Front Page Titles (by Subject) Chapter XII: Final Productivity the Regulator of Both Wages and Interest17 - The Distribution of Wealth: A Theory of Wages, Interest and Profits
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Chapter XII: Final Productivity the Regulator of Both Wages and Interest17 - John Bates Clark, The Distribution of Wealth: A Theory of Wages, Interest and Profits 
The Distribution of Wealth: A Theory of Wages, Interest and Profits (New York: Macmillan, 1908).
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Final Productivity the Regulator of Both Wages and Interest17
Instead of the plantation in our late illustration, we will think at once of the world, with its innumerable industries and its complete outfit of agents and appliances. It is, of course, isolated, since neither products, workers nor instruments can migrate to it or from it; and the rate of wages that it affords must be determined entirely within itself.
We can now derive an advantage from the imaginary process of supplying the labor for this community, unit by unit, provided that we can do this without getting the impression that the action of the law of final productivity depends on it. This is only one way of illustrating the action of that law. The actual and practical test of the productive power of one unit of labor is made, if one unit only is taken out of a complete force and if the ensuing reduction of the product is noted. This test we have already applied. It is for the sake of having a more complete view of the action of the law of final productivity that we now build up a working force, unit by unit, leaving capital unchanged in amount, though changing in its forms with the arrival of each new unit of labor. We will let a thousand workers constitute each increment of labor, and let farmers, carpenters, smiths, weavers, printers, etc., be represented in it in carefully adjusted proportions. Every occupation must have its representatives, and the comparative number of them must be fixed according to a law that it will soon be our duty to study. All that we now need to know about this law is, that it so apportions labor among the different groups and sub-groups that the productive power of labor is brought to a certain uniformity is the various occupations. Common and adaptable labor is made to produce as in much in one sub-group as in another.
Give, now, to this isolated community a hundred million dollars' worth of capital, and introduce gradually a corresponding force of workers. Put a thousand laborers into the rich environment that these conditions afford, and their product per capita will be enormous. Their work will be aided by capital to the extent of a hundred thousand dollars per man. This sum will take such forms as the workers can best use, and a profusion of the available tools, machines, materials, etc., will be at every laborer's hand. If we were to try to imagine the forms of productive wealth that such a condition would require, we should bring before the mind a picture of automatic machinery, of electrical motors and of power obtained from cataracts, tides and waves. We should see chemical wonders performed in the preparing of materials, the creating of soil and the like. We should place the worker in the position of a lordly director of natural forces so great and so varied that they would seem more like occult powers of the air than like tools of mundane trades. All this, however, is only a picture of what would be slowly and remotely approached, if capital were quietly to outgrow population and were to reveal its power of taking the forms that the needs of the relatively few workers would require. Something like this is the goal of natural economic tendencies.
Add, now, a second thousand workers to the force; and, with the appliances at their service changed in form—as they must be—to adapt them to the uses of the larger number of men, the output per man will be smaller than before. This second increment of labor has at its disposal capital amounting to only half a hundred thousand dollars per man; and this it has taken from the men who were formerly using it. In using capital, the new force of workers goes share in share with the force that was already in the field. Where one of the original workers had an elaborate machine, he now has a cheaper and less efficient one; and the new workers by his side also have machines of the cheaper variety. This reduction in the efficiency of the instrument that the original worker used most be taken into account, in estimating how much the new worker can add to the product of industry. His presence has cheapened the instruments used by the first set of workers and has taken something from their efficiency. His own share of the original capital, as it is made over to him by the workers formerly in his immediate part of the field, consists also in the cheaper and less efficient instruments. For two reasons, therefore, he brings into existence less wealth than did one of the first division of laborers.
All over the field the hundred million dollars has, as it were, stretched itself out to meet the needs of a double force of workers. Of some kinds of tools there are now twice as many as before; but they are all less costly and less efficient. Cheaper buildings and more of them, is the rule. Railroads have more curves and grades less durable bridges and, in general, less substantial plants. There are two sailing vessels, where there was formerly one steamer; and there are two wooden ships, where there was one of steel. The capital of the community, without changing in amount, has taken a form that is more extended than its earlier one—the instruments are everywhere multiplied and cheapened.
We must be careful as to the arithmetic of the change. The product that can be attributed to this second increment of labor is, of course, not all that it creates by the aid of the capital that the earlier division of workers has surrendered to it; it is only what its presence adds to the product previously created. With a thousand workers using the whole capital, the product was four units of value; with two thousand, it is four plus; and the plus quantity, whatever it is, measures the product that is attributable to the second increment of labor only. There is a minus quantity to be taken into account in calculating the product that is attributable to the final unit of labor. If we take, first, all that it creates by the aid of the capital that is surrendered to it, and then deduct what is taken from the product of the earlier workers and their capital by reason of the share of capital that they surrender to the new workers, we shall have the net addition that the new workers make to the product of industry.
With the vast capital utilized, the product that the new unit of labor adds to the product that could have been had without it will be very great, though it will be less than was created by the first unit. Every man in the new working force produces enough to rival a fortunate gold hunter. Add increment after increment of labor, till the force is decupled; and the product that is due to the last of the addition is still great. Continue to add to the force till it numbers a hundred thousand, having still the hundred million dollars' worth of capital, but in changed form. The workers are then about as well equipped as are those of the United States at the present day. The last increment of labor may be supposed to add to the product that the society would have realized without its aid about as much as a working force of the same size, in this country, could separately create, by adding itself to the force already employed.
If, now, this hundredth increment of labor is the last one that the isolated society contains, we have the law of wages. We have set the population working till no reserve exists from which we can get more. The last composite unit of labor—the final division of a thousand men—has created its own distinguishable product. This is less than the product that was attributable to any of the earlier divisions; but, now that this section of the laboring force is in the field, no division is effectively worth any more than is this one. If any earlier section of the working force were to demand more than the last one produces, the employer could discharge it and put into its place the last section of men. What he would lose by the departure of any body of a thousand men, is measured by the product that was brought into existence by the last body that was set working.
Each unit of labor, then, is worth to its employer what the last unit produces. When the force is complete, no one body of a thousand men can withdraw without lessening the product of the whole society by the same amount that we have attributed to the one that we last set working. The effective value of any unit of labor is always what the whole society with all its capital produces, minus what it would produce if that unit were to be taken away. This sets the universal standard of pay. A unit of labor consists, in the supposed case, of a thousand men, and the product of it is the natural pay of a thousand men. If the men are equal, a thousandth part of this amount is the natural pay of any one of them.
We are seeking, of course, a static standard of wages; but the process that gradually builds up a force of laborers from a thousand to a hundred thousand, and causes capital to modify its forms as the increase of the force goes on, is not a static process. It is a dynamic operation which brings the working force up to its static complement. From the time that the force is complete, however, we leave it unchanged: we let the static condition thus attained continue forever. The importance of going through the illustrative dynamic process, and making up the permanent force unit by unit, lies in the clear view that this gives of the product that can be attributed to the "final" unit.
Actually, no unit is last in time. The hundred thousand men, with the hundred million dollars' worth of capital, work on year after year, and no one division of a thousand can be singled out as constituting the particular division whose product fixes wages. Any one such body of men is always worth to its employers what the final division would produce, if we were to set them working in such an order of succession as, for illustration, we have described. That the men will get this amount, is insured by employers' competition. The final division of a thousand men has in its hands a certain potential product, when it offers its service to employers. If one set of entrepreneurs will not give them the value of it, another will, provided that competition is perfect. With an ideally complete and free competitive system, each unit of labor can get exactly what a final unit produces. With an imperfect competition, it still tends to get that amount. The final product of labor sets a standard for the pay of labor; and actual wages tend toward it, with variations.
We have noted the fact that an entrepreneur's net profit is an incentive to competition. Such a profit is mercantile, and means that employees are selling their products for more than they are paying out in wages and interest—that the price of the goods exceeds the cost of the elements that compose them. We noted the fact that "natural price," as defined by economists, is really a wages-and-interest price; for it equals the sum of these two outlays. A profit-giving price exceeds that sum, but the competition that tends to annihilate the profit cuts it off at both ends. By bidding against each other in selling goods, employers make the prices smaller; and by bidding against each other in hiring labor and capital, they make wages and interest larger. There is a profit on labor, so long as the men in a working force are paid less than the final one produces; but competition tends to annihilate that profit and to make the pay of labor equal to the product of the final unit of it.
As has again and again been said, we have constructed an ideal society in which disturbing facts are omitted, and we have so far described none of the obstacles that pure law encounters in real life. We have made no estimate of the amount of deviations from the final productivity standard that the pay of workmen actually reveals. All such studies have a place in the dynamic division of our work. As real as gravitation is the force that draws the actual pay of men toward a standard that is set by the final productivity law. This law is universal and permanent: everywhere it will outlive the local and changeful influences that modify its operation. We are to get what we produce—such is the dominant rule of life; and what we are able to produce by means of labor, is determined by what a final unit of mere labor can add to the product that can be created without its aid. Final productivity governs wages. We may now summarize the conclusions that we have thus far reached, concerning the natural standard of wages, in the following series of propositions:—
In like manner, we may find it useful, in presenting the law by which wages are fixed, to go through an imaginary operation of setting men at work, one man at a time or one company of men at a time, and thus to find what importance the market places on the last one. This reveals the operation of a law of diminishing productivity; and whether we take a single man or a body of men as the unit of labor, any unit can get, as pay, what the last one would produce, if the force were set working in this way.
Let the number of units of labor be measured, in the following figure, along the line AD. Let them be set working in a series, in connection with a fixed amount of capital. The product of the first unit of labor, as aided by all the capital, is measured by the line AB. What the second unit of labor adds to this product is the amount expressed by A'B'. The third unit enlarges the output by the amount A''B'', the next by A'''B''', the next by A''''B'''' and the last by DC. DC measures the effective productivity of any unit of labor in the series and fixes the general rate of pay. If the first unit of labor claims more than the amount DC, employers will let it withdraw, and will substitute for it the last unit. What they lose by the withdrawal of any one unit in the entire force is the amount DC.
A fact of great importance now appears. We may reverse the application of this law, and by so doing get a law of interest. Let the labor be the element that is unchanged in amount, and let capital be the one that is supplied in a succession of increments.
AB is now the product gained by using one increment of capital in connection with the whole working force. A'A' is the additional product that is created increment of capital. A''B'' is the product of the third increment and DC is the amount last. This amount, DC, fixes the rate of interest. No one of the series of units of capital can secure for its owner more than the last one produces. If the owner of the first increment asks more than this for the use of it, the entrepreneur will relinquish this bit of capital and will put the last unit in its place. What he will lose, in the way of product, is measured by the amount DC, the direct product of the final increment of capital. This expresses the effective product of every increment, since it is the amount that would be lost if any one of the series were withdrawn.
All that we have said about the change that must take place in the forms of capital, when the amount of it is fixed and the working force is increasing, applies here, where these conditions are reversed. The steady increase of the capital, if the amount of the labor be fixed, compels a similar change of forms. With one unit of capital and ten units of labor, the instruments will be simple and cheap. Hand tools will generally prevail; and buildings, roadways, bridges, vehicles, etc., will be of a makeshift kind, which will, at a small cost for each instrument, enable the men in some way to work. With two units of capital, a better type of instruments begins to prevail. Every increase in the amount of the capital shows itself primarily in transmuting poor appliances into better ones. There are, indeed, more tools, and there is more raw material; but the striking fact is that all the tools, etc., are costlier and more efficient. With the addition of the tenth unit of capital, the condition may be thought of as approximating that of our own country at the present day. There is much costly machinery, many durable buildings, a good supply of large ships, efficient railroads, etc.
At the cost of what may be a tedious repetition, we have now described the series of changes that an increasing capital undergoes, because this is what is actually taking place. Capital is the element that is outgrowing labor. We may take the world that exists instead of an imaginary one, as our illustration. As the accumulation of capital actually goes on, it shows itself more and more in qualitative changes of existing instruments. Society pulls down its barns and builds others, better as well as larger; it carries its mercantile buildings farther into the air, and makes them fireproof and durable; it substitutes steel ships for wooden ones and steamers for sailing craft; it takes the curves and grades out of its railroads, and makes bridges and viaducts of the kind that defies time and strain; it bores tunnels through mountain ranges to avoid climbing over them and cuts canals across isthmuses to shorten the voyages of ships. As capital grows very abundant, there are made longer tunnels and canals; and they have, as their purpose, the avoiding of climbs that are easier and voyages that are shorter than were those that were avoided by the earlier engineering works. They thus represent a greater outlay incurred for a smaller gain. Society also makes all its machinery as nearly automatic as it can, so that one laborer's guidance shall keep much machinery in successful motion. Everywhere there are taking place such adaptations of capital as fit a large amount of it to the needs of a relatively small amount of labor.
The changes that have to be made in the forms of the capital, as the amount of it increases, reveal a reason for the decline in the rate of its earnings. The rudest hatchet that can be made may vastly increase the owner's power to get firewood. It may wear out in a year; but in that period it may save enough of time, that would otherwise have been devoted to a slow and painful mode of wood gathering, to enable the owner to make six new hatchets. Though he will probably not use the liberated time for this particular purpose, whatever he does secure by it represents an interest of five hundred per cent on the capital invested in this first and most productive tool. A second tool may liberate labor enough to replace itself only five times. The owner will actually replace it once, and will employ the time that could give him four duplicates of it in making other things for his own use; but the fruit of the spare time that the second tool makes available is now four hundred per cent of the cost of the tool, as computed in terms of unaided labor.
Tools are, of course, employed in the order of their productivity, so far as men judge their several powers of production correctly. It soon ceases to be possible to add to a working equipment anything that produces a multiple of its own cost in a year, and the interest on the final increment of capital becomes a fraction of that capital itself. This fraction steadily diminishes, as the productive fund grows larger, and as improvement in the quality of tools, etc., becomes one form of investment for the growing accumulations. The difference between the cost of a rude and poor hatchet and that of a better one represents an increment of capital; but it has less power to reproduce itself, in amount, than had the investment that was made in the original tool.
As accumulation proceeds, there are always made costlier machines, representing more capital; and the product that comes from using them is a smaller fraction of their cost. The straightening of the curves in railroads is one of the ways in which capital may find investment. This may cost as much as the first making of the corresponding parts of the road themselves; but it does not liberate as much labor, in proportion to its cost, as did the building of the old and crooked road. The boring of a long tunnel, to avoid a short climb over the mountains, does not result in as large earnings for the capital that is thus invested as did the making of a short tunnel to avoid a higher climb. Everywhere do the forms of the capital show differences in earning power; and the owners choose first the most productive forms, and later the less productive. To this fact is due the present low rate of interest. We are utilizing the opportunities for investment that stand late in the series and are low in the scale of productivity.
We have said that no increment of capital can get for its owner more than the last increment produces. We may state this in another way by saying that no form of capital can claim and get for its owners in a year a larger fraction of its cost than the least productive form produces. Under modern conditions, if the man who lends "money" for the procuring of a highly necessary tool demands the whole amount that is secured through the use of it, the entrepreneur, who is the borrower, will refuse the money and will use, for the procuring of the tool which is so much needed, the money that formerly went into the tool that was last and least important on the list. In terms of more primitive life, if the man who performs the labor of making a very necessary tool demands the whole product that it creates, the entrepreneur will decline to utilize this tool-making labor and will divert to the making of the needed instrument that labor which has been used for the making of the least important part of his working equipment. Capital is, it thus appears, completely transmutable in form. Society can quit making one kind of instrument and make another. Capital-goods are, then, interchangeable; and while this is so, no increment of capital can ever secure for its owner more than the final increment produces.
It is, of course, true that labor also has to change its forms, as capital accumulates. The man who watches a complicated machine is going through a set of movements very different from those executed by a man working with a hand tool. Every time that we change the form of the capital, we change, by that very fact, the character of the labor. Mutual adaptation in form is the general rule for these two producing agents. Change the merely quantitative ratio of one of them to the other, and you make it necessary to transform both of them in character. As with ten units of capital for ten units of labor there will be one grade of instruments and certain kinds of work performed in connection with them, so with eleven units of capital for ten units of labor there will be somewhat different kinds of instruments, and different modes of working. This double transformation must, moreover, theoretically extend through the whole mass of capital and the whole process of labor. Everywhere there are to be seen new and improved kinds of capital-goods and new modes of using them.
With this qualification, we may represent the law of interest by the process of building up, increment by increment, the fund of social capital and measuring the product produced by each unit of it. In this imaginary process we have revealed a true law of varying productivity. As we have said, the addition to the product caused by the last unit of capital fixes the rate of interest. Every unit of capital can secure for its owner what the last unit produces, and it can secure no more. The principle of final productivity, in short, acts in two ways, affording a theory of wages and of interest.
[17.]The theory advanced in this chapter and the two following ones was first published in the Quarterly Journal of Economics, in two articles entitled, respectively, "Distribution as Determined by the Law of Rent" (April, 1891), and "A Universal Law of Economic Variation" (April, 1894).