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

John Bates Clark, from the Warren J. Samuels Portrait Collection
Clark, John Bates
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First Pub. Date
New York: The Macmillan Company
Pub. Date
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Chapter XXI

The Theory of Economic Causation


If a society is static and capital is not increasing, both wages and interest consist in goods of the type A''', B''' and C''' of the illustrative table. They come into existence in a steady flow that is synchronous with the productive action of labor and capital in all the sub-groups, and they go simultaneously to the men in all of these groups for consumption.


It is capital, as such, which earns the interest that is embodied in these goods; and the earnings of it are made to be uniform—that is, they are made to secure as much of A''', B''' and C''' to the men in A as they do to the men at A''', at B''' or elsewhere. The products of labor are, in a like way, uniform. Is it certain that capital, as a whole, gets exactly what it produces? Obviously, what the last unit of capital gets is what it produces, and that is what every other unit must take; but is there not a chance that the earlier units may be exploited? The same question arises in connection with labor: The last unit of labor gets its product, it may be admitted; but do the earlier ones get their full product? Does the income of the whole body of laborers tend at all, under natural law, to equal what they produce? Is there not an exploitation of all early increments of labor, if the law of final productivity works in perfection?


With this question in view, let us revert to the familiar graphic statement of the law of final productivity.


Figure.  Click to enlarge in new window.Letting the amount of capital remain fixed and causing the amount of labor to be measured by the line AD, we will go through the imaginary process of supplying this labor, unit by unit. The first unit, then, so long as it remains alone, has a vast amount of capital to coöperate with it. For simplicity, let us say that each unit of labor is a tenth of the whole force and that, while the first unit is alone, it has a profusion of appliances, all of the costliest grade, to coöperate with it. It is, in fact, aided by ten times the amount of capital that a single unit will, in the end, lave to aid it. If we are to think of an actual society in which labor is thus, as it were, over-saturated with capital, we shall have to imagine costly materials, buildings of the most solid and enduring kind, motive power in abundance, and automatic machinery of a degree of costliness and perfection that is far from having been attained as yet, even in the departments of industry in which invention has done its best. With all that machinery to aid it, the product of the one unit of labor will be enormous.


In our figure, we measure the amount of a unit of labor by distance along the line AD, and indicate one unit by a tenth of this line, or the distance AA'. We may measure the amount of the product of the first unit of labor by the area of the figure ABB'A'. This area measures the amount of wealth that is called into existence by one unit of social labor, assisted by a nearly inconceivable profusion of social capital; and the wealth measured by this area consists in consumers' goods of every kind, destined for the use of a whole population.


Let us now add a second unit of labor, the quantity A'A'', measuring the quantity that it produces by the area A'B'B''A''. Here we must be careful. The quantity that this second increment of labor produces is, as we have said, measured by the area of this second figure. This statement may easily bear an interpretation that will make the entire theory lead to an erroneous conclusion—to one, in fact, which is the direct opposite of the truth. With a certain interpretation, the statement that the second increment of labor produces less than the first may lead to the inference that,—so long as all are paid at the same rate,—nearly all labor is robbed of a part of what it produces, and that too by the action of competitive law. This is a natural inference from the law of final productivity, when it is left incomplete. If one man produces the value of a dollar and a half a day, while another produces the value of a dollar, and if each gets a dollar, there is a clear case of exploitation of labor.*44


The surrender of a share of capital by the first division of the working force is the important fact here to be considered. With the coming of the second increment of labor, tools are multiplied; but they are so cheapened that all of them together embody only the original amount of capital. How do we estimate the specific product of the new increment of labor? The essential fact is that the new working force and the old one share alike in the use of the whole capital, and with its aid they now create equal amounts of product. The earlier men have relinquished a half of the capital that they formerly had; and in making this surrender, these men of the earlier division have reduced the productive power of their industry, by the amount that the extra share of capital formerly imparted to it. This reduction measures the amount of product that is attributable to the relinquished capital. Of prime importance is this fact that the product which is now attributable to the first section of the working force, with its tools and other appliances, has now become smaller than it formerly was, solely by reason of the capital that has been taken from it. The excess of its former product over its present one is not attributable to labor; and no exploiting of labor takes place, though each of the two units now receives less than the first one formerly received.


Two facts are now clear; and we may state them briefly in two proposition which include a whole theory of economic causation—a theory that tells to what agency each fraction of a composite social product is to be traced. (1) The difference between what the first division of workers created by the use of the whole capital and what they now create is an amount that is solely attributable to the extra capital which they formerly had. (2) The difference between what one increment of labor produced, when it used the whole of the capital, and what two increments are now producing, by the aid of that same amount of capital, is attributable solely to the second increment of labor. We have, in this way, tested the specific productivity of a certain amount of capital, and we have also tested the specific productivity of one unit of labor.


It is with the latter test that we are immediately concerned; and what we have been careful to guard against is the notion that, at any one time, there is a difference between the products of different units of labor, as such. Each of them, with its share of the capital, produces one-half of the whole present output of the industry; but a half of the present output is less than was the whole output, when only one man was working with the aid of the entire capital. This reduction measures the product of one-half of the capital, as used by one unit of labor. On the other hand, the whole product, now that the two units of labor are working, is greater than was the whole product with one working; and this addition to the product is due solely to an accession of labor. The amount of the addition measures the product of that labor and of all labor under the present changed conditions.


If C stands for the amount of capital that is used in the industry and if L stands for one unit of labor, the difference between the product of C+L and that of (C+2L)/2 is the amount that is attributable to one-half of the capital. The difference between the product of C+2L and that of C+L is the amount that is attributable to a unit of labor. In the first of these formulas, the minuend is what one man can produce with the whole capital, and the subtrahend is what one man can produce with a half of the capital. In the second formula, the minuend is what two men can produce with the whole capital, and the subtrahend is what one man can produce with the whole of it.


In the following diagram the amount of capital is not represented, but it remains fixed. Figure.  Click to enlarge in new window.The product that is imputable to one-half of the capital is the area ABB'A', minus one-half of the area ABB''A''. The product that is traceable solely to one unit of labor is the area A'B'B''A'', and this is now the amount that is specifically attributable to either of the two units. It will be seen that here there is no unnatural cramping of the productive power of the second man—there is no limitation of his produce to the gleanings of any field, agricultural or other. Each man gets what one unit of labor, under fair conditions, creates; while capital gets what is imputable to it.


Let us now revert to our graphic statement of the law of specific productivity. Keeping the original capital intact, and changing only its forms, let us add a third unit of labor to the force. Figure.  Click to enlarge in new window.The product of it is the area A''B''B'''A''' in the figure on the following page; and, if we continue to make similar additions to the force till it is complete, the product of the last unit of labor will be the area AixBixCD. This is the standard of wages. It is the specific product of any one unit of labor, at the time when there are ten units of it. All that we have said about the product of the second man, when he was the last one, applies here. Before the arrival of the tenth man there were nine in the field; and they were utilizing the whole of the capital, having it, of course, in forms adapted to the use of that number of workers. Each produced an amount that is measured by the rectangle the sides of which are AviiiAix and AixBix. All of them together produced the amount that is expressed by the area AEiBixAix. A narrow strip between the lines EF and EiBix measures the difference between what nine men of themselves produce at the time when they are working in connection with the whole of the capital and what the nine men produce when they are working in connection with nine-tenths of the capital; for it is fair to consider that, when ten men are using the whole of the fund, each of them virtually uses a tenth of it. The area AEFAix represents nine-tenths of the product that is specifically attributable to the whole working force when it has the entire capital coöperating with it, and of course adding its own further share to the joint product. The area EE'BixF represents, not the entire addition that a certain amount of capital makes to the output of the industry, but only the addition that an increment of capital makes to that part of the output of the industry as a whole which is separately attributable to labor.


So, when there were eight men at work, each one produced the amount of AviiBviiBviiiAviii; and all of them together produced the amount AEiiBviiiAviii. A second narrow strip, between the horizontal lines EiiBviii and EiBix, measures the difference between what eight men of themselves produce when they have all of the capital coöperating with them and what they produce after they have shared the capital with the ninth man. They give him one-ninth of the entire capital, and the strip between EiiBviii and EiBix, therefore, measures what the eight men lose in their own productive power by this surrender. In like manner, when the working force is enlarged from seven to eight, there is a surrender of one-eighth of the entire capital and a reduction in the distinctive product of the labor of the seven men ensues. Every per capita reduction of the productive fund takes something from the amount that is specifically traceable to the labor of each man.*45


Knowing that the area AixBixCD, in Fig. 1 below, measures the product of the final unit of labor, we may be sure that no unit in the working force produces less than this amount. Figure.  Click to enlarge in new window.Brief statements of the law of final productivity may raise the question, whether the earlier units of labor in the series do not produce more than does the last one; but that they produce as much as does this one cannot be doubted. AECD, then, is the smallest amount that can be trailed to labor as the cause of its existence.


In Fig. 2, let the line AD measure capital instead of labor, let the amount of labor be a fixed quantity, and let the product of successive units of capital decline along the curve BC. AixBixCD is, then, the product that the last unit of capital brings into existence. No other unit of capital produces any less; and the area AECD is the least that can be attributed to the entire ten units of capital.


Now, in Fig. 1, EBC is all that is left of the entire product that is not produced by labor. If AECD, of the second figure, is as large as EBC, of the first, this amount, EBC, is the product of capital; since the rectangle AECD is certainly the product of capital. We know that, by our hypothesis of perfect competition and a complete static adjustment, there is no profit realized by the entrepreneur, as such; and the figure ABCD cannot contain more than wages and interest. The amount EBC is, therefore, not larger than is AECD of the second, and all of EBC is the product of capital.


Again, EBC is shown, in the same way, to be the product of labor. It is not larger than AECD, of Fig. 1. The static hypothesis prevents the entire figure ABCD from containing more than wages and interest. There is, then, no area in it representing entrepreneur's profit; and EBC, which equals AECD of Fig. 1, is the product of labor solely, since the rectangle AECD measures the least amount that can be ascribed to labor.


As we have, throughout this study, kept constantly before our eyes the fact that, whenever one man comes into the force, the capital changes its forms and adapts itself to the number of men who are to use it, so we have to keep as constantly in mind the fact that the modes of labor itself have to change in a parallel way. A working force may be built up, unit by unit, so that the enlargement of the force seems to be quantitative; but the change in labor, abstractly regarded, is mainly qualitative. More effort is expended, as the force enlarges; but it shows itself, not so much in doing things that were formerly left entirely undone, as it does in doing nearly everything in a more perfect manner. If the work is agricultural, the ground will be more evenly fertilized, the seed more uniformly distributed, etc. This is one type of change that labor, as a process, undergoes when workers become more numerous. Another type of change is that which is caused by the altered character of the tools and other appliances that a laborer has to use, as the force becomes larger, while the amount of the capital remains the same. Every change in the instruments with which men work changes the mechanical movements in which work consists. Labor, however, is capable of being measured in units, as though it were homogeneous; and there is a practical method of measuring the product of all of it.


It will be remembered that, in an early chapter, we described a zone of indifference, within which an employer can take a very few more men, at the rate of wages that he is now paying, without sustaining a loss. In a great establishment, there is often such a limited elasticity in the size of the working force. If the establishment were a great farm, an extra man might somewhere be employed without being forced to do any gleaning in which he would produce perceptibly less than other men. This man's product would, as we have said, express the rate of wages. Men on the zone of indifference are also an aid in adjusting wages. Our whole study requires that a man on this zone in one industry shall be as productive as a man on the similar zone in another industry. It requires, in fact, that there shall be a comprehensive zone of indifference extending through the whole industrial field, and that labor on all parts of this social zone shall be uniformly productive. It is now doubly clear that labor on all parts of the industrial field has the same degree of productivity that it has on the marginal zone.


The practical usefulness of this zone lies in its influence in facilitating competition. A single unit of labor, in seeking employment, always has alternatives open to it. A young man who has not mastered a particular craft has many employments open to him, and can count on getting about what he is worth, anywhere on this social zone; and one who, after learning one trade, has to take up another may often get a new employment on some new part of this comprehensive area. An entrepreneur who is entering a sub-group, as a competitor of the men who are already there, can gather a force of workers for his mill by withdrawing men from this large social area of indifference—from which they may be taken without causing disturbances, either within any sub-group or in the relations between the different sub-groups. The scientific importance of this zone, however, depends on the test that it affords of the productive power of all labor. If only the adjustments which have lately been described have already taken place, and if labor and capital are now apportioned in a nicely accurate way among the different industries, the product realized from labor on this zone has become an indicator of the product that may be attributed to labor everywhere.

Notes for this chapter

The most brilliant of early German economists, Von Thünen, offered a theory that applied a final productivity test to both labor and capital, and made wages and interest depend on the result. In his work, Der isolirte Staat, he said that, when new men are taken into an industry,—the tilling of a farm, for example,—they produce less than did the men who were earlier employed. What the farmer gets by means of the labor of the last man, is what he pays for the work of every man. Von Thünen also asserted that a final unit of capital, tested in the same way, shows a similar reduction in its productive power, and that the product of the unit last applied sets the standard of interest.

It is a startling fact that the statements of Von Thünen did not lead directly to the solution of the problem of wages and interest. With such a brilliant beginning of a true theory before them, why should economists still account for the rate of wages, by saying that it depends on the amount of capital that is foreordained to be divided among laborers in the form of wages? Why, also, should they account for the rate of interest merely by saying that it depends on demand and supply? It is doubtless true that Von Thünen himself attached far less importance to his final-productivity formula than he did to that entirely different formula by which, in his view, the socially desirable and rightful rate of wages is expressed; yet it would seem that his statement of the principle of final productivity should have put investigators on the right track.

The explanation is to be found in the incompleteness of Von Thünen's actual theory. It was left in a shape in which it not only fails to reveal the most important fact about wages and interest, but seems actually to contradict it. This fact is that, under the influence of perfectly free competition, the pay of all labor tends to equal the product of all labor, and that interest on all capital mark to conform to the product of all capital.

Von Thünen's theory of wages is apparently a theory of the exploitation of labor. In his illustration, there is a certain force of laborers working on a farm and a man is now added to the force. His presence enables the farmer to glean his fields more closely. As Von Thünen suggested, he can now gather a smaller grade of potatoes than it was formerly profitable to gather; and if the new man is taken in the harvesting season, his product is embodied in the addition that, in such ways as this, is made to the crop. This man, however, produces distinctly less than the men who are before him in the order of the series; and their pay is scaled down to his product. There are expressions in Von Thünen's discussion which seem to imply that, in his own view, the law of final productivity is a law of exploitation of labor. There are also indications that his theory of the final productivity of capital involved a similar exploitation of the earlier units of capital.

What is first needed, it order to make Von Thünen's statement cover a principle that is of cardinal importance in connection with wages, is a theory of what has been called "imputation," or of what, in the foregoing chapter, has been called economic causation. At any one time, all units of labor tend to be equally productive. There is, then, no class of workers who are degraded and virtually robbed, because of the pressure of others who produce less than they do and who set the standard of their pay. The excess of pay that the men on the illustrative farm formerly got is attributable to the greater product that they formerly created and that is solely due to the excess of capital which they had in the earlier period. The theory needs to trace to capital, and not to labor, that extra product which an overplus of capital insures to the men who, in the assumed case, are made to come early in the series. It needs, also, in studying the products that are attributable to a series of units of capital, to use the same discrimination and to show that the earlier units of this agent are not exploited.

As between a theory which asserts that every unit of labor naturally tends to get, as its pay, its entire product and one which says that the great mass of laborers are, by competition, regularly robbed of a part of their product, the difference is radical; and yet these theories may use identical language, in telling how the pay of all labor is directly determined. Both may apply to labor the commercial principle of final valuation and say, in effect, that there cannot be two prices of the same article in the same market—that what the last unit labor brings, all labor brings; and that the last unit brings what it produces. If it produces less than do other units, these others are sufferers by their connection with it, for they lose a part of their products. If, however, all units under present conditions produce the same amount, there is no robbery involved in fixing the pay of all by the product of the final one. Von Thünen's theory is a final productivity theory; but it needs to become, in addition, a specific productivity theory, which makes the pay of each unit of labor conform to its own specific product.

A theory that is to explain the adjustment of wages and interest needs to make clear what is the mature of that "last dose" of capital, on the product of which interest depends; and this involves discriminating between capital and capital-goods. Particularly, also, does the study need to enforce its scope, so as to include, not one industry merely, but the whole system of groups and sub-groups that make an economic society. The final increment of labor, the product of which fixes wages, is a social increment, some of which is found in every sub-group in the series; and the same thing is true of the final increment of capital. The law of value is active in making these apportionments, and it needs to be included as a part of the theory of distribution as a social phenomenon. With Von Thünen's work before us, no one else can claim as his own the application to labor and to capital of the principle of final valuation and the basing of valuation on productivity. A prospector in a mining country may, indeed, independently discover and re-occupy an abandoned claim; and this is all that one would do who should re-discover the single principle of final valuation of labor and capital and should stop where Von Thünen stopped. Going farther and discovering laws that tend to bring the products of different units of labor at any one time to a equality, to bring the products of different units of capital to an equality, and to make wages equal to the entire product of labor and interest equal to the whole product of capital—this is attaining the essential truth in the theory of wages and interest; since it establishes the fact that natural law, so far as it has it way, excludes all spoliation. Such further study reveals the fact that what are apparently surplus parts of the products of early increments of labor are really products of capital. This result is gained by following the line of study in which Van Thünen took the initial steps; and it may, perhaps, give so much of a title to the final result as a miner secures when he strikes a new vein of metal by using, as an entrance way, an abandoned shaft that had led only to a deposit of ore of a different kind. As Von Thünen did not suspect, the natural law of wages gives a result that would satisfy his own requirement, as being desirable and morally justifiable.

Figure.  Click to enlarge in new window.In all the foregoing graphic representation there is a slight mathematical inaccuracy, due to the fact that the upper boundary of the figure is made to be a curve with a continuous downward trend. Strictly, the whole figure should have been made of rectangles, and the upper boundary should have been the tops of the contiguous rectangles. With ten units of capital one man produces the amount that is expressed by the first rectangle in the following figure; while, after he has relinquished one-half of the capital to the second man, he produces only the amount indicated by the smaller rectangle on the right of the figure. The difference between these areas, or the space above the dotted line in the larger rectangle expresses the product of five units of capital in the hands of one man. If we continued thus to build up the figure, we should avoid the small inaccuracies just referred to; but we should have a somewhat cumbersome mode of description to contend with, when we should describe the figure by letters.

End of Notes

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