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

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.

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.

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

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

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.

Call the product that the single worker creates, when he has the whole field to himself, P
^1st. Call the additional product that the second man is able to bring into existence P
^2d, etc.; call the enlargement in the output made by the last man P
^10th.

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.

The sum of P
^1st + P
^2d + P
^3d, etc., to and including P
^10th, 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 × P
^10th 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.

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.
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.

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.

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.

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.

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.

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.

Labor, applied to the whole fund of capital, in land and all other instruments, is now subject to the law of diminishing returns.
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.

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.

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

ABCD is the total product.
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?

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.

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.

One law governs wages and interest—the law of final productivity.
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.

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.

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?

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.

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.

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.

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.

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.

22.

In the case of the first increment of labor, we might, by different dialectics, attribute the whole product to the land.
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.