Essentials of Economic Theory / As Applied to Modern Problems of Industry and Public Policy

by John Bates Clark

Products of a Series of Units of Labor.—If we continue this process till we have ten units of labor, employing the same amount of capital as was formerly used by one, we shall find that each unit as it begins to work adds less to the previous product than did the unit which preceded it, and that the tenth unit adds the least of all.

Care must be taken not to confound the addition that is made to the product in consequence of the additional working force with the amount which, after the enlargement of the force, is created by the last unit of labor and its pro rata share of the capital. When the tenth unit of labor is working, it is using a tenth of the capital and the two together create a tenth of the product. This is more than the amount which is added to the product by the advent of the tenth unit of labor. That addition is merely the difference between the product of all the capital and nine units of labor and that of all the capital and ten units of labor. This extra product can be attributed entirely to the increment of labor.

It is also carefully to be noted that when the units are all working together, their products are equal and the particular one which happened to arrive last is not less productive than the others. Each one of them is now less productive than each one of the force of nine was under the earlier conditions. In like manner each unit of the nine is less productive than was, in the still earlier period, each unit of the force of eight. At any one period, all units produce the same amount. At any one period, then, what any one unit of labor produces by the aid of its pro rata share of the capital is a larger amount than what each can be regarded as producing by itself. Though one of ten units creates, with the aid of a tenth of the capital, a tenth of the product, of itself it creates less; for we can only regard as its own product what it adds to the product that was creating before it arrived on the scene. It is the bare product of a unit of labor alone that we are seeking to distinguish from other elements in the general output of the industry, and that consists in the difference between what nine units of labor and all the capital can produce, and what ten units of labor and all the capital can produce.

We will consider the amount of capital fixed and let the amount of labor increase along the line AE, and we will let the product of successive units of labor be measured by the vertical distance from the points on the line AE to the descending curve CD. AC is the product of the first unit of labor. The product of later units is measured by lines to the right of AC and parallel with it, which grow shorter as the number of units increases. ED is the product of the last unit. In each case we impute to an increment of labor whatever amount of product its presence adds to that which was created before.

Summary of Essential Facts.—The facts that are to be remembered then are: first, that the capital remains fixed in amount, though the forms of it change as the number of units of labor increases; secondly, that that which we call the product of a unit of labor is what that unit, coming into the field without any capital, can add to the product of the labor and capital that were there before; and thirdly, that this specific product of labor grows smaller as the amount of labor grows larger, rendering the product of the last unit the smallest of all. When the tenth and last unit is working, each one of the nine earlier units is, of itself, producing no more than does the final one, though it formerly produced more because of the larger quota of capital with which it was formerly supplied.

The Test of Final Productivity.—There are now at work ten units of capital and ten of labor, and we cannot go through the process of building up the working force from the beginning. How, then, do we measure the true product of a single unit of labor? By withdrawing that unit, letting the industry go on by the aid of all the capital and one unit of labor the less. Whatever one of the ten units of labor we take away we leave only nine working. If the forms of the capital change so as to allow the nine units to use it advantageously, the product will not be reduced to nine tenths of its former size, but it will still be reduced; and the amount of the diminution measures the amount of product that can be attributed to one unit of bare labor. Or we may add a certain number of workmen to a social force already at work, making no change in the amount of the capital,—though changing its forms,—and see how much additional product we get. That also is a test of final productivity. It gives the same measurement as does the experiment of taking away the little detachment of men and seeing how much the product shrinks. By either process we measure an amount that is attributable altogether to bare labor and not to capital.

The whole area BCD in the diagram is an amount of product that is attributable to capital and not to labor. It represents the total surplus produced by labor and capital over the amount that can be traced to the labor alone. The product of all the capital and all the labor minus ten times the product of a single unit of labor is the amount that is attributable to the productive fund only.

The area ABDE represents this amount. The last unit of labor creates the amount DE and the number of units is represented by the amount AE. All of them are now equally productive and what all create, as apart from what capital creates, is the amount ABDE.

Only the Final Part of this Mode of gathering a Working Force practically resorted To.—The process of building up the working force from a single unit is imaginary. In practical life we see the process only in its final stage. Entrepreneurs do continually have to test the effect of making their working forces a little larger or a little smaller, and in so doing they test the final productivity of labor; and this is all that is necessary. Tracing the process of building up the force of labor unit by unit reveals a law which is important, namely, that of the diminishing productivity of single units of labor as the number of units increases. If we crowd the world full of people but do not proportionately multiply working appliances of every kind, we shall make labor poorer.