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BOOK VII

THE RATE OF INTEREST

Book VII, Chapter I

The Rate in Isolated Exchange

The exchange of present goods for future, in which interest has its origin, is only a special case of the exchange of goods in general. It goes, then, without saying that the formation of price in this case is subject to the same laws as govern the formation of price in economical exchange generally. The question whether present goods in general obtain an agio, and also the further question of the height of that agio, are both to be answered according to the rules laid down in Book IV. as regards prices of goods in general. What remains for us here is only to amplify and vivify the colourless scheme which demonstrated that the current price of goods is the resultant of subjective valuations coming together in a market, by pointing out those concrete circumstances which in this case—the exchange of present against future commodities—influence the mutual valuation of both.

As before, it is advisable to distinguish between isolated exchange and competitive exchange.

In the exchange which takes place between an owner of a present commodity and a suitor for it, the price, according to the formula laid down on p. 199, will be fixed somewhere between the value of the present good to its owner as under limit, and its value to the suitor as upper limit. If, for instance, £100 present money are worth to their owner exactly as much as £100 of next year's money,1 while to the suitor they are worth, on subjective grounds (say, on account of temporarily pressing circumstances), as much as £200 of next year's money, the price of £100 present money will be fixed somewhere between £100 and £200 of next year's money, and the agio at something between nothing and 100%. The precise figure that is fixed, in the individual case, within these wide limits, depends on the skill and "staying power" displayed by both parties in conducting the negotiations. As a rule, the owner of present goods will be in a position of advantage, because he can do without the exchange and yet suffer no loss, while the suitor is often driven to pay any price for present goods. Hence the familiar cases where, in the absence of competition, usuriously high rates of 50%, 100%, even 200% and 300%, are extorted.

When we go farther, and inquire as to the deeper reasons which affect the subjective valuation of the suitors,2 and thus affect the economic upper limit of the agio, we find them a little different in the case of the consumption loan from what they are in the production loan, to which latter the buying of labour is closely allied.

In the case of the consumption loan the determinants are;—the urgency of want at the time, the probable provision at the time when the loan is to be paid back, and, finally, the degree of the suitor's underestimate of the future. The more urgently he requires the loan, the more easily he expects to be able to replace it;3 and the less he takes thought for the morrow, the higher the agio to which he will, in the worst case, consent and vice versâ.

In the production loan we find different concrete determinants. Here the important thing is the difference in productiveness between the methods open to him who gets the loan, and those open to him who has to do without it. To recur to our old illustration. If the fisher, who has no capital, and can catch only 3 fish a day by hand, gets a loan of 90 fish, and is thus put in a position to make a boat and net in the course of a month, and with these to catch 30 fish a day for the remaining eleven months, the balance stands as follows:—without the loan he catches in a year 3 × 365 = 1095 fish; with the loan he catches nothing in the first month, but 30 per day for the other eleven months, that is, 335 × 30 = 10,050, or a surplus of 8955 fish. So long, then, as he has to give anything less than 8955 (next year's) fish for the borrowed 90 (present) fish, he gains by the transaction.

In this illustration the difference in possible return between the two productive methods, and, with it, the upper limit of the economically possible agio, is absurdly high—8955 next year's units for 90 present units is something like 10,000%. But there will always be a very important difference when the choice lies between capitalist production and hand-to-mouth production, as the latter is, of course, always extremely unremunerative. The difference, again, will tend to grow less when the choice lies between two different capitalist methods; and will become more rapidly less in proportion to the length of the process already secured without the loan. This fact is of very great importance as regards the rate of interest, not only in isolated, but also in competitive exchange. If we put it in the clearest possible way now, it will give a good basis for what comes later.

In an earlier chapter I called attention to the well-attested fact that the lengthening of the capitalist process always leads to extra returns, but that, beyond a certain point, these extra returns are of decreasing amount. Take again the case of fishing. If what we might call the one month's production process of making of a boat and net leads to the return of the day's labour being increased from 3 to 30,—i.e. by 27 fish,—it is scarcely likely that the lengthening of the process to two or three months will double or treble the return: Certainly the lengthening it to 100 months will not increase the surplus by a hundredfold. The surplus return—for there will always be a surplus return—will increase by a slower progression than the production period. We may, therefore, with approximate correctness represent the increasing productivity of extending production periods by the following typical scheme.

Production Period.	Return per annum.	Surplus.
Without Capital	ţ15	舒
1 year	35	ţ20
2 years	45	10
3	53	8
4	58	5
5	62	4
6	65	3
7	67	2
8	68:10s.	1:10s.
9	69:10s.	1
10	70	0:10s.

It must be understood that I do not attach any importance to these particular figures. Everybody knows that, in every branch of production and at every stage of technical knowledge, the figures will differ. In one branch the fall of surplus return may be slower, in another it may be more rapid. All I lay stress on is the fact that the figures express the general tendency of surplus returns to fall.—Assume, to complete the hypothesis, that a worker needs £30 a year to maintain him in suitable circumstances, and let us try to find out on this basis the limit of the economically possible agio which a suitor for productive credit may, in the worst case, offer for a loan of £30 a year.

If the suitor has no capital whatever, he can get a return of only £15 without the loan: with the loan, in a one year's production period he can get a return of £35. In the most extreme case he may therefore, without altering his position for the worse by the transaction, offer an agio of £20; that is 66 2/3%. If, on the other hand, the suitor already has a capital of £30 (whence he gets it—whether it is his own or advanced from other quarters—does not affect the case), he can, without borrowing, engage in a one year's process and obtain a product of £35, and all that depends on his getting the loan is the extension of the process from one year to two, and the raising of the return from £35 to £45; i.e. a yearly surplus of £10.4 Here, then, the suitor can economically offer, at the most, an agio of £10 on £30; i.e. an interest rate of 33 1/3%. Similarly, if the suitor, by whatever means, is already equipped for a two years' process, the loan of £30 is now the cause of a surplus return of £8 (£53 - £45) = 26 2/3%. Thus the more ample the suitor's equipment is already—the more capital he has—the lower fall the surplus returns and the ratio of agio dependent on the loan. That is to say, the surplus falls to £5, £4, £3, £2, 30s., 20s., 10s., and the rate to 16 2/3, 13 1/3, 10, 6 2/3, 5, 3 1/3, 1 2/3 per cent. This fall is bound to emerge unless the returns obtainable in 1, 2, 3, 4, x, production periods should run, not, as we have assumed, in the progression of 35, 45, 53, 58, 62, etc, but steadily in the much sharper progression of 35, 45, 55, 65, 75.... 105.... 1005, etc. In this latter case, on every one-year extension of the production period made possible by the £30, there would depend a constant surplus return of £10, and the upper limit of the economically possible again would remain uniform at 33 1/3%. But a ratio of increase like this cannot in any case go beyond a few stages in some few productions;5 it cannot go on permanently and without limit in any production.

We come, then, to the important proposition that to intending producers, generally speaking, a present loan has less value in proportion to the length of the production periods already provided for from other sources. The proposition directly applies to the rate of interest in isolated exchange, inasmuch as the valuation of the borrower for productive purposes directly gives the upper limit of the economically possible rate. It also allows us, however, to judge in what direction this proposition must influence the rate of interest in competitive exchange, where the price is the resultant of the subjective valuations of individuals, of whom many are intending producers.

As has been said above, the case of productive credit is closely related to the case of the purchase of labour, the employment of productive labourers by the capitalists themselves. Here, however, there enter certain complications which may be as easily and briefly stated under competitive exchange. I shall not, therefore, discuss them separately, but shall go on at once to explain the rate of interest in developed competitive exchange.

Book VII, Chapter II

The Rate in Market Transactions

The character of the market in which present goods are exchanged against future goods has already been described.6 We now know the people who appear in that market as buyers and sellers. We know that the supply of present goods is represented by the community's current stock of wealth—with certain unimportant exceptions—and that the demand for them comes (1) from the suitors for productive credit who wish to equip themselves for their own work in production, (2) from the suitors for wage-paid labour, and (3) from the suitors for consumption credit. To these three categories we may add, under certain reservations, the maintenance of the landowners. Finally, it will be remembered that the resultant market price must, as a rule, be in favour of present goods, and must lead to an agio on the same. What we have now to do is to group together the causes which determine the height of this agio in one adequate and typical picture.

If we were to attempt all at once to draw a picture like this, covering, as it does, the whole area of the varied influences that cross and intersect each other on the market, we should meet with great, indeed insuperable difficulties, in the way of statement. I shall, therefore, act on the principle, divide et impera, and first consider how the price is determined under the assumption that, confronting the supply of present goods, there is one single branch of demand, though, in present circumstances, by far the most important branch, viz. the demand of the Wage-Earners. Once we have drawn in broad clear lines the most important and difficult part of the whole picture, it will be relatively easy to define the kind and measure of the share which all the remaining market factors have in forming the resultant, and so gradually to make the picture true to the full complexity of practical life. For good reasons I also retain provisionally the former assumption, that the whole supply and the whole demand for present goods meet in one single market embracing the entire community. And, finally, we shall suppose meanwhile that all branches of production show the same productiveness, and also the same increment of productiveness on each extension of the production period: that is to say, we shall assume an identical scale of surplus returns.

Suppose, then, that in our community the stock of wealth in the market, as supply, amounts to £1500,000,000, and that there are 10,000,000 of wage-earners. Following the scheme on p. 378, the annual product of each worker increases in all branches of production, in proportion to the length of the production period, from £35 (in a one year's process7 ) to £70 (in a ten years' process). The question is; in these circumstances of the market how high will rise the agio on present goods?

It is quite certain, as we have already explained, that the agio will settle at that level where supply and demand exactly balance each other, and this lies between the subjective valuations of the last pair who actually exchange. But the fixing of these valuations here encounters a quite exceptional difficulty, and one which does not occur in any other exchange transaction, but has its basis in a special peculiarity of the commodity "labour." Every other commodity, that is to say, has a predetermined subjective value to the one who wishes to buy it. Labour has not, and for this reason. It is valued according to its prospective product, while the prospective product varies according as that labour is invested in a short or in a long production process. We said above that, in the subjective circumstances of the capitalist, a sum of present goods was, as a rule, worth as much as the same sum of future goods. The capitalist will, therefore, count the value of labour equal to just as many present shillings as it will bring him in in the future. But, according as this labour is invested in a short or a roundabout process, it may bring him in £35 or £58 or £70. At which of these figures is the capitalist to value it?

It may be answered: According to the product aimed at in entering upon the method of production which is, economically, the most reasonable. He will, therefore, value the year's labour at £35 if, on reasonable grounds, he meditates adopting a one year's process; at £70 if he considers a ten years' period the most suitable. This would be very well if only it was certain beforehand what period was the most suitable for the undertaker. But this is not certain: on the contrary, the length of the process is itself dependent on the rate of wage fixed as resultant price on the labour market. If the wage, for instance, stands at £25, a one year's process is the most favourable for the undertaker. At £25 he gains £10 in the year—or, to put it exactly, in the six months, since, on the average, the advance extends over only six months;8 that is, 80% per annum. In a ten years' process for the £25 in wages he gets £70, and the surplus return of £45 is, absolutely, much greater, but, when divided as profit over an average of five years,9 gives only £9 for one year, or a profit of 36%. On the other hand, if the year's wage is £50, it is quite clear that it would be as absurd to choose a one year's process, with its product of £35, as it was most reasonable in the previous circumstances, and only those longer production periods which show an annual product over £50 could be thought of.

The matter, therefore, stands as follows. Elsewhere, in the case of other commodities, the employment for which the buyers wish to acquire them is already determined. It is the fixed point,—the thing which first of all helps to determine the price offered by the buyers, and then through that the resultant market price. Here, in the case of the commodity Labour on the contrary, the employment is an undetermined amount, an x, which is first determined by the resultant price. In these circumstances it is clear that the fixed point of the price transactions must be got somewhat differently from the ordinary way; not, of course, according to different principles or laws, but with a certain casuistical modification in detail which we have now to examine.10

In place of the fixed point, which is not available because the employment of the labour itself is not fixed, we find a substitute in the fact that another amount, usually indetermined, is here fixed, viz. the quantities sold. It may be taken as certain that all the labour offered, like the whole sum of present goods offered, finds a market. The certainty of this is based on a peculiar circumstance. Exactly as, in the science of money, it is a familiar dogma that, in the long-run, any sum of money, be it great or small, is sufficient to do the work of circulation in a community, so is it true that any sum of present goods, be it great or small, is sufficient to buy up the whole supply of wage labour that exists in the community, and to pay its wages. All that requires to be done is to contract or extend the production period. If there are ten million wage workers, and fifteen hundred millions of capital, this stock is just sufficient to pay the ten million workers £30 a year each over a ten years' production process.11 If there are only five hundred millions of capital no labourers need go idle on that account: only, of course, they cannot have their maintenance advanced them for a ten years' process, but (at the same wage of £30) only for a three and a third years' process, and the average duration of the production period must be curtailed accordingly. Suppose there are only fifty millions of capital, all the labour could still be bought, but now only for a four months' process, and it must be secured, by a further shortening of the production period, that the scanty amount of present goods is renewed after every short period by the accession of fresh returns.

It is, therefore, always possible for the existing stock of wealth to buy all the labour, and there are certain reasons in this case that work very strongly towards always making the possible into the actual. Between capitalists and labourers the economic conditions are—with very few exceptions—extremely favourable to the effecting of exchange. The labourers urgently need present goods, and cannot, or can scarcely turn their own labour to any account; they will, therefore, to a man rather sell their labour cheaply than not sell it at all. But very much the same is true of the capitalists. In their peculiar circumstances of want and provision for want, their present goods—which they, in any case, would lay up against the future—are not worth more to them than a similar sum of future goods. They will, therefore, prefer any purchase of labour where there is an agio, however little it may be, rather than let their capital lie dead; and the consequence is that all capital, like all labour, actually comes to a sale. As a fact we see that, in all economic communities, although the quantitative relations between wealth and number of wage-earners are extremely various, these two amounts exactly buy up each other. There are everywhere a few labourers who have no work, and a few capitals which are not employed, but this is, of course, not in contradiction to what has been said. I need scarcely point out that the presence of such unemployed is never traceable to the purchasing power of capital being insufficient to the whole number of the labourers—in a poorer country, indeed, a capital of half the amount would have to pay the same number of labourers, and actually does pay them—but always to certain frictional and temporary disturbances of organisation, such as are inevitable in a mechanism so complicated as the industrial division of labour in a great country.

We may, therefore, assume it as certain that the whole supply of labour, and the whole supply of present goods, come to mutual exchange. In this fact the length of the production period, and thus the amount of product which the undertaker may obtain through the labour he buys, obtains a certain definiteness. That is to say, we must, in any case, assume such a period of production that, during its continuance, the entire disposable fund of subsistence is required for, and is sufficient to pay for, the entire quantity of labour offering itself. If the period were to be shorter than this, some capital would remain unemployed; if longer, all the workers could not be provided for over the whole period; the result would always be a supply of unemployed economic elements urgently offering their services, and this could not fail to upset the offending arrangements.12

But we are not yet finished with the subject. It is not one single definite production period that harmonises with the above assumption, but a great many different periods. Obviously, given the capital and the number of workers, a very varying number of years can be provided for according as the wage of labour is high or low. With a capital of fifteen hundred millions for instance, our ten million workers can be kept in work and wage for ten years at a wage of £30, or for five years at a wage of £60, or for six years at a wage of £50. Now which of these possible cases will be the one actually adopted?—This will be determined, by the play of the same egoistic motives as regulate the formation of price in competition generally, in the following way.

Assume for a moment that the usual wage is £30. A capitalist then with £1000—for convenience sake we shall take this amount as the unit throughout the following discussion—may employ either 66.6 labourers in a one year's process, or 33.3 labourers in a two years' process, or 22.2 in a three years' process.13 Naturally he will choose the process which he finds most advantageous. Which process that is will be seen from the following table, based on the former scheme of productivity on p. 378, showing how many workers can be employed by £1000 in each production period, and how much annual profit may be got from that sum.

TABLE I
WAGE £30.
Production Period in years.	Annual Product.	Annual profit per labourer.	Number of employed.	Total annual profit on the £1000.
1	£35 0	£5 0	66.66	£333.30
2	45 0	15 0	33.33	500
3	53 0	23 0	22.22	511.11
4	58 0	28 0	16.66	466.66
5	62 0	32 0	13.33	426.66
6	65 0	35 0	11.11	388.85
7	67 0	37 0	9.52	352.84
8	68 10	38 10	8.33	320.82
9	69 10	39 10	7.4	292.5
10	70 0	40 0	6.66	266.66

The table shows that, in the given circumstances of all the factors, it is most profitable for the undertakers to devote themselves to a three years' production period. They obtain thereby the very considerable rate of 51.1%, while both in the longer and in the shorter processes the profit is lower. In these circumstances naturally all undertakers will seek to adopt this length of process. But to what does this lead? In a three years' process £1000 can employ 22.2 workers, and therefore to employ all the available capital in the community (viz. £1500,000,000) 33 1/3 million workers would be needed—while there are only ten millions. These ten million workers could be employed by a sum of four and a half million pounds, leaving capital to the amount of ten and a half millions lying idle. Of course these ten and a half millions of capital could not and would not remain so: they would compete for employment; attract labourers by offering higher wages; and the necessary result would be a rise of the rate of wages. The £30 rate, then, assuming the above position of the factors, cannot possibly be a permanent one.

This table proves that, if we assume £60 as the rate of wages, production in anything less than a five years' period shows a positive loss, while, of the longer periods, the eight years' process is the most profitable. It yields the modest interest of 3.54%, but, relatively speaking, it is the most favourable rate that can be got. It is easy to see, however, that it is as impossible for a wage of £60, as it was for £30, to be the definite resultant price of labour. Under the assumed circumstances of productivity the eight years' period is the most profitable length of process at a £60 rate of wage. By adopting it a capital of £1000 can employ only 4.16 labourers; consequently the entire capital of £1500,000,000 can employ only six and a quarter million workers; and the remaining three and three-quarter millions must starve. This again is impossible; the unemployed will offer their services in competition with each other; and wages will be pressed below the rate of £60.

At what point, then, will this overbidding and underbidding, which come from unemployed capital when wage is too low and from unemployed labour when wage is too high, come to an end? Obviously it will be when the most reasonable production period exactly absorbs the wage fund on the one side, and the labour offered on the other. This will be the case, as the following table shows, at a wage of £50.

TABLE III
WAGE £50.
Production Period in years.	Annual Product.	Annual profit per labourer.	Number of employed.	Total annual profit on the £1000.
1	£35 0	— £15 0	40	Loss
2	45 0	— 5 0	20	"
3	53 0	3 0	13.33	£40
4	58 0	8 0	10	80
5	62 0	12 0	8	96
6	65 0	15 0	6.66	100
7	67 0	17 0	5.71	97.07
8	68 10	18 10	5	92.5
9	69 10	19 10	4.44	86.66
10	70 0	20 0	4	80

At a wage of £50 the six years' production period proves the most profitable. It gives an interest of 10% on the invested capital, while a five years' process would return only 9.6%, and a seven years', 9.7%. Moreover, as at that wage the £1000 employs 6 2/3 labourers, the entire ten million workers and the entire fifteen hundred millions of capital find employment; and the point is reached where the formation of price may come to rest. All who have it in their power to disturb the settlement by further over or under bidding have no inducement to do so, and all who might have an inducement have not the power, as, on economic grounds, they are already excluded from competition. There is no idle capital which might be tempted to seek employment by overbidding, and there are no idle labourers who might be tempted to seek employment by underbidding. And, finally, the undertakers who have placed their production on the footing which makes this favourable position of things possible are rewarded by this arrangement being at the same time the most profitable for them, and they too have no inducement to make any change. Those undertakers, on the other hand, who might have wished to engage in longer or shorter processes, and would thus have made either capital or labour insufficient, are excluded from any such disturbing competition by the fact that such methods of production show either a loss or a smaller profit.

The price of labour, then, will and must15 settle at a wage of £50, and this involves, at the same time, an agio of 10% on present goods. I say, it must do so, for, so long as this point is not reached, there are certain tendencies always at work to force the price towards it. If, for example, the wage were only a little higher, say £51, the six years' process would still be the most profitable, but only 9,800,000 labourers could be employed by the available capital of £1500,000,000; the unemployed, by the urgency of their circumstances, would exert a pressure on the price of labour, till such time as they also could be taken in, which would be the case when wage came down to £50. If, on the contrary, the wage were a little lower; say £49, the employment of the ten million workers would take up only £1470,000,000 of capital; the unemployed remainder would attract employment through overbidding; and the result again would be a rise of wage till such time as the point was reached at which equilibrium all round could take place.

In the assumed state of all the factors an agio of 10% is therefore the economically necessary result. Why exactly 10%?—The considerations hitherto presented can only answer negatively that the necessary equilibrium could have been reached at no other rate of interest. But we may now inquire whether our figures do not bring out some other circumstances which may positively indicate a rate of 10%, and give us matter for a precise positive law of the interest rate.

To arrive at a position of equilibrium, the capital of the community had to be taken out of shorter processes where full employment could not be found for the existing stock of labour, and employed in gradually extending methods till all the labourers were fully occupied. This was arrived at in the six years' process. On the other hand, the adoption of still longer processes, for which again the capital is not sufficient, had, economically, to be prevented. In these circumstances the six years' producers are the last buyers, the "marginal buyers"; the would-be seven years' producers are the most capable excluded suitors for means of subsistence; and, according to our well-known law, the price that results must fall between the subjective valuations of these two. How does it stand with these valuations?

What we have to look to simply is: What is the utility which, for those two sets of buyers, depends on the disposal over a definite sum of means of subsistence? Here, first of all, it may be put down generally that, on the disposal over each half year's wage,—in the present case, £25,—depends one year's extension of the production period per worker.16 Accordingly, with respect to the six years' producers, it specially depends on their possession or non-possession of the £25 whether, as regards one labourer, they can embark on or continue in the six years' process instead of the shorter five years' process. But according to our scheme of productivity the year's return of one worker in a five years' process amounts to only £62, while in a six years' process it amounts to £65. What, therefore, as regards the marginal buyer, depends on his having the disposal over £25, is the obtaining of a yearly surplus product of £3. On the other hand, those would-be producers who are trying to take means of subsistence out of the market in order to extend the production period to a seventh year, could gain by their extension only a surplus return of £2 (£67 - £65). For them, therefore, all that depends on their disposal over the £25 is a surplus of £2, and they are excluded from competition inasmuch as the resultant price has established an agio which exceeds the rate of 2 on 25 (8%).

If therefore—and this is indispensable to equilibrium being reached—the extension of the production period is to halt at the limit of six years, the agio established by the fixing of the price must lie between the rate that represents the valuation of the last buyers (£3 on £25, or 12%) as upper limit, and the rate representing the valuation of the competitors first excluded (8%) as lower limit. And thus our former empirical and circumstantial demonstration of the rate of wage and the rate of interest at which equilibrium may be reached on the market, must point provisionally to the rate of 10%. It must at least point to the zone between 8% and 12%. The fact that, within this zone, the rate of 10% is exactly brought out, is due, of course, not to the limitations indicated by the valuations of the marginal pair, but, as described on p. 215 simply to the quantitative effect of supply and demand. We shall see immediately, however, that the wide latitude (8% to 12%) which our abstract scheme leaves for the narrowing action of supply and demand, looks considerable only on account of the figures accidentally chosen; in practical life the latitude given is almost always vanishingly small.

Meanwhile we may put the results at which we have arrived in general form as follows:—

The rate of interest—on the assumptions already made—is limited and determined by the productiveness of the last extension of process economically permissible, and of the further extension economically not permissible; in this way that the unit of capital, which makes this extension of process possible, must always bear an amount of interest less than the surplus return of the first-named, and more than the surplus return of the last-named extension.17 Within these marginal limits the price may be more exactly determined by the quantitative relation between wage fund and number of workers, according to the law of supply and demand.

In practical life, however, the latter method of determining price is seldom taken. It is true that in our abstract scheme there was an unusually wide latitude to come and go on, because we had assumed a sudden decrease of the surplus return from £3 to £2; that is, a fall of fully one-half. But in practical life sudden differences like this scarcely ever occur. The figures which represent the productiveness of the last permissible, and the first non-permissible extension come usually very close to each other, and, consequently, they are sufficient to limit the variations of the interest rate so strictly and sharply that the theoretically more exact determination by means of the relation of supply and demand is practically unimportant.18 Indeed, assuming that these two marginal limits are very near each other, one of them may even be left out of account without any serious inaccuracy,19 and the law be simply formulated thus:—The rate is determined by the surplus return of the last permissible extension of production. This coincides almost to a word with Thünen's celebrated law which makes the rate of interest depend on the productiveness of the "last applied dose of capital."20

Book VII, Chapter III

The Rate in Market Transactions—(continued)

But our task is not yet finished. Following the same lines as we took in developing the general law of the price of goods,21 we must attempt to lay down the concrete determinants which decide the degree of productiveness of the last extension, and from our knowledge of these we must, in particular, try to get an explanation of the variations to which the interest rate is subject in practical life,—sometimes rising, sometimes falling, but with a constant tendency in the latter direction, over the whole field of economical development in historical times. This analysis too will give us a welcome opportunity of verifying our abstract theory by experience. If we find that our theory, starting with certain assumed conditions of fact, leads us, of internal necessity, to expect just that movement of interest which, in the experience of practical life and history, we see actually and always taking place when these conditions are realised, we shall be justified in taking it is a strong guarantee that our theory, although it uses such abstract machinery in the stating, is no vain imagining, but a theory obtained from the study of practical life. Moreover in what follows I shall be in much less marked opposition to old doctrines than I have been in the foregoing chapters. For certain connections between the rate of interest on the one side, and definite facts on the other, are so distinctly and unquestionably given by experience, that it was impossible for the adherents of any interest theory, however erroneous, to overlook them; and, however different the theoretical points from which they may have started, they find themselves at one in recognising these.22 All the same I venture to hope that what follows will give more accuracy and definiteness, as well as a new and more adequate explanation, to many a proposition long accredited by experience.

Following the line of inquiry already pursued, I shall try to investigate the concrete determinants of the rate of interest, and the manner of their working, in such a way that we can successively vary the individual assumptions in our illustrative scheme, and then see what result the variation gives us as regards the formation of the interest rate. Let us look first, then, at the influence of the amount of the national subsistence fund.

Assume that, other circumstances remaining unchanged, the available subsistence fund amounts, not to £1500,000,000 but to £2400,000,000. The repetition of the same calculation as made above leads us to the conclusion that the equilibrium of the market cannot now be attained otherwise than by an eight years' production period, a £60 rate of wages, and a corresponding interest rate of 3.54%. We may check this result from Table II. on p. 389, which is calculated on the £60 rate of wage. It shows that, where the rate of wages is £60—the rate of productivity being given—the undertaker finds an eight years' production period the most profitable; that 4.16 labourers may be employed by £1000 of capital, and, therefore, 10,000,000 of labourers by £2400,000,000; and, finally, that this (relatively) most profitable method of production yields 3.54% interest on the undertaker's capital.

As compared with the earlier ones this rate shows a considerable decline, the reason of which is very easily explained. When the subsistence fund is increased men can only keep it fully employed by entering on further extensions of the production period, which extensions are accompanied by steadily decreasing surplus returns. Indeed the surplus return of the last extension of production economically possible (from seven to eight years) is only 30s., and the surplus return of the first non-permissible extension (from eight to nine years) is only 20s. And since the rise of the year's wage from £50 to £60 requires, for the one year's extension, not a capital of £25, but a capital of £30 per man, the marginal limits for the interest rate are 30s. or £30 (i.e. 5%) as upper limit, and 20s. on £30 (i.e. 3 1/3%) as lower limit. As a fact the agio of 3.54%, which we found empirically, falls between these determining marginal limits.23

TABLE IV
WAGE £42.
Production Period in years.	Annual Product.	Annual profit per labourer.	Number of employed.	Total annual profit on the £1000.
1	£35 0	— £7 0	47.62	Loss
2	45 0	3 0	23.81	£71.43
3	53 0	11 0	15.87	174.57
4	58 0	16 0	11.905	190.48
5	62 0	20 0	9.524	190.48
6	65 0	23 0	7.93	182.39
7	67 0	25 0	6.8	170
8	68 10	26 10	5.95	157.675
9	69 10	27 10	5.29	145.475
10	70 0	28 0	4.76	133.28

Assume, conversely, that the available subsistence fund amounts only to £1000,000,000, the equilibrium, as will be seen from Table IV., is attained at a rate of wage of £42, and an agio of 19.048%. This is accompanied by some interesting circumstances which will repay a moment's attention, as they may be often enough realised in practical life, although not seen there in their full abstract purity. At a prevailing wage of £42, as it happens, two different production periods of four and five years respectively are equally profitable, and pay 19.048% interest on the capital invested in them. The result of this is that neither of them economically shuts out the other; both may be adopted simultaneously; indeed, not only may, but must, to keep the equilibrium. If the four years' period alone were adopted, only £840,000,000 of capital would find employment at a wage of £42.24 If, again, the five years' period were exclusively adopted, the existing capital would employ only 9,524,000 labourers;25 and in either case the unemployed elements would, as we know, disturb the equilibrium by overbidding and underbidding. The equilibrium can only be found if the two equally profitable methods of production are engaged in simultaneously, when 7,619,000 labourers will be employed by a capital of £800,000,000 in five years' production and 2,381,000 labourers by a capital of £200,000,000 in four years' production.

And, in virtue of this peculiarity, the latitude allowed in fixing the agio by the valuations of the marginal pair will be much more sharply limited in this than in the former examples. The last economically permissible extension of production is from four to five years, which brings in a surplus return of £4, that being a surplus on £21, half the year's wage. But, as it happens, the first excluded extension of production is also that from four to five years, inasmuch as—as shown above—the existing capital allows only a portion of the producers to take the five years' production period. Consequently the surplus return of the first excluded process—that which forms the lower limit of the interest—is also fixed at £4. The upper and lower limit, therefore, coincide, and the interest must be determined strictly at the rate of £4 on £21; that is, at 19.048%, just as actually shown in our former scheme.26

Now the agio here is considerably higher than in the former cases. And our theory again explains it quite simply. The reason is that the diminished subsistence fund allows only of comparatively short processes on the average, and consequently the "last extension of production"—that which decides the interest rate—falls in a sphere where any extension of the production periods is attended by very considerable surplus returns.

So much for the effect of an alteration in the amount of the subsistence fund: we have still to follow the effect of an alteration in number of workers. Any detailed calculation here, however, should not be necessary. It does not require much consideration to see that a change in the number of labourers must exert its influence on the rate of interest in exactly the opposite direction. Whether, for example, the number of labourers remains steady at 10,000,000, and the subsistence fund contracts from £1500,000,000 to £1000,000,000; or whether the subsistence fund remains at £1500,000,000 and the labourers increase from 10,000,000 to 1500,000,000;—in either case the subsistence fund is just sufficient to employ the existing labourers partly in four, partly in five years periods, while the "last" and decisive surplus return is £4 on £21, and the resulting rate 19.048%. And it is as clear that, if subsistence and labourers vary simultaneously in the same direction—say that both increase—the variations will weaken the efficiency of both, and the final movement of the rate will follow that direction taken by the stronger of the varying factors; and that, on the other hand, if both factors vary not only in the same direction but also in the same ratio, the rate will remain unchanged. Suppose, for instance, that the number of workers and the amount of the subsistence fund both double, it is evident that the doubled fund will be sufficient to provide for the doubled numbers over the same production periods as before, and that the "last" and decisive surplus, and with it the interest rate, will remain unchanged. If, again, the fund were to double while the numbers increased only by a half, it is obvious that, on the average, a longer production period could be adopted than formerly; in which case the decisive "last" surplus return would be reduced to a lower point on the descending scale of surpluses, and the interest rate would also fall.

Finally, we might inquire, on the same lines, what will be the effect of an alteration in a third factor, the state of productivity, assuming that subsistence fund and number of labourers remain constant. Here also we may spare ourselves any detailed tabular statement. It does not require any exact calculation to prove that if, other circumstances remaining unchanged, the scale of surplus returns constantly shows higher figures, the surplus return yielded by the last extension of production that is economically permissible—that which decides the interest rate—must be higher, and vice versâ. Say that subsistence fund and number of labourers stand in such a relation as to permit of an average five years' production period, the interest will be higher if the extension of the production period from four to five years is attended by a surplus return of £6 as against £4, or of £4 against £l.

We have, then, over the sphere of our investigations so far, to record three elements or factors which act as decisive determinants of the rate of interest: the Amount of the rational subsistence fund, the Number of workers provided for by it, and the Degree of productivity in extending production periods. And the way in which these three factors affect the rate may be put as follows:—

In a community interest will be high in proportion as the national subsistence fund is low, as the number of labourers employed by the same is great, and as the surplus returns connected with any further extension of the production period continue high. Conversely, interest will be low the greater the subsistence fund, the fewer the labourers, and the quicker the fall of the surplus returns.

This is the way in which the interest rate should be formed, and the way in which it should alter, if our theory is correct. How is it in actual life?—Exactly as our formula predicts, and thus experience gives that formula the most complete verification. For, first, it is one of the best accredited and recognised facts of economic history that the increase of the subsistence fund, or, to use an expression not quite so accurate but yet roughly significant, the increase of the community's capital, has a tendency to depress the rate of interest. Second, it is no less familiar and self-evident that here we do not speak of the absolute amount of the national capital, but of the relation between that capital and the numbers of the population: in other words, we mean that an increase of population, without a simultaneous increase of capital, has a tendency to raise the interest rate. And, thirdly, it is also an acknowledged empirical fact that the discovery of new and more productive methods of production, outlets, business opportunities, etc., which conduce to check the fall of surplus returns, tend to raise the rate of interest, while the closing of former opportunities of production or sale, or other occurrences which end in a reduction of the previous degree of productiveness, tend to lower the interest rate. We find, therefore, that all those factors to which, on the lines of our former inquiry, we were forced to ascribe a decisive influence on the interest rate, do, as a fact, possess and exert that influence.

And now it is time to give, one by one, the features and forms of actual life to our abstract scheme.

Book VII, Chapter IV

The Market for Capital in Its Full Development

Up till this point we have assumed that the annual product of each worker, and also the annual wage, is the same in all branches of employment. Of course, in actual life this is not the case. But that does not in the least disturb the normal connections and relations we have laid down, otherwise than by acting as if there were a somewhat different number of unskilled labourers with ordinary wages and ordinary productivity. For even if the absolute amount of the return to labour on the one hand, and that of the wage of labour on the other, be ever so various in the various branches of employment, still the ratio between these two amounts will, in virtue of the familiar law of equalisation of profits, remain the same all over, and this is the essential matter in the question of Interest. If, for instance, in one branch of production, the wage of unskilled labour be £50, and the product of a year's labour £65, in another branch, carried on mostly by skilled labour, the worker's annual product may, perhaps, be double, say £130. But then the wage of such a worker will also rise to double, say to £100. For, if it did not rise, the undertakers in this branch of business would obtain an abnormal surplus; this would attract stronger competition; and competition would either raise wages by creating an active demand for workers, or press down the price of products by increasing supply. But if the wage of the skilled labourer were to rise higher than £100, the undertakers in question would again obtain too small a profit, and the consequent limitation of that branch of production would undoubtedly either press down the wage of workers, who would now have become partly superfluous, or raise the price of the restricted product, till such time as wage and product, here as everywhere, stand in the ratio of £50 to £65, or £100 to £l30. But if this ratio between wages and product holds, all the ratios relating to the formation of interest are exactly as they have been assumed to be in our earlier tabular statement, with the single qualification already mentioned, that the existence of better paid skilled labour has exactly the same effect as a somewhat greater number of normally paid unskilled labourers. For, obviously, it is all the same as regards the resultant arrived at in the subsistence market, whether two labourers produce £65 each, and claim £50 each of subsistence, or one labourer produces £130 and claims £100.

Further, we have assumed up till now that, in all branches of business, the increment of annual return that accompanies the increasing extension of the production period, moves in the same rate of progression. This also is not the case in real life. On the contrary, each branch of production, in virtue of its technical circumstances, has a different and often, indeed, a very different scale of productivity. It is, for instance, quite possible that three different branches of production—call them A, B, and C—which were each turning out in a one year's process an annual product of £50, might show an exceedingly divergent return (or surplus return) if the process were extended for two to five years more. We might have, something like the following:—

Production Period.	A				B				C
	Return.		Surplus.		Return.		Surplus.		Return.		Surplus.
1 year	£50	0	—		£50	0	—		£50	0	—
2 years	51	0	£1	0	52	0	£2	0	60	0	£10	0
3 "	51	10	0	10	53	0	1	0	65	0	5	0
4 "	51	16	0	6	53	10	0	10	67	10	2	10
5 "	52	0	0	4	53	16	0	6	69	0	1	10

Naturally this has its practical consequences. It is the producers' interest to obtain the greatest returns or surplus returns. They will, therefore, invest the available capital where they are tempted by the greatest returns. If there is capital over, or if new capital is added, they will look out for the next best paying employments, and so on, in such a way that they will only take a less paying employment when all the more paying chances have been utilised.

Now if, as we have hitherto assumed, the progression of surplus returns obtainable from similar extensions of production were the same in all branches of employment, then, in all branches of employment, the same surplus would be reached by the same length of process, and, consequently, an equally long production period would prevail simultaneously over all employments. As capital increased it would press on, with one united front, from one to two, from two to three years' production, and so on. But, as we have said, owing to different technical circumstances in the various branches of production, we actually meet the same surplus return in productive periods of different lengths. While, then, in the investing of capital we pursue an isohypse—to borrow a geographical term—of surplus returns, we must diverge from an isohypse of extensions of production. Production in its various branches must be carried on in unequally long processes; and, indeed, in those branches where the surplus return sinks rapidly, it must be carried on in shorter periods.

The above scheme will illustrate this. First of all production is carried on, in all three branches, in a one year's process with a return of £50 per labour-year. If the subsistence fund increases so much that at least a partial extension over the one year's period is possible, people will pass first to a two years' process in branch C, which bears a surplus return of £10 for a half-year's payment.27 Then the production period will be extended in the same branch C to three years (with a surplus return of £5), and to four years (with a surplus of £2:10s.), while the other two branches of production are all the time persisting in the comparatively unremunerative one year's process. Only where the subsistence fund increases still further will they pass in branch B to two years' production (with a surplus return of £2). But in branch A they will not be able to extend the period of their production (which only gives a surplus return of £1), until all opportunities of production have been utilised up to the isohypse of £1. This will only be the case when in branch C the production period has been extended to five years, and in branch B to three years. Production, then, will and must be carried on simultaneously in the three different branches in two, three, and five years' periods—a conclusion which we see verified in economic practice in the familiar fact that different products are produced with very different degrees of capitalism. Food, for instance, is a much less capitalistic product than metallic goods, or clothing stuffs, or manufacturing products generally.28

How, then, is our law of the rate of interest affected by this complexity of actual circumstances?—It is not disturbed in the least. For all the essential circumstances on which it rests remain unchanged. It is still the case that the existent capital is employed in gradually extending processes till it is fully occupied. It is still the case that there is a certain level of these extensions, yielding a certain surplus return, which is the last economically permissible, and a succeeding level yielding a somewhat less surplus return which is economically not permissible. And, finally, it is still the case that the surplus returns of these "marginal employments" also form the marginal limits of the interest rate. The single difference—and that not an essential one—is that the isohypse of the surplus returns, and with it the line of the last permissible extensions of production, is not a straight line, but runs in an undulatory or zigzag fashion through the different branches of production, according as the same surplus return is reached by them in longer or shorter processes. But this modification gives our law a still sharper power of definition. For as, in consequence of the complexity of actual life, the scale of productivity is much more finely graduated than was our simple typical scheme, the two marginal limits, as a rule, stand much nearer each other, and consequently narrow the zone within which price is determined very much more closely than is shown in our abstract illustration.29

To proceed. Hitherto we have assumed that the demand for present goods comes simply from the wage-earners (either directly or through the mediation of undertakers). But this, again, in actual life is not correct: there are a few other competitors in the market.

There are, first, the suitors for Consumption credit. Their demand is graduated and stratified according to the urgency of their need for present goods.30 One class will be in such pressing need that, in the worst case, they will be glad to offer an agio of 100%: another class will only go the length of 80%: a third will offer 60%: others 50%, and so on down the scale, perhaps, to 2%. Now these suitors join their claims to the demand which comes from the wage-earners and each class or layer of them is satisfied concurrently with that layer of productive employments yielding a surplus return that represents the same percentage. If, for instance, the investing of capital reaches the isohypse of a surplus of £4 on £21, all those suitors for loans will be satisfied simultaneously who, in the worst circumstances, are able to offer 19.048% or more: if it reaches the isohypse of a surplus of £2:10s. on £25 all suitors will be served who are willing to offer at least 10%, and so on.

It would be quite erroneous to understand this as meaning that the rate of loan interest is determined simply by the rate of interest obtained in production. It contributes just as much to determine the latter, as it is determined by it. Both classes of demand work in entire co-ordination. The fact that here is a certain class of suitors for consumption loans, and that this class takes a portion of the existent means of subsistence out of the market, involves that there are fewer means at the disposal of productive investors; investment must call a halt at a higher isohypse of surplus returns; and this again involves a higher rate of interest in the sphere of production. Conversely the presence of the productive demand results in a considerable portion of the means of subsistence being claimed for productive purposes, and this again has the result that the wants of consumption credit are not satisfied at such low levels as would otherwise have been the case. In the present day, of course, the productive demand is so much the more important of the two that one is apt to suppose that it alone rules the rate of interest. But this false impression is now and then sensibly corrected by experience when some great state-loan for consumption purposes—say for a war—makes the general interest rate fly up. But even when the demand for consumption credit is quite insignificant, it does not fail to exert some influence on the rate; it may always be contended that, if it were to disappear, the interest rate would be at least a fraction lower than it is now.

Another competitor in the market for capital is the Landowner. If owners work their own lands, and are content to maintain themselves by the fruits of their labour (whereby they lay past their rent as saving), they are no burden on the subsistence fund of the community. If, however, they live wholly or partially on their rents, their subsistence also must be advanced out of the community's fund, for a length of time proportional to the production periods in which their land is laid down. Suppose, for instance, that the wealthy cotton planter lives in idleness on his rents, and that the total production process of textiles, including the various stages of spinning, weaving, etc., down to the manufacture of the finished cotton stuffs, takes five years, the maintenance of the planter, just as much as that of his fieldworker, must be advanced out of the subsistence fund over five years. The advance will then, of course, be refunded out of that quota of product which—according to the law of complementary goods—is due to the co-operation of the uses of land; but, in the meantime, the landowner lives at the expense of the subsistence fund.

What kind of effect has this on the rate of interest?—Its effect is entirely similar to that of consumption credit. The competition of landowners takes a certain amount of subsistence out of the market; it thus curtails the investment of capital in production, and makes it call a halt at a higher isohypse of surplus returns; and this, finally, keeps up the rate of interest. In doing so, however, the claim of the landowner on subsistence comes under a reflex influence from the height of the interest rate. This, of course, has no reference to the height of the annual rents—for this is fixed by those circumstances which influence the economic value of uses of land, and need not be mentioned here—but to the number of annual rents for which advances of subsistence are demanded. That is to say: if interest is high, lengthy periods of production are not profitable;31 the uses of land will be invested in comparatively short processes; and, as consequence, the advances made to landowners will only be for short periods. If, whenever, the interest rate is low, then, concurrently with the increase in production and consumption credit, increases the subsistence advanced to the landowners; it now extends over greater number of annual rents according as the uses of their land can now be invested in much longer processes.

There is one other competing party in the market, the capitalists themselves. So far as they live, entirely or partially on their interest, their maintenance also will be defrayed from the subsistence fund, and, in so far as the fund available for other purposes is thereby contracted, will the interest rate tend to rise. There is, however, one important difference between the claims of the capitalist on subsistence, and those of the wage-earners, the suitors for loans, and the landowners. The claims of the latter are the cause of the agio on present goods: the claims of the former are simply its effect. If the claims on subsistence presented by the wage-earners, borrowers, and landowners did not by themselves alone exceed the existent subsistence fund, there would be no agio on present goods, and, as consequence, the capitalists, as such, could make no valid claim for subsistence on the funds of the community: in default of an income from interest they would have to support themselves by work. It is only because there is an agio, as effect of the other classes of demand, that the capitalists can claim a quota of the product as interest, and claim it indeed in advance. Reflexly, of course, this claim of the capitalists influences the rate of interest. It is exactly as, for instance, in electrical induction. The chief current first calls out the induction current, and then the latter reflexly influences, and indeed strengthens, the chief current. Just in the same way does the demand of the other competing parties in the market, by creating an agio, first call out the claims of the capitalists on subsistence: but, so soon as the agio is a fact, it diverts a portion of the subsistence fund into the income of the capitalists; it thus contracts the disposable remainder; determines the "saturation point;" in the remaining branches, at a higher marginal utility; and so, in the last resort, causes a rise of the agio.

Suppose we try now to unite the scattered features into one picture. In its collective stock of wealth every people possesses a greater or less fund of subsistence. This is consumed definitively by uneconomic persons who waste their parent wealth,32 and by the suitors for consumption credit: it is consumed as an advance by landowners, capitalists, and wage-earners during the social period of production.33 The greater the subsistence fund, the longer can the social period of production be extended, and the more completely can the demands for consumption credit be satisfied. The return of the last extensions of production still possible, and, concurrently, the valuation of the last suitors who obtain loans, determine the height of the agio on present goods.

Consequently, on the basis of our completed inquiries, the following factors emerge as the most important concrete circumstances or "determinants" which influence the rate of interest.

First come the same three factors which from our inquiry into the circumstances of the labour market in its most abstract form we were forced to recognise as decisive:—

1. The amount of the National Subsistence Fund.
2. The number of producers to be provided for out of the same.
3. The position of the scale of surplus returns connected with the increasing extensions of process.

After these come:—

4. The extent and the intensity of the desire for consumption loans.
5. The existence and the height of land rent. The higher that rent is, the more persons there are who can live on their rents without working, and the higher will be the standard of living by which they regulate their maintenance. Naturally, if the amount of subsistence which they take as advances out of the social subsistence fund goes parallel with that standard of comfort, there will be the less for other purposes, and interest will remain at a higher level. The existence of land rent, therefore, tends to enhance the rate of interest.34
6. The existence of a numerous capitalist class living on their interest—for reasons which apply equally to landowners and capitalists.
7. Finally; the economical habits of the population have a great influence directly and indirectly. Indirectly, inasmuch as national thrift gathers together a greater stock of wealth: directly, inasmuch as thrifty living diminishes the claims on subsistence, whereby, if subsistence remains constant, the population is maintained for a longer period, and the investment of capital is extended till there is a lower isohypse of surplus returns. If a nation is thrifty, neither landowners nor capitalists will consume all their rents; they will either work as undertakers, and live simply by their own labour, or at least they will save a portion of their income. The portion saved represents, as it were, a certain amount of the subsistence fund allotted but not taken up, and the amount is left free for another employment, particularly for a further extension of the production period. The same is true of savings which the labourers, or such persons as are in possession of a secondary income, are able to make.35

If we pursue this line of thought a little further we shall repair an omission in our former analysis. Hitherto we have considered subsistence fund and subsistence claims as something actually existing and present: we must now consider them in the act of becoming. Hitherto we have looked at the subsistence fund as standing over against, and disputing the claims which the open market made on it: we have still to consider the noiseless but never-ceasing war waged on wealth in each individual economy by the desire of enjoyment. What follows will form both continuation and conclusion of another line of thought on the subject of the formation of capital begun on p. 124.

Book VII, Chapter V

The Market for Capital in Its Full Development—(continued)

Every man has the power of disposal over a certain amount of goods, small or great, partly delivered him as "parent wealth" by the past, partly obtained by him as "income" in the present, and these two together form his "wealth" (Vermögen). The natural destination of this wealth is to satisfy his wants. It may be said wealth exists for wants. But many wants compete with each other and put in rival claims. On the one hand, wants of different kinds compete at the same point of time; on the other hand, wants of different times—wants of the present and wants of the future—conipete with each other. How are these various claims to be adjusted?

In a good economical system they will be adjusted in accordance with the principle of "economical conduct," which prescribes that the goods available should secure the highest possible personal utility. And since even the richest man's wealth is not sufficient to satisfy all his wants and wishes, this again demands that he make a wise selection among his wants so that he may procure satisfaction, as his available means will allow, to the most important, and leave the unimportant unsatisfied. Applied to the competition of different classes of wants this leads to the principle of harmonious satisfaction; by which is meant that, in all branches of want, satisfaction reaches down to the same level of importance, so that, over the whole field, the unit of goods procures the same marginal utility. For if in one department of want a man were to break off the satisfaction he gets at a high level, in order to seek for satisfaction in another department at a lower level, it would mean that he deliberately renounced a greater utility for a less one, and this would be to run counter to economical principles.36

But we employ the very same principle of harmonious satisfaction, and for the same reasons, to regulate the competition between the wants of various times. In the economical furtherance of our life we reach the highest possible point, when we distribute the means of satisfaction, which we have at our disposal, over the various periods of time in such a way that the last unit of goods procures the same marginal utility at all points of time. For, so long as this is not the case, we shall, obviously, be able to increase the amount of our gain by withdrawing units of goods from those times in which they procure a smaller marginal utility, and applying them to the provision of those times in which they are fitted to procure a greater marginal utility.37

Rationally speaking, therefore, of the presently existing stock of goods we should only consume so much in the present that the satisfaction of present wants is broken off at the same level as the satisfaction of wants will be broken off in future economic periods—considering the then state of wants and satisfactions: everything over that should be preserved for the service of the future. In terms of this rule "parent wealth" should, economically, almost always be saved. For, if it were consumed in the present along with income, the present would be, relatively, over-provided, and provision would be made for unimportant classes of want; while, in the following years, only the current income, and that in decreased amount, would be available, and the consequence would be a loss of satisfaction affecting even important classes of want. In exceptional cases, on the other hand, it is directly on the lines of rational economic management to lay hands on this parent wealth: at such times, say, as the income of the present is abnormally small, or want is abnormally urgent, while the prospects are that the future will bring a more favourable state of provision.

As regards the employment of the current income, the standard law of harmonious satisfaction of present and future will lead to a very different method of treatment in different cases. People whose future is secured by safe permanent income, and who, at the same time, do not expect any essential increase of their wants, may, quite reasonably, consume their entire current income in the current period;—such people, for instance, as rich landowners who have not a very large family, or who have no wish to secure each of their children in a similarly comfortable life. People, again, whose future income is uncertain or decreasing, or people whose future wants—either their own or their families'—will rise while their income is likely to remain unchanged, must, economically, retain a portion of their present income against the more poorly provided for wants of the future: they must "save," and must save enough to put the present and the future on a level as regards provision.

To be exact: something more should be saved, and the provision be made a gradually augmenting one. The reason for this lies indeed in the existence of interest. Interest on capital being a fact, what we have to choose between is not whether £100 worth of wealth gives us more utility according as we consume it to-day, or consume it next year, or consume it in two years. The £100 saved to-day increases in the next year, through interest, to £105; in the next again to £110, and so on; and the choice now is whether it is more useful to us to consume £100 to-day, or £105 next year, or £110 the next again. And we shall increase the total amount of our utility by withdrawing more and more goods from the present so long as, with £105 in next year, or £110 in next again, and so on, we can secure a greater marginal utility than by £100 in the present year. Thus while, if there were no interest, the limit of rational saving would be the point at which the utility obtainable with just £100 now, and with £100 obtainable at various future periods, is exactly the same, that limit, when interest is a fact, is the point where the provision for the various periods is so adjusted that £100 to-day are as useful as £105 next year, £110 in two years, and so on. But if an increasing expenditure in the future only gives the same amount of utility, it presupposes that, as time goes on, wants of less and less urgency are satisfied—in other words, that the provision for future periods is becoming progressively more ample.38

Thus it would be if the principle of "economical conduct" were followed with mathematical exactitude. But one might almost say that there is no point where it would be so difficult for men to act up to the claims of this principle as here. To divide their stock of goods adequately between present and future, they would require to know exactly both the future's want and the future's provision—the provision which the future periods when they come will make for themselves. But men have merely vague conjectures as to both amounts. Even as to the momentous question of how many future periods should in general be provided for, the uncertainty of human life makes them grope about completely in the dark—an uncertainty which, it must be said, has no disturbing influence on the economical transactions of that very large class who are anxious to provide, not only for themselves, but, with as much or even more devotion, for their heirs. All the more sensibly, however, is economical conduct disturbed by the familiar psychological fact that almost all men, in greater or less degree, underestimate the future and its wants.

Under the influence of the circumstances just described the economical conduct of human affairs suffers a twofold deviation from the ideal of economical provision. First: men provide for the future, on the average, more insufficiently than they should. They do not distribute their goods between present and future in such a way, that the marginal utility of the unit of goods allotted to the present is equal to the effective marginal utilities of those units allotted to future periods and increased by the intermediate interest. They distribute them in such a way that the marginal utility of the present unit of goods is equal to the marginal utility of the units assigned to the future, as that marginal utility is perspectively reduced. They save something for the future only in so far as it is clear that, if they did not, they would have to do without future satisfactions whose urgency, even as partially underestimated by them, still appears as great as the urgency of the last present wants which are satisfied, while its real urgency is, to a more or less degree, greater. Since the partial undervaluation of the future varies excessively in different individuals, classes, and nations, the divergence from the ideal of economic provision caused by it is, naturally, very different in degree. Among prudent and savingly disposed peoples its influence will be almost nil; in others it will show itself only in an insufficient percentage of saving; in others, again, in the absence of all saving, or even in light-hearted squandering of parent wealth. Second: economical deliberation on the claims of present and future is not often a finely worked-out piece of economic calculation. For the most part it is only a rough and ready reckoning of tendencies. For exact action, before deciding whether to "spend" or "save" a particular sum of goods, one would always have to be making an accurate picture of want, provision, and marginal utility for the current period, and another picture of want, provision, and marginal utility for all future periods. But this is a piece of work which is somewhat difficult, always troublesome, and one that, in spite of all care, offers no guarantee of any correct result; for, in dealing with the future, one is always compelled to work with very uncertain and conjectural data. In these circumstances not only is it easily explained, but, from the point of view of economical conduct, it is even commendable39 that the majority of men, instead of repeating from one case to another, or from one year to another, the troublesome and yet deceptive calculation of the claims of present and future, should, once for all, accept the guidance of an economic tendency which suits their circumstances fairly well, and only make a revision on occasion of great changes in their economical position, such as a marriage, receiving a legacy, and the like.

Very often this rough and ready way of economic deliberation takes this form;—that persons, to whom the exact application of the principal rules of economical conduct is too troublesome, make a secondary rule for their circumstances, and for the time live up to it. One man, for example, makes it an inviolable rule to keep his parent wealth intact: another, to leave his cumbered estate free to his children: a third, to put past so much that he may leave each child a farm: a fourth, to save enough to yield himself £500 a year, and so on. Secondary rules like these will generally coincide, more or less, for those who adopt them, with the demands of the true principle of economic conduct. Sometimes, however, they do not thus coincide, with the result that the people who faithfully follow their secondary rule sin grievously against the primary law. For instance, it is grossly uneconomic conduct in any one to cling doggedly to his resolution of not breaking on his parent wealth, and refuse the costly treatment necessary to restore his health; it is uneconomic not to make some sacrifice for the education of one's children; and so on. Finally, a great deal of uneconomic conduct arises from the fact that people who have once got into a definite habit of saving, quite reasonable at the time when it was commenced, persist in it, in a wooden sort of way, when their economic position has entirely altered. How often do we see people on the very brink of the grave, who have become rich through great saving, still grudging everything to themselves and others, and continuing to scrape and hoard mechanically for love of it. They begin with saving for love, and they end with love for saving.

Of these two deviations from the ideal economic conduct, the first mentioned is the more important and the more pernicious. The neglect of exact calculations prevents people from following closely the guidance of economic conduct, but it very seldom prevents them from being more or less true to it; while the psychological undervaluation of the future forces men positively—and often far—off the lines of economic conduct. In the undervaluation of the future, we have thus to notice a factor of interest and of the interest rate which, economically, is not at all a pleasing one, but, practically, is a very active one. In an earlier chapter we saw that it co-operates in the origin of the phenomenon of interest, in so far as it assists to give a foundation for an undervaluation of future as against present goods: now we come to recognise it also as an exceedingly active indirect determinant of the rate of interest. The stronger its action in a community, the higher will interest rise in that community. For the partial undervaluation of the future leads to curtailing the claims of the future as against those of the present; to assigning too many instruments of satisfaction to present wants and too few to future. But this leads, on the one hand, to an increase of the present claims on subsistence, and, on the other hand, to a wasteful nibbling at the stock, or, at least, to an inadequate renewal and increase of it through saving: and thus emerges the situation favourable to a high rate of interest, viz. that a (relatively) small subsistence fund is eaten up by (relatively) heavy claims on subsistence, and so suffices only to defray these claims for a relatively short period.

The theory I have put forward has a certain resemblance to the noted, or perhaps I should say notorious, "Wage Fund theory" of the older English school. Like it I maintain the existence of a certain Subsistence Fund, from which the wages of labour in any country are defrayed, and, like it, I attribute to the amount of the subsistence fund an important influence on the reciprocal height of wage and interest. But here the resemblance ends. All the other features, and, among them, the most essential features of both theories, are widely divergent. The Wage Fund of English economists, although considered by them a given and fixed amount, is really a fluctuating indefinite amount; an amount which, consequently, cannot give any secure point of support on which to base any conclusion as to the height of wage. I mean that the "amount of capital destined by capitalists to pay wages" is neither equivalent to the total national capital, nor to the total "circulating capital;" nor yet to any one fixed quota of the national capital. It represents a variable portion of the community's wealth, and a portion the extent of which varies directly, among other things, with the height of wages: it is greater when and because wages have risen, smaller when and because wages have fallen. In explaining, then, the rate of wages by an amount which itself is conditioned by the rate of wages, the Wage Fund theory describes a circle.40 My Subsistence Fund, on the other hand, starts with a fixed given amount—the stock of wealth accumulated in a community. Of course that amount of goods which specially serves as subsistence for labourers, and which I might call the "Wage Fund," forms a part of the total subsistence fund. But the amount of this portion does not hang in the air, as it does in the English theory: in exactly analysing what parties share in the total subsistence fund, and according to what laws, my "wage fund" becomes—at least relatively—fixed and definite.

But the most important difference is the following. The English theory has it that the rate of wages is simply got by dividing the wage fund by the number of existing workers. This is entirely wrong. In any case the labourers get the wage fund wholly and entirely as wage: but that does not say wage for what time;—for one year, or two years, or three years, or more. The increasing of the subsistence fund has not at all the result, assumed by the English school, that, the number of labourers remaining constant, the rate of wage rises in the same proportion as the amount of the fund increases. The increase of the subsistence fund is, in the first instance and principally, used up in lengthening the production period; and it is only in so far as the lengthening of the production period leads, at the same time, to a decrease of the surplus returns (according to the diminishing scale of surplus returns which accompanies successive extensions of production) that it leads to a curtailment of the capitalist's share, and to a proportionate rise in the wages of labour; the rise too being in a much weaker ratio than the increase of the subsistence fund. The English Wage Fund theory has thus a core of truth, but it is wrapped up in a quite overpowering mass of error.41

And now we may dispense with one last abstraction which has served us as scaffolding in our work of explanation. Hitherto we have represented the total supply and the total demand for present goods as concentrated in one single great market. Instead of this, the commerce in present and future commodities is split up into innumerable part markets. First it is divided into certain great groups, such as the Loan market, the Labour market, the Land market, the market for Concrete Capital. And each of these markets is divided up again and again, partly according to branches, partly according to districts of business. There is one market for mortgages, another for business credit in connection with large undertakings, and still another for business credit in connection with small. There are different loan markets for the peasant and for the citizen, for men of position and for the poor artisan or factory hand, and so on. And, again, within each of these subdivisions there are as many distinct local markets as there are natural or artificial districts devoted to that particular department of economic life. The Labour market, too, is as much split up as the Loan market; first, there are as many groups as there are branches of labour, and then each group is divided up into as many part markets as there are local districts. And so on through all the chief groups above named.

What results from this division and subdivision?—As there is not one market only for present goods, neither is there only one price for them, but many and diverging market prices, as these arise directly out of the relation of supply and demand ruling in each of the individual part markets. There are in the community at the same moment perhaps a hundred different agios on present goods, and, accordingly, a hundred different rates of interest. But the hundreds or thousands of part markets are not hermetically sealed against one another. They are all in communication, and constantly engaged in arbitrating each other's prices. If in one part market the agio on present goods is for the time abnormally high, new amounts of capital quickly press into it to get the advantage, and thus reduce the advantage again to zero. If, conversely, in one part market the agio is for the moment abnormally low, the fact is sufficient to prevent any further accession of capital, and even to convey a part of the capital employed in it to other and more favourable part markets, till such time as the unfavourable difference of price again disappears.

It is, therefore, quite right to say that the price which obtains in each part market is, indeed, first determined by the relation of supply and demand as it exists in the special part market, while this local condition of the market itself, and with it the local price also, is determined indirectly by the immensely more powerful pressure exerted by the totality of supply and demand over the whole community. The vast mass of the national supply, acting under the influence of those tendencies to equalisation with which we are familiar, forces itself into all part markets in proportional amounts. Part markets, where there is not sufficient capital, it hurries from other quarters to supply: from part markets over-supplied it flows off to other communicating part markets. And if there is neither inflowing nor outflowing, and if, therefore, the local market seems to form its local price purely of its own power, it is then that it is really least independent: it does not require to yield to any foreign market influences at the moment just because it has so completely yielded to them already. It is for the moment at rest only because it is supplied, in exactly the proportion which is required and effected, by the pressure coming from the total relation of supply and demand over the community.

It was then no empty abstraction when we spoke of one united gigantic market for present goods, and of the laws of its united market price. The circumstances of the whole decide on the average amount of supply given to the part markets. Local influences may, for long or for short periods, raise the supply above the average level in one place, and depress it below the level in another, but these are only secondary phenomena, showing themselves, as it were, on the surface of the principal movement, and carried up or down with it—just as the surface of a great wave is furrowed and ridged by smaller wavelets that rise and fall with it.

If the mobility of capital were perfect, the particular divergences from the normal rate of interest could not have any considerable strength, and still less any considerable duration. But as matter of fact there are numerous hindrances, little and great, which check the levelling ebb and flow of capital like weirs on a stream, and these raise or depress local prices. People do not so easily change their employments of capital. If sugar-refining yields one per cent more than cloth-making a powerloom weaver does not become a refiner on a snap of the fingers, and it may be a pretty long time before so many people have put capital in sugar-refining that the rate of profit is pressed down to the normal level. Indeed, in specially favourable circumstances, one special branch of industry may retain permanently an abnormal rate of agio. The disinclination of a great many affluent people to lend their capital, in small amounts and without security, to necessitous persons, from whom it is difficult to get it back without strong personal effort and supervision—or, it may be, lengthy processes and processes of distraint which are painful to one's own feelings,—almost universally keeps the supply in this particular loan market permanently and abnormally low, and the agio permanently and abnormally high—even disregarding the deduction which must, of course, be made in this case for premium against risk. And, similarly, the discount market may enjoy a permanently and abnormally low rate of interest, owing to the frequent inflow of large amounts of capital seeking short temporary employments, and, naturally, not finding such either in the mortgage market, or in agricultural loans, or in industrial investments. The great security of the investment, again, and the prospect of future rise in value, keeps the rate of interest in immovables always low; and considerations closely akin to this account for the present lower return of interest on state bonds, preferences, etc., payable in gold as compared with those payable in silver or paper.

It is not my intention to pursue the fate of the rate of interest into all these much-tangled bypaths, where special circumstances and special considerations by the thousand may drive it. The divergences from the normal rate—temporary divergences even more than permanent—are, in truth, in their totality a highly important phenomenon. In them lies the soul and the source of the greater part of "undertakers' profit"; that profit which falls to the undertakers as fruit of their prosperous arbitrage transactions in present goods. But to work this out in detail is a task by itself; an important and grateful task, but one which in importance comes behind the developing of the great law of the rate of interest. In any case it is a task much too troublesome and much too lengthy to tempt me to a new effort, when I am in sight of home after a long and difficult journey. I have stated the way in which the particular abnormalities are connected with the chief law, and for the moment enough has been done towards understanding the theory of them.

And now to finish. On a former occasion, at the end of the historical part of my work, I laid down the programme for my positive theory in the following words.—"To find for the vexed problem a solution which invents nothing and assumes nothing, but simply and truly attempts to deduce the phenomena of the formation of interest from the simplest natural and psychological principles of our science." I cannot wish more than the recognition that, in the carrying out of the work, I have been true to my programme. For if, through logically developing the elementary theory of value, I have succeeded in obtaining the explanation of interest, it will give the strongest security that could be wished that we are moving on the right lines with two theories, that of value and that of capital. It can be nothing but a support for my theory of capital, if that theory can assert its existence as the legitimate and natural outcome of a value theory which has already given so many fair proofs of its correctness, and which is now receiving adherence among all systematic schools and in all countries that have shared in the advance of economical theory. And for the value theory, again, it will be a new proof and, perhaps, the most powerful one, if, by its instrumentality, a problem is solved which all theoretical systems hitherto have attempted in vain.

APPENDIX TO PAGE 327 [Book VI, Chapter V]

Amount of Subsistence Fund Necessary Before Entering on a Production Period of Given Length

If one year be the period of the production process and the stage period also be one year, so that no new goods, finished and ready for consumption, are turned out under a year's time, then, obviously, before beginning such a process, there must be on hand a fund of subsistence containing sufficient to cover the entire wants of the workers for one year, and that in a finished state. If we call the Subsistence Fund S, and the year's Want Y, then, in this case, S = Y.

If two years be the production period, and the stage period, as before, be annual, it is necessary that, at the beginning of the production period, there should be on hand one year's supply finished, and a second year's supply half finished. In each year the finished year's supply is consumed by the workers, while the half-finished is finished by the workers of the second stage—thus securing the subsistence for the next year—and a fresh year's supply is put in hands by the workers of the first stage, and, in turn, half finished. Here, therefore, if we call the half-finished year's supply a half year's supply, S = 1½ Y.

Similarly for a three years' production process, with annual stages, we require one year's want entirely covered, another 2/3 covered, and another 1/3 covered: or, one year's supply finished, another 2/3 finished, another 1/3 finished. In each year, then, the finished year's supply is consumed, the 2/3 finished is finished by the workers of the third stage, the 1/3 finished becomes 2/3 finished by the workers of the second stage, and a further year's supply is newly created by the workers of the first stage, and is finished to the extent of 1/3—whereby, at the end of the year, the status quo is restored, and continuous provision is guaranteed. S, therefore, here = 1Y × 2/3 Y × 1/3 Y = 2Y.

Similarly, if the stage is still one year, then in a four years' process S=(1 + ¾ + ½ + ¼)Y = 2½Y:

in a five years' process S=(1 + 4/5 + 3/5 + 2/5 + 1/5)Y = 3Y:
in a six years' process S = (1 + 5/6 + 4/6 + 5/6 + 2/6 + 1/6) Y = 3½Y:
in a seven years' process S = (1 + 6/7 + 5/7 + 6/7 + 3/7 + 2/7 + 1/7)Y = 4Y:
in a ten years' process S = (1 + 9/10 + 8/10 + 7/10 + 6/10 + 5/10 + 4/10 + 3/10 + 2/10 + 1/10)Y = 5½Y.

If we look closely into these figures we shall easily discover the law that underlies them: Every production period requires a fund of subsistence containing sufficient to cover half a year more than half the production period.

Suppose we continue our inquiry under the assumption of a different stage period, say, half a year. Here it is quite the same whether the stage period occurs under the division of labour or not, the only thing essential being that, every half-year, finished consumption goods are turned out from the total process. To enter upon a one year's process, with half-yearly stages, what we require is a finished supply for one half-year—during which no fresh consumption goods are turned out—and half-finished supply for the second half-year. During each six months, then, the finished supply is consumed; the half-finished is finished by the workers of the second stage; and a new six months' supply is begun and half finished by the workers of the first stage, whereby the status quo is restored. S here = ½Y + ½ &times ½Y = ½Y + ¼Y = ¾Y.

Similarly in a two years' production process, with half-yearly stages, we require ½Y + ½ × ¾Y + ½ × ½Y + ½ &times ¼Y = (½ + 3/8 + ¼ + 1/8)Y = 1¼Y, while in a three years' period we require ½ + ½ × 5/6 + ½ &times 4/6 + ½ × 3/6 + ½ × 2/6 + ½ &times 1/6 = ½ + 5/12 + 4/12 + 3/12 + 2/12 + 1/12 = 1¾Y.

Here, again, the underlying law is plain: If the stage period be six months the fund necessary contains subsistence for three months longer than half the production period.

If we were to carry out our inquiry still further we should find, similarly, that, where the stage is three months, the fund must contain six weeks' more subsistence, where it is one month, must contain two weeks' more subsistence, than half the production period. And thus we arrive at the general formula of p. 327, that the fund of means of subsistence most be sufficient for half the production period plus half the usual stage period.

[1.]An assumption which, for the reasons shown on p. 315, holds very widely;—that is to say, among all persons who own more wealth than they can or will spend in their own productive equipment.

[2.]As regards the sellers of present goods, for simplicity's sake, we shall adhere throughout the argument to the assumption that their personal circumstances are such that they value present and future commodities alike.

[3.]We may take the case, e.g., of a youth standing on the brink of manhood, kept very short of cash at the moment by his tutor, but with the prospect of a great fortune coming into his absolute disposal in a few months.

[4.]The total surplus return, due to the loan, figures out at £20, since, in each of the two years of the extended production period, the surplus return to labour is £10. But this surplus return is all the same divided over two years, so that only the amount of £10 is to be reckoned to one year. In more skilful disposition, however, the borrower need not take up, at the beginning of the production period, the whole amount of the loan from which he defrays his subsistence during that period: he may raise the loan by successive instalments, and this has for result that the loan is outstanding and requires to pay interest only for half the production period. If such a disposition is arranged the yearly surplus return may in the most extreme case be offered as a half-year's interest on the subsistence loan, and in this case the most extreme interest rate economically possible is double the figures given is the text. The raising of such subsistence loans by instalments thus exerts exactly the same influence on the relation between subsistence fund and surplus return, and, at the same time, on the height of the interest rate, as does a suitable "Staffelung" of production (see above, p. 325), with which phenomenon, as may be easily seen, it is closely and intimately connected.

[5.]Up to a certain point the surplus return may now and then increase even in a greater ratio than the duration of the production period. It may, e.g., happen that the transition from rod-fishing to net-fishing shows a greater advance than the transition from primitive modes of fishing to rod-fishing. But beyond a certain point this cannot be maintained, and the surplus returns show a decreasing ratio.

[6.]See above, p. 319, and particularly p. 330.

[7.]The case of production carried on entirely without capital, which, according to the scheme, would return only £15, we may leave out of account as practically of no importance.

[8.]Only the wages of the first month are outstanding nearly a whole year; those of the second month are outstanding only eleven months, and so on; all wages of the first six months outstanding more than half a year. Against this the wages of the second six months are outstanding for as much less than the half-year.

[9.]The calculation is exactly similar to the foregoing.

[10.]Perhaps one or other of my readers will take exception to my looking upon the production period, in which the work of undertaking is carried on, as not a fixed immovable amount. It will be said that each undertaker has made the arrangements for his production on a quite definite footing, and works in any case in the production period corresponding to and determined by these given arrangements. This is not the case. Even where the visible outlines of the arrangements, such as workshops, number and kind of employés, and so on, may be pretty permanent, yet, within these fixed lines, a number of little noticed alterations are possible, by which the length of the production period might be changed not inconsiderably. In the simplest shoemaking shop, e.g., the buying of a new machine-made tool, the wholesale purchase of finished uppers, or, above all, the acquiring of labour-saving instruments such as sewing-machines and the like, involves no unimportant extension of the production period. True, in the shoemaking shop itself one does not notice that the production of shoes has now become a more lengthy process. But all the more noticeable will it be in those preparatory stages of production where, on account of the shoemaker's demand—not, of course, the demand of the one shoemaker, but of many,—people must now stretch away back in time, as it were, and invest original productive powers in machine-making, founding of factories, and so on. The shoemaker, therefore, according as he covers his demand for the instruments of his business in one way or the other, may as a fact cause a lengthening or shortening of the total production period, and naturally he makes the choice which, in the circumstances, is economically the more advantageous. If, e.g., the level of wages is very high, he will prefer to buy machine-made uppers, put up a sewing-machine in his own shop, etc.; that is to say, in entire correspondence with the statement given in the text, he will prolong the production period: while, if the level of wages is low, he will prefer directly to employ the cheap hand labour—that is to say, so far as in him lies, to keep the production period short.

[11.]On the assumption of a production arranged in the form of stages, whereby (as shown on p. 328, and in Appendix I.) the initial fund need only contain subsistence for half the production period.

[12.]If, e.g., the existing stock of subsistence is so great as to defray four million years pay—in which case, as we know, where production is by stages, an initial capital amounting to two millions of wages only would be required—and if there are one million labourers in the country, then it is shown that an average four years' production period must be taken. For if, say, a three years' period were taken, the three years' payment of one million of workers would take up only a capital of one and a half millions of wage, and the rest of the capital would have to go idle. In a five years' production, again, an initial fund of two millions of wages would only defray the subsistence of 800,000 labourers for five years, and the remaining 200,000 would go starving—a position which evidently is as untenable.

[13.]I here assume a well-organised production by stages, where no portion of the capital remains idle, and where, consequently, the initial fund need only contain something like half the amount of subsistence required during the course of the whole production period. I may note, however, that the correctness of the conclusions drawn in the text is quite independent of the pure question of fact whether the initial capital must be exactly half, or something more than half, or, perhaps, just so much as the amount of subsistence successively consumed by the workers during the production period. According as this is determined the figures puat down in the following tables will, of course, vary—they have no value, indeed, but as illustrative—but not the laws that underlie these figures. With other figures representing the productiveness and the capital, the calculation would lead to different concrete rates of interest, but to the same laws as regards height of the interest rate, as will be shown more clearly further on.

[15.]Leaving out of account special disturbing causes, the influence of which I cannot pursue here: my business just now is to develop the fundamental law of the interest rate, just as I have already developed the fundamental law of the formation of price. See Conrad's Jahrbücher, vol. xiii. p. 480.

[16.]Always assuming a complete arrangement of production by stages. I may add the mathematical proof of this somewhat paradoxical thesis. To employ 30 labourers in a 5 years' period arranged by yearly stages, the 6 labourers of the first stage need an advance of wage over full 5 years, that is, in all, 30 annual wages: the 6 labourers of the second stage require an advance over 4 years, that is, 24 wages: similarly, the labourers of the third stage require 18, those of the fourth 12, those of the fifth 6: a total of 90 wages. To support the same 30 labourers in a 6 years' production, the first stage, now embracing only 5 labourers, requires the advance for 6 years, that is, 30 wages; the second stage, 25; the third, 20; the others, respectively, 15, 10, and 5 wages: in all, 105 wages. The extension of the production period for 30 labourers by a whole year requires therefore, as a fact, the augmenting of the wage fund by the amount of only 15 wages, which gives the case maintained in the text.

[17.]From this formulation it will be seen why the law now deduced does not depend, and has no need to depend, for its correctness on the concrete numerical ratio between the amount of the wage fund and the length of the production period. (See above, p. 387, note 1.) Suppose, e.g., that not a half but a whole year's wage were necessary to extend the production period by a year, all the same a capital sufficient to defray the wages of a whole year would require to bear something like the return of the last extension of the production period as interest. The figures may change as they will, but the typical relation holds, that the interest of that unit of capital required for a definite extension of the production period lies between the surplus return of the last permissible and the first non-permissible extension.

[18.]See above, p. 217.

[19.]See above, p. 221.

[20.]Der isolirte Staat, second edition, part ii. div. i. p. 100. It is very notable that Thünen, without knowing the law of marginal utility, without any general price theory based on that law, and, finally, even without any clear insight into the origin of interest, was able to solve the special problem of the rate of interest with almost entire correctness, and in the sense of those general theories of which he had perhaps a dim

[21.]See above, p. 218.

[22.]As, e.g., in the familiar proposition that an increase of the national capital tends to reduce the interest rate. In the points here raised, I am in very thorough agreement with Walras, who, like Thünen, starts from a theory of interest which, in my opinion, is essentially wrong, and yet is able to arrive at many details correctly and with fine scientific feeling. The coming second edition of his Élements,d'Économie Politique Pure, the proof sheets of which, by the kindness of the author, I was permitted to see, contains many forcible and noteworthy passages on this subject. I can only regret that they are expressed in the troublesome and difficult language of mathematics. The conception of political economy as pre-eminently a mathematical science is one on which, notwithstanding what the distinguished economist has recently said (p. 191 in new edition), I fear we shall never be able to agree.

[23.]In this case it falls considerably nearer the under limit on account of the relative abundance of the capital, which would be almost sufficient for general adoption of a nine years' production period.

[24.]That is to say, with £1000 capital, as the table shows, 11.905 labourers could be employed in four years' production. To employ all the existing ten million labourers, therefore, a capital is required which follows this proportion

1000 : x = 11.905 : 10,000,000.

The solution of this proportion gives

x = 10,000,000,000 : 11.905 = 840,000,000.

[25.]With £1000 capital 9.524 labourers are employed in five years' production; with 1000 millions of capital, therefore, 9.524 millions of labourers.

[26.]I may call attention to the fact that now we arrive at the figure 19.048 by a quite different way, by quite different lines of thought, and by quite different calculations, than in the above table. There we sought and found empirically the figures of wage and interest at which, under the given assumptions, the equilibrium of Supply and Demand may be established. Now, applying the law of the marginal pair to the concrete case, we have deduced that the interest must lie between the surplus returns of the last extension of production still permissible, and the first excluded, and arrived thereby exactly at the same figure 19.048. In the former case we get our figures immediately by multiplication of the number employed by the gain made per labourer (11.905 × 16 and 9.524 × 20). Here we get the same figure by dividing the dependent last surplus product by half the wage (4 : 21). I may, therefore, take this agreement as a proof that our deductive reasoning correctly expressed the results empirically established.—Here also it may be the most suitable place to point out the error into which Jevons fell as regards this question. Jevons recognises perfectly correctly that the "last surplus return" decides the interest rate; but, owing to an oversight in principle, he makes the mistake of fixing on that other amount to which this surplus return must be put in relation, and deduces the rate of interest, not from the relation of the last surplus return to the sum of subsistence which allows the last extension of production, but from the quite different relation in which that surplus return stands to the value of the whole product which might have been obtained without the last extension of production. "The interest of capital is the rate of increase of the produce divided by the whole produce" (Pol. Econ. second edition, p. 267). The seriousness of this oversight will be best seen from a concrete example, which, for the sake of easier comprehension, I shall take from the case of isolated exchange spoken of above (p. 378). Remembering what was then said, let us suppose the case of an undertaker whose means would allow him to carry through an eight years' production period with a yearly return of £68:10s., and who, by a loan of £30, which would guarantee him subsistence for a ninth year, is put in a position to go on to a nine years' production period with a return of £69:10s., or a surplus return of 20s. According to Jevons this should allow an interest rate of £1 on £68:10s., or 1.46%. But evidently there is no ground whatever why the suitor for the loan should be ready to offer £1 per year and no more as interest for a sum of £68:10s. It is not the amount of £68:10s., but that of £30, whose acquisition makes the extension of production possible, calls forth the surplus return of £1, and, consequently, maybe paid, in the most extreme case, by £l, but, on the assumption noted on p. 378, note 1, by as much as £2 per year. As a fact, then, in the case of this illustration, it is not, as Jevons assumed, an interest of £1 on £68:10s., or 1.46%, that is economically possible, but an interest of £1 on £30, or 3 1/3%, indeed, on the above assumption, a rate of £1 on £15, or 6 2/3%. A certain very modest kernel of truth may be found, all the same, in Jevons's t error; but to point it out I should require to go still further afield into discussions in which I could not assume that the majority of many readers would find sufficient interest.

[27.]See above, p. 392.

[28.]See what was said above on p. 334: the two passages mutually supplement each other.

[29.]See above, p. 394.

[30.]See above,p. 376.

[31.]Which can be quite easily calculated from our tabular examples. See, too, close connection of what was said on p. 382.

[32.]See above, p. 319.

[33.]Members of the community not here mentioned, as women, children, persons who occupy themselves with the performance of personal services, as artists, officials, domestics; must also, of course, get part of the subsistence fund. But they are not to be counted separately, for the reason that they are not a direct charge on the social subsistence fund, but on the portions secured by the economical classes already mentioned in the text. Violin-players, e.g., receive a portion of the subsistence obtained by concert-goers; the establishment of a rich landowner is supported and paid out of his rent, and so on

[34.]I must guard myself against a misunderstanding very apt to occur. What I maintain is that the position of land rent as a form of income—the absorption of a portion of the national product by landowners who live without working,—tends to raise the rate of interest. On the other hand, I do not say that the causes which call forth land rent, and raise it, raise also the rate of interest. On the contrary, the well-known law of Diminishing Returns, according to which (in the absence of technical discoveries or improvements) new additions of capital and labour in agriculture lead to a decreasing surplus return, while it exerts an upward influence on land rent, certainly exerts a depressing influence on interest (see point 3 in the text). The full bearing of my contention is best expressed in this;—that in event of the taking away of private right to land, or heavy and confiscatory taxation of land rent, interest in that community would stand lower than it would otherwise. The causes of land rent, in themselves, would depress interest, but land rent, as one of the shares in the division, through its effects on the division, makes up for a portion of these influences.

[35.]It may, perhaps, have been noticed that the often-mentioned factor of Insurance or Risk, which plays so great a part in practical life, especially in determining the rate of interest on loans, is missed out in my enumeration. This factor, however, has no place here. For the surplus return which this gives the capitalist, if to all appearance it raises the rate of interest, is in truth no real interest,—no net income accruing from the possession of capital,—but only a replacement for a loss of parent stock which shows itself as unavoidable over a great average of cases.—Finally, from the whole course of my research, it will be self-evident that it was not my intention to introduce exhaustively all the secondary determinants of the rate of interest. I have contented myself intentionally with enumerating the most important of those determinants which come into view as typical if the economical interests of the market are followed without let and hindrance. On the other hand, the influence of motives such as generosity, national prejudice, vanity, etc. (see Conrad's Jahrbücher, vol. xiii. p. 486) I have purposely left out of account here. See also below.

[36.]The possibility of a complete harmony of satisfaction is only now and then prevented through an imperfect divisibility of wants on the one side, and of units of goods on the other. See my Grundzüge in Conrad's Jahrbücher, vol. xiii. p. 68, and in particular Wieser's Ursprung und Hauptgesetze, p. 148.

[37.]It must not be thought that this equilibrium of provision is reached if the available sum of goods is divided over the various periods of time in entirely equal amounts, so that each period obtains, allotted to its consumption, exactly the same quantity of goods. The position of wants also changes. A bachelor has to provide for fewer wants than the father of a family; a healthy man has to make much less expenditure on the preservation of his health than an invalid and frail old man, and so on. Now, obviously, any one would make a very unsymmetrical provision for his wants, who proposed to consume mechanically the same amount of goods during all periods of his life, whether as bachelor, father of a family, or old man. To secure anything like harmonious provision a man must anticipate a probable increase of wants, and meet it by an increase of provision.

[38.]I That is to say;—the utility of £105 in the future is equal to the utility of £100 now, only on the condition that the community's wealth is increasing.

[39.]See my Grundzüge in Conrad's Jahrbücher, vol. xiii. p. 74.

[40.]See the short and clear statement by Mithoff in Schönberg's Handbuch, second edition, vol. i. p. 643, particularly note 53.

[41.]I do not at all pretend, in the somewhat sketchy suggestions which this chapter contains on the subject of wage, to have given a perfect theory of that matter. In particular, my occasional remarks have only dealt—in a half-complete sort of way—with one of the sides that comes into consideration as regards wages; viz. the relation of wage and interest. On the other hand, I have given no express consideration to another side which is at least as important,—the question as to the influence exerted on the rate of wages by the difficulty that exists, in consonance with the law of diminishing returns, for an increased number of people to obtain the necessary subsistence from the earth. All the same, the attentive reader may find in this book, if in scattered form yet tolerably completely, the foundation-stones on which the principles of a theory of wage might be built; partly in the theory of complementary goods (p. 170), partly in my explanation of the law of costs (p. 223), partly in the present chapter.

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BOOK VII: THE RATE OF INTEREST - Eugen von Böhm-Bawerk, The Positive Theory of Capital [1889]

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