1 Cf. Rae's Sociological Theory 01 Capital, p. 54. Also Bohm Bawerk, The Positive Theory oj Capital, Book V, Chap. III. 2 To be exact, we should observe that lack of foresight may either increase or decrease timepreference. Although most persons who lack foresight err by failing to give due weight to the importance of futur~ needs, or, what amounts to the same thing, by overestimating the provision existing for such future needs, cases are not lacking in which the opposite error is committed; that is, the individual exagger ates the needs of the future or underestimates the provision likely to be made for them·. In order not to complicate the text, only the former 104 THE RATE OF INTEREST [CHAP. VI classes of society, the future is seldom considered in its true proportions. The story is told of such a person that he would not mend his leaky roof when it was raining, for fear of getting more wet, nor when it was not raining, be cause he did not then need shelter. Among such persons, the preference for present gratification is powerful because their comprehension of the future is weak. In regard to foresight, Rae states: 1_ "The actual presence of the immediate object of desire in the mind, by exciting the attention, seems to rouse all the faculties, as it were, to fix their view on it, and leads them to a very lively conception of the enjoyments which it offers to their instant pos session. The prospects of future good, which future years may hold out to us, seem at such a moment dull and dubious, and are apt to be slighted, for objects on which the daylight is falling strongly, and showing us in all their freshness just within our grasp.

There is no man, perhaps, to whom a good to be enjoyed to-day, would not seem of very different importance, from one exactly similar to be enjoyed twelve years hence, even though the arrival of both were equally certain." The sagacious business man represents the other ex treme; he is constantly forecasting. These differences in degrees of foresight produce corresponding differences in the dependence of timepreference on the character of in come. Thus, for a given income, say $1000 a year, the reckless might have a timepreference of 10 per cent., when the forehanded would experience a preference of only 5 per cent. In both cases the preference will depend on the size of the income, being higher the lower the income; but the particular rates corresponding to a particular income in the two cases will be entirely different. Therefore the rate of preference, in .general, will be higher in a com munity consisting of reckless individuals than in one consisting of the opposite type.

and more common error will be hereafter referred to when" lack of fore sight" is mentioned. But the reader may in each such case readily add the possibility of the contrary error. 1 Sociological Theory of Capital, p. 54.

SEC. 9] TIMEPREFERENCE 105 (2) We come next to ~Q9Dtrol This trait, though distinct from foresight, is usually associated with it and has very similar effects. Foresight has to do with think ing, selfcontrol with willing. A weak will usually goes with a weak intellect, though not necessarily, and not always. The effect of a weak will is similar to the effect of inferior foresight. Like those workingmen who cannot carry their pay home Saturday night, but spend it on the way in the 'grogshop, many persons cannot deny themselves any present indulgence, even when they know definitely what the consequences will be in the future. 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~ That to which'one is accu,stomed exerts necessarily a powerful'influence upon his valuations and therefore upon his timepreference. This influence :way be in either directiaD Rich men's sons, accustomed to the enjoyment of a large income, are apt to put a higher valuation on present compared with future income than would persons of the same income who were brought up under different conditions. If they suffer a reverse of fortune, they find it harder to live moderately than those of equal means who have risen instead of fallen in the economic scale; and this will be true even if foresight and selfcontrol are the same in the two cases.

(4) The fourth circumstance which may influence the form of the function by which timepreference depends on the character of ,income has to do with the ~ of life of the recipient of that income. We have already ~een in a different connection that the timepreference of an individual will be affected by the prospect of a long or short life, both because the termination of life brings the termina tion of the income from labor, and because it also ter minates the enjoyment of all income. It is the latter fact in which we are here interested; the expectation of life af fects the dependence of timepreference on income. There 106 THE RATE OF INTEREST [CHAP. VI will be differences among different classes, different indi viduals, and different ages of the same individual. So far as age is concerned, the usual course of events is as follows: The timepreference in the early periods of life is high because foresight and selfcontrol are weak.

Children are notorious spendthrifts. A little later, when the individual has acquired some selfcontrol and fore sight, he will still have a high rate of preference, but for another reason, - the prospect of an ascending in come-stream. His present income is small, but he looks forward to having an ample income in five or ten years. As the time of marriage and middle life approaches, the opposite tendency may assert itself. Foreseeing the needs of middle life and anticipating no increase in the provision for those needs, he will cease to borrow and begin to save. Mter he has passed middle age, when his children have become self-supporting, and he looks forward to de.. elining years, matters are reversed again. He will want to enjoy his income while he may, the income beyond his death being of no significance to him except as it can be bequeathed to his descendants. The prospect of death plays an important role in the thoughts of the old. One evidence of this is the prominence given to it in all philosophical and religious systems. 1 The philosophy of Horace, for instance, was summed up in the maxim "carpe diem," which is practically the same as the still older maxim, l' eat, drink, and be merry, for to morrow we die." The chance of death may be said to be the most important rational factor tending to make the rate of timepreference high, and anything that would tend to prolong human life would tend at the same time to reduce the rate of timepreference. As Rae says: 2 "Were life to endure forever, were the capacity to enjoy in per fection all its goods, both mental and corporeal, to be prolonged 1 See Metchnikoff, Nature of Man, English translation, New York (Putnams), 1903, Part II.

2 The Sociological Theory ot Capital, pp. 53-54.

SEC. 9] TIMEPREFERENCE 107 with it, and were we guided solely by the dictates of reason, there could be no limit to the formation of means for future gratification, till our utmost wishes were supplied. A pleasure to be enjoyed, or a pain to be endured, fifty or a hundred years hence, would be considered deserving the same attention as if it were to' befall us fifty ora hundred minutes hence, and the sacrifice of a smaller present good, for a greater future good, would be readily made, to whatever period that futurity might extend. But life, and the power to enjoy it, are the most uncertain of all things, and we are not guided altogether by reason. We know not. the period when death may come upon us, but we know that it may come in a few days, and must come in a few years. Why then be providing goods that cannot be enjoyed until times, which, though not very remote, may never come to us, or until times still more remote, and which we are convinced we shall never see? If life, too, is of uncertain duration and the time that death comes between us and all our possessions unknown, the approaches of old age are at ,least certain, and are dulling, day by day, the relish of every pleasure."

The shortness of life th!!~__ tends powerfully to rn,ise t~ rate of time-Ereference, This is especially evident when the income-streams compared are long. A lover of music 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 the piano available at once. From what has been said it is clear that there are three periods in his life when a man's timepreference is espe cially high: (1) in early life it is high because of youthful recklessness; (2) in the preparatory stage, because future income seems relatively abundant; and (3) late in life, because future income seems relatively superfluous. (5) But whereas the shortness or uncertainty of life tends to raise the rate of timepreference, its effect is greatly giliiga,ted by the fifth circumstance,_th~re for the welfare of'posteri . Probably the t!!Q.stpowerfulcause tending to re uce the rate of interest is the love of one's children ana.

the desire to provide for their good. . When these sentiments decay, as-they did at the time of the decline and fall of the Roman Empire, and the fashion is to exhaust wealth-in 108 THE RATE OF INTEREST [CHAP. VI self-indulgence and leave little or nothing to offspring, the rate of timepreference and rate of interest will 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. 1 In a community 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 which tends, therefore, to produce a low rate of timepreference. It is this sentiment which is responsible for the enormous extension of life insurance. At present in the United States the insurance on lives amounts to $20,000,000,000. This represents, for the most part, an investment of the present generation for the next. The investment of this sum springs out of a low timepreference, and tends to produce a low rate of interest.

Not only does the regard for posterity lower interest, but the increase of posterity has in part the same effect. So far as an increase in the size of a family reduces the income per capita of that family, it operates, like impoverishnlent, to increase timepreference. So far as it adds to future needs rather than to immediate needs, it operates, like a descending income-strealll, to diminish timepreference. Parents with large families feel the importance of providing for future years far more than parents otherwise similar but with small families. They try harder to save and to take out life insurance. In other words, their rate of preference for present over future income is lowered. An increase of population, therefore, will, other things being equal, reduce the rate of interest. This proposition must not be thought to conflict with the reciprocal proposition that the same prudent regard for the future which is created by the re sponsibilities of parenthood itself tends to diminish the number of offspring. An increase of population tends toward a low timepreference, but reciprocally a low 1 See Rae, The Sociological Theory of Capital, p. 97.

SEC. 10] TIMEPREFERENCE 109 timepreference tends to check such increase. Hence it is that the thrifty Frenchman and Scotchman have small families. §10 f~. I.. ~~!~re, depends for ~!L.iu.ili~J I 1~~~~~O~~2~~~;:~=~ . I J~~s~~~i:ll~·~i~t~~J~~oqJm~"~~~Y\=~ preference high are (1) shortsightedness, (2) a weak will, (3) the habit of spending freely, (4) the shortness and uncertainty of his life, (5) selfishness, or the absence of any desire to provide for posterity. The reverse conditions will tend to make his rate of preference low; namely, (1) a high degree of foresight, which enables him to give to the future such attention as it .deserves ; (2) a higll degree of ·selfcontrol, which enables him to abstain from present income in order to increase - future income; (3) the habit of thrift; I (4) the probability of long life; (5) the possession of a family and a high regard for their welfare after his death.

The resultant of these various tendencies in anyone in dividual will determine the degree of his timepreference in relation to any particular incom'e. This result will differ as between individuals, and as between different times for the same individual. The essential fact, however, is that for any given individual at any given time, his timeprefer ence depends in a definite manner upon the size, shape, composition, and probability of his income..,stream. § 11 This view, that the rate of time-preferenceand conse-I quently the rate of interest depend upon income, needs,_ to be ~ontrasted with -the qg.mmoA vie~ which makes the/\ .~ 110 THE RATE OF INTEREST [CHAP. VI 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, in terest is low. In a general way there is undoubtedly some truth in this proposition; and yet it contains a misinterpre. tation of borrowing and lending. It is true that when and where men are anxious to lend, interest is low, and when and where men are anxious to borrow, interest is high.

} But it is not true that the more capital a man has the more . anxious he is to lend, and the less capital he has the more Ianxious he is to borrow. The willingness to lend or bor t row depends primarily, not upon the amount of one's capital, but upon the character of the income which he gets from it, -whether this income is large or small, im mediate or deferred, of what elements it consists, whether it is certain or uncertain. The proposition that abundance of capital tends to lower interest is thus very superficial; for abundant capital merely means abundant income. ~pital-value is 1 discounted jncome. Behind, or rather beyond, a capital , ofsioo,oOO is the income which that capital represents. To fix attention on the $100,000 capital instead of on the income is to use the capital as a cloak to cover up the real factor in the case. Moreover, capital-value is itself dependent on the rate of interest. The capital-value of a farm will be doubled if the rate of interest is halved.

In such a case there would be found more capital in farms; for the farms in a community would rise, say, from $10,000,000 to $20,000,000. But it is not the rise in cap ital which produces the fall in interest. On the contrary, it is the fall in the interest rate which produces the rise in the valuation of 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 oj 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 SEC. 11] TIMEPREFERENCE 111 its dependence on income as the only fact of real signifi cance. But ,even as thus amended and explained, the proposition that the rate of interest depends on the amount of capital is not satisfactory. The mere amount of capital does not Ii tell us much about the income for which that capital stands. .• To know that one man has a capital worth $100,000, and, another $200,000, shows, to be sure, that the latter man may hav~ an income of double the value of the former; but it tells us absolutely nothing as to the "time-shapes" of the two incomes; and the time-shape of income has, as we have seen, a most profound influence on the time preference of its possessor.

Let us suppose two communities similar in population, distribution of wealth, and all other particulars except in the amount of their capital and the character of the income which that capital represents. One of these two communi ties we shall suppose has a capital of $100,000 invested, as in Nevada, in mines and quarries nearly exhausted, while in the other community there is $200,000 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. But it is evident that, unless other circumstances should interfere, the opposite would be the case; for Nevada has to contemplate a decreasing future income, and.in order to offset the depreciation of capital which follows from this condition,l 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, notwith standing the fact that the lending community was the 1 See The Nature 01 Capital and Income, Chap. XIV.

112 THE RATE OF INTEREST [CHAP. VI poorer in capital of the two. From the 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.! Apologists for the common statement 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 ltloanable capital" is merely another cloalc to cover the fact that it is not the amount of capital, but the decision to lend or borrow it, which is important. To give this proposition meaning, "loanable capital" must be taken, not in the literal sense of capital which can be lent, - for all capital is loanable in this sense; but in the sense of capital which persons are willing to lend. Hence, to state that in any community there is abundance of loanable capital is merely to state that there is in that community a willingness to lend a great deal of capital. Consequently, the proposition that the rate of interest, or preference for present over future goods, is low when loanable capital is abUlldant becomes reduced to the platitude that the rate of preference for present over future goods is low when men wish to lend.

But it may be said, surely in a money market there exists at one time a large visible supply of loanable money and at another time a small visible supply, and this supply affects the rate of interest. This, again, is a true but a superficial statement. A little examination will show that the abun dance or shortage of loanable bank funds is merely a measure ofthe decision of merchants to discount or deposit, in:other words, to borrow or lend, -and does not give us any clew as to the reason why they do so. The money or credit lOne of the few defects in Rae's analysis of interest is his em phasis on the accumulation of capital. Since this accumulation is merely in anticipation of future income, the emphasis belongs on the latter.

SEC. 12] TIME-P:a.~FERENCE 113 is, of course, the mere vehicle by which the bank acts as an intermediary or broker between borrowers and lenders, and does not represent any independent factor in the case. We end, therefore, by emphasizing anew the importance of fixing our eyes on income and not on capital. It is only as we look through capital-value, beyond to the income which it represents, that we reach the efficient causes which operate upon the rate of interest. The absence hitherto of a definite theory and conception of income has prevented economists from doing this. 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 com munity, but the income for which that capital stands. § 12 Unfortunately for purposes of exposition, the relation between timepreference and income cannot be expressed in a simple schedule or curve, as~can the relation between demand and price, or supply and price, or utility and quantity consumed, for the reason that income means not a I single magnitude merely, but a conglomeration of a number I of magnitudes. As mathematicians would express it, to ; , ..!.M J, state that timepreference depends on the character of ~-, ; income, its size~ shape, compo~ition, and. probability, iS~J ~I to state that timepreference IS a functIOn of all the ~ -II) ~ A,t.different magnitudes which need to be specified in a com-~· J tr !

plete description of that income. A geometrical represen- ~,f{ ". I tation, therefore, of the dependence of timepreference on ~ the various magnitudes which characterize income, would ~.~ be impossible. For a curve can only represent the dependI ence of a magnitude on one independent variable; even a surface can only represent dependence on two; but for our requirements we should need a space of n dimensions. We may represent the relation between timepreference 114 THE RATE OF INTEREST [CHAP. VI and income by a "schedule" like the ordinary U demand schedule" and "supply schedule," if we make a list of all possible incomes, specifying for each individual income all its characteristics, -its size, time-shape (that is, its relative magnitude for each successive time-interval considered), its composition (or the amount, at each period, of each in dividual constituent, as nourishment, shelter, etc.), and the certainty or uncertainty attached to all these elements.

Having thus compiled a list of all possible incomes, it would only be necessary for us to assign to each of them the rate of timepreference pertaining to it. Such a schedule would be too complicated and cumbersome to carry out in detail; but the following will roughly indicate some of the main groups of which it would consist. In this schedule we have represented by the three vertical lines three different classes of income, - two extreme types and one mean type, - so that the corresponding rates of timepreference range them selves in a descending series of numbers. We have also represented by the three vertical columns three different classes of individuals, two being of extreme types of in dividuals, and the third of a mixed or medium type. Thus the numbers in the table descend as we proceed either down or toward the right, the lowest number of all being in the lower right-hand corner.

DESCRIPTION OF INCOME CORRESPONDING TIMEPREFERENCE to an individual who is shortsighted, farsighted, weak-willed, . of a mixed self-controlled, SIZE TIME-SHAPE COMPOSITION PROBABILITY accustomed or medium accustomed to save, to spend, type desirous to provide without heirs for heirs small increasing food scanty precarious 20% 10% 5% of a mixed or medium type 10% 5% 2% large I decreasing Ifood abundant I assured 5% 2% 1% rnI!!t P.... ~ ~ ~ ~ ~ ~ ~ gJ ~ ~ ~ ~ :J1 116 THE RATE OF INTEREST [CHAP. VI Out of the large number of possible incomes represented in such a schedule, of course only one can be the actual income of the individual. The one which exists in any case is to a large extent a matter of choice, as we shall see in the next chapter. Since timepreference may be varied by voluntarily varying the character of the income-stream on which it depends, it follows that the shortsighted, weak willed spendthrift individual may not have, as a matter of fact, any higher rate of timepreference than his farsighted, self-controlled, abstemious brother. In fact, where a loan market is in full operation, the tendency is for the two in dividuals to select such income-streams as will bring their timepreference into unison. How this is accomplished will form the subject of the following chapter.

CHAPTER VII FffiST APPROXIMATION TO THE THEORY OF INTEREST (ASSUMING INCOME RIGID) § 1 IN the last chapter we saw that the rate of preference for present over future goods was, in the last analysis, a prefer ence for present over future income; that this preference depends, for any given individual, upon the character of his income-stream, - its size, time-shape, composition, and probability, - and that the nature of this dependence varies with different individuals. The question at once arises, will not the rates of preference of different individuals be very different, and if so, what relation do these different rates have to the rate of interest? John Rae assumed th~t the rates differed widely, and that the rate of interest was a sort of average of their different magnitudes. But this is incorrect. In a nation of hermits, in which there was no mutual lending and borrowing, the timepreferences of 'fJ individuals, would diverge widely; but in modern society, .

borrowing and lending tend to bring into equality the rates of preference in different minds. It is only .because of the limitations of the .loan market that absolute equality is not reached. The chief limitation to lending is due to the risk involved, and to the difficulty or impossibility of obtaining the s~ curity necessary to eliminate or reduce that· risk. Those 'yJ who are most willing to borrow are oftentimes those who are least· able to give security. It will then happen that these persons, shut off from the loa~ market, experience ~a higher rate of timepreference than the. rate of interest ruling 117 118 THE RATE OF INTEREST [CHAP. VII in that market. If they can contract loans at all, it will be only through the pawn shop or other high-rate agencies. But, for the moment, let us assume a perfect market, in which the element of risk is 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 is initially possessed of a fore known income-stream, and that he is free to exchange any part of it to some other person, in consideration of receiving back at some future time an addition to his in come for the prospective period. We assume further that to buy and sell various parts of his income-stream (by loans, etc.), is his only method of altering that income stream. Prior to such exchange, his income-stream is rigid, i.e. fixed in size, time-shape, and composition. The capital-instruments which he possesses are each capable of only a single definite series of services contributing to his income-stream. These assumptions that each man's income-stream is initially certain and fixed, will be used in our first approximation to the theory of interest.

§ 2 Under these hypothetical conditions, the rates of time preference for different individuals would be perfectly equalized. Borrowing and lending evidently affect the time-shape of the incomes of borrower and lender; and since the time-shape of their incomes affects their time preference, such a modification of time-shape will react upon and modify their timepreference, and bring the market into equilibrium. If, for any particular individual, the rate of preference differs from the market rate, he will, if he can, ~a~d.L:·u~ .......... ime-sha eof his income-stream so as to harmonize his r f.., ,. erence rate wit the interest rate. Those who, for 8 given -ncome-stream, have a rate of preference above the market FIRST APPROXIMATION 119 rate,will sell some of their surplus future income to obtain . an addition to their present meager income. This will have the effect of enhancing the value of the future income and '1 decreasing that of the present. The process will continue until the rate of preference of this individual is equal to the rate of interest. In other words, a person whose preference rate exceeds the current rate of interest will borrow up to the point which will make the two rates equal.

Reversely, those who, with a given income..,stream,have a preference rate below the market rate, will sell some of their abundant present income to eke out the future, the effect being to increase their preference rate until it also harmo nizes 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 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 is able to obtain $1 for this year by spending only $1.05 of next year. This ratio is, to him, 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, by increasing his present income and decreasing his future, tends to reduce his timepreference 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 having to pay only 5 per cent. This operation will still further reduce his timepreference, until it has been finally brought down to 5 per cent. Then, for the last or "marginal"

$100,-his rate of timepreference will agree with the market rate of interest. 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 in come. Every comparative estimate of present and-future which he actually makes must. be lC on the margin" of his income-stream as actually determined. The -above-men120 THE RATE OF INTEREST [CHAP. VII tioned 10 per cent. and 8 per cent. rates are not actually experienced by him; they merely mean the rates of prefer erence which he would have experienced had his income not been transformed to the time-shape correspondent to 5 per cent. In like manner, if another individual, entering the loan market from the other side, has a rate of preference of 2 per cent., he will become a lender instead of a borrower. He will be willing to accept $102 of next year's income for $100 of this. But in the market he is able, instead of the $102, to get $105. As he can lend at 5 per cent. when he would gladly do so at 2 per cent., he jumps at the chance and invests, not one $100 only, but another and another.

But his present income, being reduced by the process, is now more highly esteemed than before, and his future income, being increased, is less highly esteemed. The result will be a higher relative valuation of the present, which, under the influence of successive additions to the sums lent, will rise gradually to the level of the market rate of interest. In such an ideal loan market, therefore, where every in dividual could freely borrow or lend, the rates of preference for present over future income for all the different indi viduals would become equal to each other and to the rate of interest. § 3 To illustrate this reasoning by a diagram, .let us suppose the income..stream to be represented as in Figure 6, and that the possessor wishes to obtain a small item X' of imme diately ensuing income, for a somewhat larger item X" later on. He therefore modifies his income-stream from ABeD to EBD. But this change will evidently produce a change in his timepreference. If the rate of timepref erence corresponding to the income-stream represented by the unbroken line is 10 per cent., the rate of preference cor responding to the broken line will be somewhat less; say SEC. 3] FIRST APPROXIMATION 121 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 o E.

'A FIG. 6. can evidently produce almost any required conformation in his income-stream. If, instead of borrowing, he wishes to lend (Fig. 7), he surrenders from his present incomeA· .-----X!E·.- .... ..;...-·------FIG. 7. stream the amount X' for the sake of the larger amount X" at a later· time. He will engage in the former series of operations if, at the start, his subjective preference for present goods exceeds the m~rk~t rate of interest, and in the latter, if it falls short of that rate. After 122 THE RATE OF INTEREST [CHAP. VII A 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. The loan is effected under the guise of money. We do B not confessedly borrow and lend incomes, but money. Yet money - that universal me dium in practice and universal FIG. 8. stumbling-block in theory - merely represents capitalized income. A hundred dol lars mean the power to secure income, - any income the present value of which is $100. A When, therefore, a person .....,'..........

"borrows" $100 to-day and A ------0:1>11ooooi:<::------ B ---returns $105 next year, in ac- - - - B' tual fact he secures the title FIG. 9. to $100 worth of future income - immediately future, perhaps - and parts with the title to $105 worth of income more remotely future. There are six principal types of individuals in a loan X market. In the first type '"'" (Fig. 8) the individual is supp." posed to be possessed of an in-, , creasing income-stream AB which in his mind results in B a rate of preference above the market rate. This leads FIG. 10. him to borrow, and relatively to level up his ascending income-stream to such a position as A'B'. The second type of individual already possesses a uniform income-stream AB (Fig. 9), but, nevertheless, being of a spending type, experiences a rate of preference also above the market rate, and will therefore modify his income-stream to the curve A'B'. The third type is rep resented in Figure 10. This individual has a rate of pref erence in excess of the market rate, even with a descending S:mc.3] FIRST APPROXIMATION 123 B B curve AB. The consequence is· that by borrowing he obtains a curve A'B' of still steeper descent.

The preceding three cases are of borrowers. In like man ner there are three types of A lenders. Figure 11 represents a descending type of income AB.which, by lending present income in return ·Jor future income, is converted into a FIG. 11. relatively uniform income A'B'; Figure 12 represents a uniform income converted, by lending, into an ascend ing income; and Figure 13 an ascending income converted into a still more steeply ascending income. In all cases we see that the borrowers change their income curve by tipping it down in the future and up in the present; whereas the lenders tip their ,/B' income curves in the opposite _______ --<e:;;-,-'-'- B direction. Of the three types _A .",. ,. ...... ,. of borrowers and of lenders, .8. -'" ,- the first in each group of three FIG. 12. (see Figs. 8 and 11) 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 (Fig. 8) being lowered and the falling curve (Fig. 11) being raised toward a common horizontal position. Figure 10 and Figure 13, on the other hand, represent extreme· and unusual cases. The former (Fig. 10) typifies the spendthrift who, in spite of lessening income, borrows, and the latter (Fig.

13) typifies the miser who, in A spite of rapidly increasing income, saves even more. FIG. 13. But whatever the personal equation, it remains true that, for each individual, the more ascending his income curve the higher his rate of preference, and the more descending 124 THE RATE OF INTEREST [CHAP. VII \Ithe curve, the lower the rate. If the descent is sufficiently '. . II rapid, the rate of preference could be made zero or even "L II negative. In these cases, the income is such that its I Ii possessor would sacrifice present income to future, even if 1\ the market rate of interest were zero.1 I\ These are, of course, not the only types which could be considered, but they are some of the most important. To them we may add the type of fluctuating income, as rep resented in Figure 14, which may result in alternate bor;."---B ---B ' A· FIG. 14. rowing and lending so as to produce a more nearly uniform income-stream.

It must not be imagined that the classes of borrowers and lenders correspond respectively with the classes of poor and rich. Personal and natural idiosyncracies, early training and acquired habits, accustomed style of living, the usages of the country, and other circumstances dis cussed in Chapter VI, will, by influencing foresight, self control, regard for posterity, etc., determine whether a man's rate of preference is high or low, and therefore whether he becomes a spender or a saver. So far as the character of the income-stream itself tends to place an individual in one or the other of these classes, the nature of the influence is in accordance with the principles stated in Chapter VI in respect to the four features, size, time-shape, composition, and probability. As to size, the larger the income the more likely, in general, is its possessor to become a lender, because large incomes, in general, reduce the rate of preference for present over future income; as to time1 This is the case mentioned by Carver (Theory 01 Distribution, pp. 232-236), when he remarks that a man with $100 in his pocket would not think of spending it all on a dinner to-day, but would save at least some of it for to-morrow.

SEC. 4] FIRST APPROXIMATION 125 shape, ascending incomes are apt to make the possessors borrowers, and descending incomes to make them lenders; as to composition, incomes well endowed with the food -element are less apt to make their possessors borrowers than incomes of the contrary type; and as to probability, incomes which are uncertain tend sometimes to make their possessors borrow, sometimes to lend. § 4 But borrowing and lending are not the only ways in which one's inOO""me-streammay be modified.. The same result may be accomplished simply bybuyillg and sellingproperty:'" or, SInce property rIg ts are mere y rIg ts to particular in come-streams, their exchange substitutes one such stream for another of equal value but differing in time-shape, composi tion, or certainty. This method of modifying one's income stream, which we shall call the method of sale, really includes the former method of loan; for a loan contract is at bottom a sale, as B6hm-Bawerk has so' clearly shown. That is, it is the exchange of the right to present or immediately ensuing income for the right to more remote or future in come. A borrower is a seller of a note of which the lender is the buyer. A bondholder is regarded indifferently as a lender and as a buyer of property. The concept of a loan may therefore now be dispensed with by being merged in that of sale. By selling some property rights and buying others it is possible to transform one's income-stream at will, whether in time-shape, composition, or probability. Thus, if a man buys an orchard, he is providing himself with future . income in the use of apples; if, instead, he buys apples, he is providing himself with similar but more immediate income. If he buys securities; he is providing hi~self with future money, convertible when received into true income. If his security is a share in a mine, his income stream is less lasting, though it should be larger, than if the security is stock in a railway. Purchasing the right to 126 THE RATE OF INTEREST [CHAP. VII remote enjoyable income is called investing; to immediate enjoyable income, spending. These, however, are purely rel ative concepts,for" remote" and "immediate" are relative terms. Buying a winter overcoat or a carpet may be called investing, and on the other hand, buying a factory or a ship may be called spending. And yet the antithesis between H 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 in come but robs the future, whereas investing provides for the future to the detriment of the present.

Popular usage has devised many other terms and phrases in this field, most of which, like "spending" and "in vesting," while containing meaning 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 the inanimate capital has of itself any power to "seek investment"; it does not mean that there is any hard and fast line between invested and uninvested capital. 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 ex change it for remoter income; it does not mean the creation of new capital, though it maylead to it. Many needless con troversies have centered about the phenomenon of "sav ing," chiefly because neither "saving" nor" income" was .

clearly defined.1 From what has been said it is clear that by buying and sellingproperty an individual may change the conformation 1 Thus, by "saving," some writers understand that capital neces sarily 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.

Smc.5] FIRST APPROXIMATION j 127 of his income-stream precisely as though he were specifically lending or borrowing. Thus, if a man's original income stream is $1000 this year and $1500 next year, and if, selling this income-stream, he buys with the proceeds another yielding $1100 this year and $1395 next year,he has not, nominally, borrowed $100 and repaid $105, but he has done what amounts to the same thing, - increased his income-stream of this year by $100 and decreased that of next year by $105, the $100 being the modification pro duced in his income for the first year by selling his original income-stream and substituting the final one, and $105 being the reverse modification in next year's income produced by the same operations. The very same dia grams which were used before may be taken to represent these operations. A man sells the income-stream ABeD (Fig. 6) and with the proceeds buys the stream ERD.

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 direct loans and, returns. § 5 In passing we may note that 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 Qf sale, and, as was shown in The Nature of Capital and Income, the valuation of every property-right involves interest. If the prohibition left individuals free to deal in bonds, it is clear that they would be still borrowing and lending, but under the name of "sale"; and if "bonds" were tabooed,they couldchange the name to "preferred stock." It can scarcely be sup posed that any prohibition of interest-taking would extend to all buying and selling; but as long as buying and selling of any kind were permitted, the virtual effect of lending and borrowing would be retained. The possessor ofa forest of young trees, not being able to mortgage theirfutur~ 128 THE RATE OF INTEREST [CHAP. VII return, and being in need of an income-stream of a less deferred type than that receivable from the forest itself, would 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 anxious to "save" instead of "spend," would sell his depreciating wealth and invest the proceeds in such instru ments 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, at the worst, the effect of restrictive laws is simply to hamper and make difficult the finer ad justments of the income-stream, compelling wouldbe bor rowers to sell wealth yielding distant returns instead of mortgaging it, and wouldbe lenders to buy the same, instead of lending to the present owners. It is conceivable that" explicit" interest might disappear unde~.(~uch }estric tions, ~t "implicit" interest would 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 bought for $10,000 would be de termined in like manner. The rate of discount in the two cases must be the same, because, by buying and selling, the various parties in the community adjust their rates of preference to a common level, - an implicit rate of in terest thus lurking in every contract, though never specifi cally appearing therein. Interest is too omnipresent a phenomenon to be eradicated by attacking any particular form; nor would anyone undertake it who perceived the substance as well as the form.1 In substance, the rate of interest represents the terms on which the earlier and later elements of income-streams are exchangeable.

lef. Fetter, Principles of Economics, New York (Century), 1904, pp. 134, 135.

SEC. 6] FIRST APPROXIMATION § 6 129 The fact that, through the loan market, the marginal rate of timepreference for each individual is made equal to the rate of interest, may be stated in another way, namely, that the total present desirability or utility of the JE.dividual income:stream is made a maximum p ., For, con sider again the individual who modifies his original fixed income-stream by borrowing until his rate of preference is brought into unison with the rate of interest. His rate of preference was at first 10 per cent.; that is, in order to secure an addition of $100 to his present income, he was willing to sacrifice $110 of next year's income. But he only needed to sacrifice $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 de sirability of $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 saves $3; that is, he adds the present desirability of $3 due next year to the present" total desirability" or "total utility "of his income stream. In like manner, each successive increment of loans adds to his present total desirability, 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; his present total desirability is then a maximum, and any further loan would decrease it. A sixth $100, for instance, is worth in his estimation less than $105, say $104, and as, in the loan market, he would have to sacrifice $105 next year to secure it, the con tracting of such a loan would mean a loss of desirability to the extent of $1 due in one year. Thus, by borrowing up to the point where the rate of preference for present over K 130 THE RATE OF INTEREST [CHAP. VII future income is equal to the rate of interest, the individual secures the greatest" total desirability." Similar reasoning, applied to the individual on the other side of the market, whose rate of preference is initially less t~an the market rate of interest, will show that he also will maximize his present total desirability 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 $102 due one year hence, whereas in the market he may secure $105. It is then clear that by lending $100 he gains the present desira bility of $3 due one year hence. By lending each successive $100 he will add something to his total present desirability, until his rate of preference for present over future income is raised to a level equal to that of the rate of interest.

Beyond that point he would lose by further lending; but at that point he will stop, and his present total desirability will therefore be a maximum. § 7 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 preference to the rate of interest. For him the rate of interest is a relatively fixed ~ct, sincehis own tUlle-preference and resulting action can affect it only infinitesimally! H~..E~~E:}_.()(.preference·' is. the variaJ2l.e. In short, for him individually the rate of interest is cause, and the rate of preference, effect. For society as a whole, however, the order of cause and effect is reversed. This change is like the correspondin inversion !f of cause and effect in the theory 0 'prIces. ach individual. regards the market price, say, of sugar, as fixed, and adjusts his marginal utility to it; whereas, for the entire group forming the market, we know that the price of sugar is due SEC. 7] FIRST APPROXIMATION 131 to its marginal utility to the consumer.1 In the same way, while for the individual the rate of interest determines the rate of preference, for society the rates of preference of the individuals determine the rate of interest. The rate of interest is simply the rate of preference, upon .which the whole community may concur in order that the market of loans may be exactly cleared.

To put the matter in figures: if the rate of interest is set very high, say 20 per cent., there will be relatively few borrowers and many wouldbe lenders, so that the total extent to which wouldbe 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, those who are willing to add to their present income at the high price of 20 per cent. interest will borrow 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· present year's income offered as loans may be 50 millions,and the amount which would be taken at that rate only 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 is· the common market rate of preferencefor present over future income, as determined by the supply and demand of present and future income. Those who, .having a high rate of preference, strive to acquire ~ more present income at the cost of future income, tend to raise the· rate of interest. These are the borrowers, the 1 See the author's II Mathematical Investigations in the Theory of Value and Prices," Transactions oj Connecticut Academy, New Haven, 1892, .p. 28.

132 THE RATE OF INTEREST [CHAP. VII spenders, the sellers of property yielding remote income, such as bonds and stocks. On the other hand, those who, having a low rate of preference, strive to acquire more future income at the cost of present income, tend to lower the rate of interest. These are the lenders, the savers, the investors. The mechanism just described will not only result in a rate which will clear the market for loans connecting the present with next year, but, applied to exchanges between the present and the remoter future, it will make similar adjustments. While some individuals may wish to ex change 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 years' future incomes. The rates of interest for these various periods are so adjusted as to clear the market for all the periods of time for which contracts are made.

If we retain our original assumption that every man is initially endowed with a fixed and certain income-stream which, by borrowing and lending, can be freely bought and sold and thereby redistributed in time, the foregoing dis cussion gives us a complete theory of the causes which determine the rate of interest, or rather, the rates of interest for various time-periods. These rates of interest would, under these circumstances, be fully determined by the fol lowing four conditions, to which all the magnitudes in the problem of interest must conform:(1) The rate of timepreference of each individual for present income, as compared with remoter income, depends upon the character of his income-stream, as finally modified and determined by the very act of borrowing or lending, buying or selling. (2) Through the variations in the income-stream pro duced by loans or sales, the rates of preference for all individuals in the market are brought into equality with each other and with the market rate of interest.

This condition is equivalent to another; namely, that SEC. 7] FIRST APPROXIMATION 133 , each individual exchanges present against future income, or vice versa, at the market rate of interest up to the point of maximum desirability. (3) The market rate of interest will be such as will just clear the market; namely, will make the loans and borrow~ ings cancel each other for each period of time. t '" (4) 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 gener ally, the modifications or departures from a person's origi nal income-stream effected by buying and selling are such that the algebraicsum of their presentvalues is zero. These four conditions not only determine the rate of in~rest, but determine also all the other variable elements which enter into the problem; namely, the individual rates of preference (equal to the rate of interest) and the amounts which are borrowed and lent.

The formulation of these four determining conditions constitutes our first approximation to the theory of interest. The sufficiencyof the four conditions and their coordination may be made clear by means of the mathematical statement contained in the Appendix to this chapter. , \/V~dl i J~!:';'/Y;~(~' I / · , tel / / ~ /' ~ . ! tJ1..';',-;:{' d .~.'- /.':. j,c...A./' -;.... .,lr'!~--I--."·-_ ..... /.//I/"!I '.,t.. ~_.... ....L:" . ~c:(' //~ ",~. __~ ~~ ~..-U i ~A .~ ~ : U, ~' .~' PART III. SECOND AND THIRD ApPROXIMATIONS CHAPTER VIII. CHAPTER IX. CHAPTER X. CHAPTER XI. SECOND ApPROXIMATION TO THE THEORY OF INTEREST (ASSUMING INCOME FLEXIBLE) CLASSES OF OPTIONS INVENTION THIRD ApPROXIMATION TO THE THEORY OF INTEREST (ASSUMING INCOME UNCERTA.IN) CHAPTER VIII SECOND APPROXIMATION TO THE THEORY OF INTEREST . (ASSUMING INCOME FLEXIBLE) § 1 HITHERTO we have assumed that the income~stream flowing from any given article of capital is both fixed and certain. We now abandon the first part of this hypothesis.