The Positive Theory of Capital

CHAPTER III

THE BATE 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,1 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 as 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.2 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 pro-position 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 3·5 4% 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 £3.0 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. 3⅓%) as lower limit. As a fact the agio of 3·54%, which we found empirically, falls between these determining marginal limits.3

TABLE IV.

WAGE £42.

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 £42.4 If, again, the five years’ period were exclusively adopted, the existing capital would employ only 9,524,000 labourers;5 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.6

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 un-changed, 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 versa. 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 £1.

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 national 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.

7 See above, p.-218.

8 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 Elements d’Economie 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 regset 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, notwith-standing what the distinguished economist has recently said (p. 191 in new edition), I fear we shall never be able to agree.

9 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.

10 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.

11 With £1000 capital 9’524 labourers are employed in five years’ production; with 1000 millions of capital, therefore, 9-524 millions of labourers.

12 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 of employed by the gain made per labourer (11 905 x 16 and 9524 x 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. Ecou. 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 show 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, may be paid, in the most extreme case, by £1, 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 T46%, that is economically possible, but an interest of £1 on £30, or 3⅓%, indeed, on the above assumption, a rate of £1 on £15, or . A certain very modest kernel of truth may be found, all the same, in Jevons’s 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 my readers would find sufficient interest.

• 1See Monger’s Grundsätze der Volkswirthschaftslehre, p. 93.
• 2See my Capital and Interest, 1890, p. 111.
• 3P. 219 (German edition, p. 266). See also my Hechte und Verhältnisse, p. 51. Innsbruck, 1881.
• 4See Mill’s Principles, i. 1. 2.
• 5Das Geld, pp. 83 and 92.
• 6If we were to carry our analysis of what man does in production a step further, we might appropriately distinguish three fundamental ways in which the producing man “moves things.” The first is what, for want of a better name, we may call simple movements or changes of place—where men transport entire objects from one locality to another. Thus the miner brings the ore from the depths of the shaft to the upper air; the merchant takes his goods from the place where they are produced to the place where they are demanded and used. The second embraces those movements of parts of one and the same object whereby it experiences a change of form, as when nails are made from iron, statues from marble, pipes from clay, dials from ivory, combs from caoutchouc, tumblers from glass, furniture from wood. The third, and much the most common way, is where different objects are brought together in space to form combinations of matter. These combinations may be merely temporary, or they may be lasting. Instances of the one are where the stamp falls on the coin, the chisel chips at the marble, the carving tool is applied to the wood, the ore put into the furnace, the yarn into the loom, the paper under the printing press, the stuff under the shears, the plough through the clods. Instances of the other are where we build a house out of wood, stone, lime, iron, etc.; where we put together a watch out of wheels, springs, pendula, weights, stop-action and many other things; in fact in manufacture generally. I must warn the reader that this division into three fundamental forms neither has, nor is meant to have, the character of strict scientific classification. Indeed, these forms merge in many instances into one another. Temporary combinations, for instance, are very often half-way to changes of form, and what I have called a simple change of place is at the same time, in a certain point of view, a material combination, a bringing together of the thing moved and the object (personal or impersonal) to which it is moved. This division, however, will make it easier to find our reckoning, and will prove too, if necessary, the correctness of the general characteristics which I have ascribed in the text to productive processes. I mean to say that it is easy to see that every productive activity which one can think of ranges itself under some one of these three fundamental forms, and to that extent it is proved that such an activity must, a fortiori, range itself also under the general formula given in the text, where we have described the nature and method of the production of material goods as the mastery of natural powers by means of putting objects in motion.
• 7If we try to represent the classification of our wants by a typical scheme we must, on the principles just laid down, give it something like the following shape:—
• 8When we are told that capital assists in the production of wealth, and then again that it assists in the obtaining of wealth for its owner, we are apt to jump to the conclusion that the two phenomena are intimately and essentially connected, and that the one is the immediate result of the other—that capital can bring wealth to its owner because capital assists in the production of wealth. As a fact, Political Economy has taken up this idea only too readily and too completely. Captivated by the deceptive symmetry that exists between the three great factors of production—Nature, Labour, Capital—and the three great branches of income—Rent, Wage, and Interest—the science, from Say’s day till the present, has taught that these three branches of income are nothing else than the payment for the three factors of production, and that Interest in particular is nothing else than the compensation which capital receives for its productive services when the product is divided out among society. Propounded by various interest theories in various forms this idea has found its most concise and, at the same time, its most naive expression, in the well-known “Productivity theories”—those theories which explain interest directly as the natural fruit of a productive power peculiar to and resident in capital.
• 9The theory of the use of goods I have already gone into at length in Capital and Interest. I there showed that material goods are nothing else than such distinct forms of matter as admit of the natural powers residing in them being directed to human advantage. I showed how the “use” they afford is realised through concrete activities of these natural powers, and, therefore, by real forth putting of power. I showed how a use (Gebrauch or Nutzung) cannot be made of them otherwise than by taking the peculiar forms of the energy of the good at the proper moment, supplying the conditions necessary to render them available where they previously existed in an unavailable form, and then bringing these forms of energy into proper connection with that object in which the useful effect is to take place. On these considerations I based the conception of the “Material Services” (Nutzleistungen) which I believe to be the only one that corresponds with facts, and rejected certain shadowy ideas which connected the old theory of interest with the word “Uses” of goods. What remains for us here is, on the same lines, to lay down certain fundamental ideas as to the origin of material goods.
• 10If we look more closely at the way in which man assists natural processes, we find that his sole but ample contribution consists in the moving of things. “Putting objects in motion” is the idea which gives the key to all human production and its results;—to all man’s mastery over nature and its powers. And this is so simply because the powers reside in the objects. Now when man by his physical powers—the power of moving things—is able to dictate where the object shall be, he obtains a control over the place at which a natural power may become effective; and this means broadly a control over the way and over the time in which it may become effective.
• 11Knies defines as capital “that complex of goods available to a community which may be applied to the satisfaction of want in the future.” This definition, as we can easily see, agrees almost word for word with that of another conspicuously important and fundamental conception. If we leave out the words “in the future,’ it takes in all the goods in a community available for the satisfaction of want, and that is an amount which most writers are in the habit of calling the “wealth” ( Vermögen) of the community. If, like Knies, we emphasise the fact that wealth embraces only the net amount of goods after deduction of debts, we may perhaps call that amount the community’s “gross property” (Guterbesitz). In any case we have in this to deal with an independent amount bearing an independent name, with which “capital” neither coincides nor should coincide.
• 12Again I say a control over the time in which a natural power may become effective. This proposition, also, must not be taken too literally. It must not be imagined that natural powers work intermittently; that man can sometimes bring them to a standstill, sometimes set them working again. On the contrary, natural powers are always at work; a natural power not active would be a contradiction in terms. But it is possible that several powers may be so combined that their activities may for a time mutually balance each other, and the resultant be rest—if not complete rest, still some movement so slight that, as regards human purposes, it may be neglected. When this is the case, before any new resultant can emerge that is of interest to man, there must be an entirely different combination of materials and powers. This suggests how man may get control of the point of time at which a definite resultant emerges. It is only necessary for him, by skilful use of his power to move objects, to provide the causes of the desired effect, all but one. So long as this one is not present the conditions are unfulfilled, and there cannot be the desired result. But when at the proper moment he adds the last condition, the movement hitherto held in leash, as it were, is suddenly set free, and the desired effect is obtained at the opportune time. Thus the sportsman moves powder and lead into the barrel of the gun; he shuts the breech; he raises the cock. Each of these things has for long possessed and expressed its peculiar powers. In the powder are present the molecular powers whose energy later on is to expel the shot from the barrel. The barrel now, as formerly, exerts its forces of cohesion and resistance. The trigger which is to let the cock smash down, strains and presses against the spring. Still the arrangement, the disposition of the collective powers, is such that the resultant of their mutual energies is rest. But the sportsman covers the wild fowl with the barrel: there is a slight pressure on the tongue, a little dislocation of the arrangements, and the shot flies.