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.