The Distribution of Wealth: A Theory of Wages, Interest and Profits

John Bates Clark, from the Warren J. Samuels Portrait Collection
Clark, John Bates
(1847-1938)
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First Pub. Date
1899
Publisher/Edition
New York: The Macmillan Company
Pub. Date
1908
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Chapter XIII

The Products of Labor and Capital, as measured by the Formula of Rent

XIII.1

It has been customary to define rent as the income derived from land. In attempting to solve problems of distribution, furthermore, it has been customary to eliminate from the earnings of society the element of ground rent, and then to try to find principles that will account for the division of what remains. That ground rent is entirely unlike wages, interest or entrepreneurs' profit, has been the most prevalent theory. According to this view, the income from land is a differential gain fixed by a law of its own, which does not apply elsewhere. The rent of a particular piece of ground is measured by comparing its product with that which can be had from the poorest piece that is utilized by the application of the same amount of labor and capital. When, by this independent reckoning, the part of the income of society that is derived from land has been disposed of, it is thought that one step has been taken in the direction of solving the really difficult problems of distribution. Wages, interest and net profits, it is believed, can be accounted for the more readily when the product of land has been put out of sight.

XIII.2

It has become obvious, however, that wages are fixed by the final productivity of the labor that is used in connection with a fixed amount of total capital; and in computing that total capital, we make confusion, if we do not take all kinds of capital-goods into account. It is the whole fund of productive wealth, in every form that such wealth takes, which constitutes the complex agency that coöperates with labor. When the amount of productive wealth in its entirety remains fixed and the quantify of labor increases, the law of diminishing returns that we have stated operates. The final unit of the agent, labor,—coöperating, as it does, with land and every other instrument,—produces less and less, as the units of labor become more numerous; and thus the standard of wages falls. When the increase in the working force ceases, the rate of wages remains fixed.

XIII.3

It may be alleged that the same result will be reached by assuming that capital in artificial forms remains fixed in amount, while the working force grows larger. Land, it may be claimed, is fixed in amount by nature; and, if we can measure the productive wealth that exists in the shape of buildings, tools, materials and the like, and keep that also unchanged in amount, we shall have the condition that we have described. The total amount of productive wealth will then be a fixed quantity; and we can let the labor increase, unit by unit, testing its final productivity as we have done.

XIII.4

This method of statement would tell the truth about the decline in the productivity of labor, but it would not assign that effect to its true cause. What the labor combines itself with is not merely the artificial capital: it is that and the land, as they are combined in one and make a general labor-aiding agency. As the working population has grown larger, some of it has betaken itself to hitherto rentless ground—the enlargement of the laboring force has pressed outward the margin of utilization of land. During the same period of growth, moreover, new labor has constantly added itself to the force that has tilled good land. More and more intensively has land everywhere been cultivated and otherwise used. The artificial capital, as such, has received, as it were, only its own fraction of the increasing force of labor. It has aided the land, and together they have received all of the new workers. Wages fall because such capital and land together cannot make the tenth unit of labor as productive as they made the first.

XIII.5

It is, therefore, the whole economic environment of the growing population that has to be considered, if the cause of the decline in the final productivity of labor is to be understood. Land and artificial goods are blended in an intimate mixture; and the last unit of labor produces what this whole composite agent enables it to produce. There are only two generic members in the combination by which the rate of wages is determined. Indeed, as we have noticed, the variations in the comparative amounts of these two agents, labor and all capital, determine both wages and interest.

XIII.6

No controversy need arise over the question of mere nomenclature. It is necessary to find some term to designate the whole permanent fund of productive wealth, and the natural name for it is capital.*18 It is also necessary to have a term for all kinds of concrete goods in which this permanent fund consists; and we shall call these things, including land, capital-goods. As our analysis of the process of distribution proceeds, we shall hope to justify this nomenclature by its fruits. In any case, it is important to note that it is the quantity of labor, on the one hand, and that of all productive wealth, on the other, that fix the natural or static standards of wages and interest.

XIII.7

Ground rent we shall study as the earnings of one kind of capital-goods—as merely a part of interest.*19 We are now able to see that wages and interest, though they are determined by the law of final productivity, are also capable of being measured exactly as ground rent has been measured. That is to say, the Ricardian formula, which describes what is earned by a piece of land, may be used to describe what is earned by the whole fund of social capital: all interest may be made to take the form of a differential gain, or a surplus. Again, the Ricardian formula may be employed to describe the earnings of the whole force of social labor; for wages, in their entirety, are a differential gain. It is one of the most striking of economic facts that the income of all labor, on the one hand, and that of all capital, on the other, should be thus entirely akin to ground rent. They are the two generic rents, if by that term we mean differential products; and the earnings of land constitute a fraction of one of them.

XIII.8

Let us now simplify the law of ground rent, by disregarding the auxiliary capital that, in advanced agricultural states, is applied in large quantities to land. Let the ground that we use as an illustration be worked by labor that is practically empty-handed. Every laborer brings with him a simple tool, but the interest on the capital that the tool represents is so small a part of what the man earns in a year that it may be disregarded. We have, then, only two producing agents to deal with, and they are the land—which now embodies all the capital that needs to be considered—and labor. The neglect of auxiliary capital affects no principle that we are studying; for what we have to prove could be established as completely, though less clearly, if we made our illustration more complex by taking all kinds of capital into account. The differential gain of labor as applied unaided to fertile land, offers the clearest illustration of the different incomes that can be measured by the Ricardian formula. It is the type of all the rents.*20

XIII.9

Labor, as thus applied to land, is subject to a law of diminishing returns. Put one man on a quarter section of land, containing prairie and forest, and he will get a rich return. Two laborers on the same ground will get less per man; three will get still less; and, if you enlarge the force to ten, it may be that the last man will get wages only. We must, however, be very careful to make sure of the reason why the tenth man gets only his wages. If the men are hired by the owner of the land at the prevalent rate of wages, what has happened is that the force has been enlarged till the last man produces only what is paid to him. In this case, as was said in the tenth chapter, wages fix the intensive margin of cultivation of this land. The rate that we must pay the men decides for us how many of them we can employ on our farm. If, however, our farm is isolated and the workers are a society by themselves, and if there are ten of them to be employed, we shall set them all working and pay to each of them much as the last one produces. Here it is the product of the marginal labor that fixes the rate of wages, as we noted in the chapter referred to; and here, also, the situation illustrates the true law of rent.*21

XIII.10

All the earlier men in the series create surplus products, over and above the amount created by the last man. They get only what the last one produces, and the farmer-landlord gets the remainder. What goes to the owner of the land is the sum of a series of remainders that are made by taking, in each case, the product that is attributable to one of the earlier men as a minuend and the product that is imputable to the last man as a subtrahend.

XIII.11

Call the product that the single worker creates, when he has the whole field to himself, P1st. Call the additional product that the second man is able to bring into existence P2d, etc.; call the enlargement in the output made by the last man P10th.

P1st - P10th = surplus created by the first worker.
P2d - P10th = surplus created by the second worker.
P9th - P10th = surplus created by the ninth worker.

If we complete the series of such subtractions and add the nine remainders, the sum of them all will be the rent of the piece of land. This is the amount that the owner can keep, from the total created by the different workers aided by the land.

XIII.12

The sum of P1st + P2d + P3d, etc., to and including P10th, is the whole product of the field and the labor that is spent on it. It is the sum of all the minuends in the foregoing series, with the product of the final man added to it. 10 × P10th equals the total subtrahend; and the total rent of the field is the difference between these amounts. It is, in other words, the whole product minus ten times the product of the tenth and last unit of labor.

XIII.13

Let us, again, measure the number of laborers by the line AD, and the product of successive increments of labor by AB, A'B', etc. Figure.  Click to enlarge in new window.If we give to these lines an appreciable width, so that a series of them will fill the entire figure, ABCD, that area will measure the product of all the labor and all the capital in our illustrative agricultural community. The capital is virtually all in the form of land; and we are now able to attribute to the land that part of the product which, in effect, it creates.

XIII.14

The last unit of labor creates the amount of product that is expressed by DC; and, accordingly, each unit of labor is effectively worth just that amount to the employing farmer, and each unit gets that amount as its wages. AECD measures total wages, and EBC measures the entire rent of the land. This amount we have spoken of as composed of a series of surpluses, or differential products, and we have measured them in each case by subtracting from what we have called the product of one of the earlier increments of labor the product of the last increment. AB minus DC gives such a surplus, and it is a part of the rent. It looks, at a careless view, as though land had the capacity to cut off and claim for itself a part of the product of labor—that is, the surplus part of the product of all the earlier increments of labor appears to be the rent of the land.

XIII.15

In reality, this surplus is the fruit of the aid that the land affords, and is attributable to the land only. A correct conception of the nature of any rent makes it a concrete addition which one producing agent is able to make to the product that is attributable to another producing agent. Land makes its own addition to the product of each unit of labor except the last one. When there was available only a piece of land, with no labor to till it, the product was nil. When one unit of labor combined itself with the land, the product was AB; and in this form of statement we impute the whole product to the labor.*22 A second unit of labor now comes, unaided by capital, into the field and adds itself, empty-handed, to the working force. Whatever it produces, it brings into existence by adding to what the field yielded to one man's cultivation. The product thus created by an addition to labor, with no addition to capital, is A'B'. The difference between AB and A'B', which is the line E'B, measures the surplus that a man can produce when he has the whole field to aid him above what he can create when he is unaided. The last man adds labor and no land to the productive combination; while the first man had land, and the addition that the land itself made to the bare product of labor constitutes the differential quantity which is the rent of the land. The science of rent is a science of economic causation, which traces products to their sources. The rent getter is a product creator.

XIII.16

The third man, also empty-handed, creates the amount A''B''; and E'B + E''E' measures the contribution that the land has thus far made to the joint product of land and labor. Extending the vertical lines and giving to them width enough to make them fill the area of the entire figure, we have AECD as the product of all the labor, when it is taken unit by unit and made to work virtually unaided. ABCD is what it creates as it is aided by the land, and EBC is the amount that the land contributes to the product of the combination. This measures the difference between the product of ten units of aided labor and ten units of unaided labor.

XIII.17

We can now make the really important application of the principle of diminishing returns, which fixes both marginal productivity and rent. This is the application that is actually making everywhere in the business world. The isolated farm, with its whole capital in land, is an illustration only; while the real field for labor, to which the farm corresponds, is the world, with its whole circle of industries and its complex equipment of capital.

XIII.18

For a fixed area of land read, now, a fixed fund of permanent social capital. It is at this moment an exact sum; and it will, as it were, prolong the conditions of this moment, remaining at exactly its present size. The artificial instruments are, of course, perishing and renewing; but, if there is no need of changing the form of the capital, a worn-out instrument will be replaced by another that is exactly like it. A hoe will replace a hoe, and a ship will succeed a ship; and the new instruments of production will be exact duplicates of the old. This would be clear in a completely static condition. We are, however, to introduce labor, increment by increment, into this general field of industry; and this, of course, compels such a change in the forms of the capital as we have already described. The amount of the capital remaining fixed, the instruments become more numerous and cheaper, as the force of labor enlarges.

XIII.19

Labor, applied to the whole fund of capital, in land and all other instruments, is now subject to the law of diminishing returns. Figure.  Click to enlarge in new window.The first unit produces the amount AB, the second produces the amount A'B', the third creates the quantity A''B'' and the last the quantity DC. This last amount sets the rate of wages, and the area AECD measures the amount of wages. It leaves the amount expressed by the area EBC as the rent of the fund of social capital. All interest is thus a surplus, entirely akin to the rent of land, as that is expressed by the Ricardian formula: it is a concrete product, attributable to the agent that claims it as an income.

XIII.20

This rent is, moreover, made up of a series of genuine differential gains. It is not like the rent of the farm, in our former illustration, which, as we found, really depends on the rate of wages that prevails elsewhere. The rent of the whole fund of social capital is the sum of a series of differences between certain products and a final, or standard, product. True differentials lie between different products, and not between products and wages. The line DC, which sets the rate of wages, expresses primarily the product of the last unit of labor. We have set all the men in the society working, we have measured the amount created by the last addition to the force, and we have measured the surplus that each earlier unit of labor creates above this amount. The surplus is, in each case, a true differential product; since it is not merely a remainder that is left after paying wages, but is a difference between one product and another. It is the difference between the product of aided labor and that of the labor that is virtually unaided, and the sum of all these differences is the rent of the social fund of capital.

XIII.21

Reverse now the situation. Let labor be the fixed element and let social capital enlarge, changing its forms of course, in the enlarging.

XIII.22

ABCD is the total product. Figure.  Click to enlarge in new window.AB is the product of the first unit of capital, A'B' the product of the second, A''B'' that of the third and DC that of the last. A unit of capital, adding itself with no new labor to the productive combination, enlarges the product by the amount DC. So much can be attributed to any unit of capital, separately considered. The effective importance of every one of the units of capital is the same. While capital-goods are not interchangeable, true capital is completely so; and all parts of it are, therefore, on a plane in their earning capacity. A merchant, a manufacturer or a farmer, if he can offer good security, can hire all the "money" that he needs at the rate that the least necessary sum which he invests in his business will earn for him. Does this imply an exploitation of the earlier units of capital? Does the borrower of these sums rob the lender?

XIII.23

If the final unit of capital produces the amount DC, it will get that amount as interest; and certainly no other unit can get any more. AECD will be the total amount of interest, and EBC will be a surplus; but it will be a surplus that is causally attributable to labor, and to labor only. The difference between the product that is solely due to capital and that which is due to capital and another agent in combination is the effect of the presence and the work of that other agent.

XIII.24

If we were to apply the term rent to all such surpluses, we should say that EBC is the rent of the force of laborers that is at work in connection with capital. This amount is made up of a series of differential products. Apparently AB - DC is the difference between the product of the first unit of capital and that of the last, A'B' - DC is the difference between the product of the second unit of capital and that of the last, etc. The rent of the labor, if we use that expression, is the sum of the surplus products connected with the earlier units of capital but not attributable to them as a cause. The laborers seem to get a part of what the earlier units of capital produce; whereas, in reality, this is the difference between what capital and labor jointly produce and what capital alone contributes to the product of the combination. EBC is, therefore, the amount that is imputable to labor only.

XIII.25

One law governs wages and interest—the law of final productivity. Figures 1 and 2.  Click to enlarge in new window.By one mode of statement of the law (Fig. 1), we get wages as an amount directly determined by this principle: it is the area AECD of our diagram. Arithmetically stated, the earnings of all labor equal the product of the final unit of labor multiplied by the number of the units. In Fig. 1, in which wages are thus determined, interest is a surplus that is of the nature of rent. By another mode of stating the law (Fig. 2), we get interest as the amount that is positively fixed by the final productivity law, and wages are now the surplus that is akin to rent. These amounts together make up the whole static income of society.

XIII.26

Profit has no place in such static conditions. The two incomes that are permanent and independent of dynamic changes are the products, respectively, of labor and of capital. Each of them is directly determined by the final productivity law, and each is also a remainder—a surplus or a differential quantity. In one use of terms, it is a rent made by subtracting the other income from the whole product of social industry.

XIII.27

Does such a remainder ever go to the persons who naturally get it, merely because it is a remainder and is not claimed by others? In Fig. 1, where EBC, representing interest, is a surplus governed by the law of rent, does the capitalist get this amount merely because labor cannot get it? The whole product is ABCD, and labor can have only AECD. If there is no profit, capital must get the remainder. Do the capitalists, then, come into the possession of this income merely because it is thus left for them by the laborers?

XIII.28

This point is of much consequence. The question at issue is nothing less than whether any static income is determined residually. Clearly it is never so determined. No static income is what it is merely because the deducting of another income from the social product leaves a certain remainder. Any income that is nothing but a remainder must go to the entrepreneur. Because EBC, in Fig. 1, is not claimed by labor, it is left in the hands of the entrepreneur. Thus far it is a residuum. It is, moreover, important that this amount should thus be left in the employer's hands, for by this means he is made able to pay the interest that the capitalist will claim; but there is in the mere fact that he has this sum nothing that makes it necessary for him to pay it to the capitalist. What the owners of capital can force entrepreneurs to pay them, is determined by the final productivity of capital. Employers of capital must pay for the final increment of it just what that increment produces, and they most pay for all other increments at the same rate. If this necessity takes from them the whole amount, EBC, which labor leaves in their hands, then EBC goes to the capitalist. It does so, however, only because the capitalist can claim and get it, by the direct action of the final productivity law. What the capitalist can get under this principle is expressed by Fig. 2. AECD is here the amount of interest, as directly and positively fixed. This amount must pass, in any case, from the entrepreneurs to the capitalists.

XIII.29

The entrepreneur, then, after paying wages, as indicated by AECD in Fig. 1, has left in his hands EBC, out of which he can pay interest. What be must pay as interest, is AECD in Fig. 2. If the area EBC in Fig. 1 were larger than AECD in Fig. 2 there would be a remainder left for the entrepreneur. This would be a pure profit, the only kind of income that is ever residually determined.

XIII.30

It is clear, on the face of the facts, that the two static incomes—those, namely, of the laborer and of the capitalist—are paid to them by the entrepreneur, who receives and sells the product of their joint industry. In the cotton mill, it is the hirer of capital and of labor who puts the goods on the market and from the proceeds pays the workmen and the owners of capital. If he pays first to the capitalists what the final productivity law, as applied to capital, calls for, he has a remainder out of which he must pay wages; and now it is the final productivity law that decides what he must pay as wages. If there is anything left on his hands after the two payments are made, it is a profit; and the terms profit and residual income are thus synonymous.

XIII.31

This truth we may demonstrate by using our diagrams in a reversed order. In Fig. 2 AECD is interest, as directly determined, and EBC is the remainder, which is left in the entrepreneur's hands for the payment of wages. What the entrepreneur must pay to the workmen is AECD of Fig. 1. If that is less than ECD of Fig. 2, there is a residuum, or profit, for the entrepreneur. Static conditions, however, exclude such a profit by making these two areas equal.

XIII.32

We have, then, established the following propositions:—

(1) Wages and interest are both determined by the law of final productivity.
(2) When, in an illustrative case, one of these incomes is so determined, the other appears to be a residuum.
(3) As a residuum, such an income would be left in the entrepreneurs' hands; but it is actually taken from them by a further action of the final productivity law.
(4) Entrepreneurs' profit and residual income are synonymous terms.*23 The static conditions assumed in the present study preclude the existence of such entrepreneurs' gains.


Notes for this chapter


18.
It will be seen that this is not calling land capital. When land is referred to, it will be called by its ordinary name. There is a constant necessity for referring to the total fund of permanent productive wealth that is embodied in land and in artificial instruments. When this is thought of, in practical life, as "money invested in business," it is designated by the term capital; and in this went it will be so called. The objection to calling land one variety of capital-goods vanishes, if it is admissible to call all productive wealth, "in the abstract," capital. Any objection that may arise to this usage is less serious than is the objection to using through a long discussion such a phrase as "permanent fund of productive wealth," or some equivalent and equally inconvenient expression. The nomenclature that we adopt guards not only against confounding land with this fund, but against confounding any other instrument, as concretely regarded, with it. In this, at least, it is a strict constructionist nomenclature.
19.
See Ch. XXII.
20.
These are (1) the rent of all capital, (2) that of all labor, (3) that of particular capital-goods, and (4) that of particular laborers.
21.
The law of rent, a commonly stated, has the defect that is illustrated by the former of these cases, where it is applied to the reward for labor. The farmer who figures in the current statement of the law hires his men at the wages that prevail in the various industries that are carried on about him; and, when he finds that men will not produce their wages, he quits enlarging his force. Each of the earlier men creates a surplus above his wages. When we are considering the rent of a limited piece of land devoted to one use, the scientific way to calculate the rent is to use as the subtrahend wages, rather than the final product of labor; since it is wages that fix final product. If what we want is a genuine differential product, we must isolate our working society, count the laborers, set them all at work and let the last produce what he can. There will then be a difference between what each of the earlier men produces and this final or standard product. This is, in each case, a true differential product. it is measured by comparing, not products created for the farmer and wages paid by him, but one product with another product.
22.
In the case of the first increment of labor, we might, by different dialectics, attribute the whole product to the land. Figure.  Click to enlarge in new window.Labor by itself creates nothing, and the addition of the land brings the whole product into existence. Again, by subdividing the one unit of labor into a series of smaller units, we might attribute the product partly to the labor and partly to the land. The product of the last fractional unit of labor would then set to standard to which wages, or the effective product of all fractional units of labor, would conform; and the figure that would express this fact would be the one in which AB' is the amount that is attributable to each fractional unit of labor, AA'B'E is the amount that is attributable to all the labor, and EB'B is the amount that is attributable to the land. It is when there is more than one unit of labor at work that it becomes clear how much should be attributed to all the labor and how much to the land.
23.
The above theses appear sharply to contradict the theory of wages advanced by the late President Francis A. Walker, in which wages are called the residual share in distribution. It is an aid in removing causes of confusion from the discussion, and in giving to the theory of this eminent economist what is due to it, to notice the fact that his study was essentially a study of a subject in economic dynamics. If the total product of industry becomes larger than it has been, and if interest, rent and profit do not become any greater than they were, wages must absorb the whole increase. In this view, the residuum may be regarded as a remainder that is left when the former product of the whole industry is subtracted from the present product. Such a view of the power of labor to get all the increase that dynamic changes create would be consistent with the view that, in the merely static adjustment that takes place at all times, wages are determined directly by the law of final productivity, as are other shares of the total product. We might claim that the progress which makes industry, as a whole, more productive makes labor, separately considered, more so, but leaves the productivity of other agents unchanged. Laborers would then, in each static adjustment that takes place, force entrepreneurs to give them their product, just as capitalists would do. Statically, wages would be determined directly; while dynamically they would consist partly in a residuum, made by deducting the former product of industry, as a whole, from the present prouduct.

In our view, progress in methods of production makes both labor and capital more productive; and the fruits of progress are thus shared by the two agents, according to the degrees of specific productivity that the progress gives to them. Labor, then, does net get the whole difference between the former product of industry and the present product. What we are trying to make clear is that, in a merely static adjustment of shares in distribution, both wages and interest must be determined directly, and not residually. After paying interest, the entrepreneur has wages left in his hands; but he is forced to pay it to labor because it is the product of labor. In making his bargain, the worker has the benefit of free competition. He is virtually selling his forthcoming product, and can resort to another employer, if the present one refuses to give him the full value of it. The capitalist, in making this contract for the payment of interest, is in the same way selling a product, and can exact the value of it. Without this power, neither laborers nor capitalists could get their shares from the entrepreneur's hands. For an early statement of the principles presented in this chapter, the reader is referred to an article by the present writer, in the Quarterly Journal of Economics, for April, 1891, on "Distribution as Determined by a Law of Rent."

End of Notes


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