CHAPTER XXXIII

THE LAW OF VARIABLE PROPORTIONS

The problem of the distribution of wealth is the problem of dividing the products of the industries of the nation among the various classes. The claim of each class to a share of the wealth is usually based upon the claim that each has contributed something to its production. The contribution may be labor, either mental or physical; it may be capital, or the results of foresight or investing; or it may be land which the owner has appropriated or otherwise come into possession of, and which he puts to use or permits someone else to use.

The market value of services. The market value of what each has to offer determines his share in the product. If the market value of labor is high, the laborer gets a large share; if it is low, he gets a small share. The same is true of that which each has to offer. Our first problem must be, therefore, to study the market value of each factor, or agent, of production in order to find out why the seller of each factor gets a large or a small share.

The income of each class, however, is a flow rather than a fund or a lump sum. The laborer sells not himself but the flow of productive energy which he can exert during a given period of time. The capitalist, when he gets interest, sells not his capital but the flow of utilities which come from his capital. during a given period of time. If the laborer were a slave he might be sold bodily, and in that case he would bring a price. The capitalist and the landlord may sell their capital and their land outright for a price. This involves a question of exchange and market price. When they sell the flow of utilities which their properties yield we have interest and rent, which are questions of distribution. The following outline will indicate the

relation of these various problems to the general problem of valuation. For convenience the flow of utilities yielded by the various factors of production are called services.

Why productive agents are desired. The reason for paying for an agent of production is that it helps to produce something which is desirable. Its value is derived from that of its product, or, as some would say, a part of the value of the product is imputed to the productive agent. At any rate, the producer of a desirable thing may itself be desired, or a thing may be desired because of what it will produce as well as for its own sake. The greater its product, or the greater its contribution to the joint product of a group of factors, the greater its value. It is therefore of the utmost importance that we find out, if such a thing is possible, how to determine the contribution of each factor. This is one of the most elusive problems in the whole field of economics. The student is requested to study this problem as carefully and intensely as he would an intricate problem in physics or chemistry.

A combination of the factors of production not a chemical combination. In Chapter XVII we saw the necessity of a proper balance not only among the factors of production but also among all the factors of national life. But some variation among the factors of production must always be allowed. What constitutes the perfect balance depends upon a number of considerations which have not yet been discussed. Factors of production, when used in combination, are not like the elements in a chemical reaction or the colors in a picture. These

1 Compare note by the author on "The Place of the Theory of Value in Economics," in the Quarterly Journal of Economics, November, 1902.

probably admit of no variation. The factors of production may always be combined in different proportions without destroying the result. One can grow a hundred bushels of wheat in a year by using little land and much labor or by using much land and little labor. Which is the more economical combination will depend upon the relative cost of land and labor. Where land is cheap and labor dear, it pays to use much land and little labor; where land is dear and labor cheap, it pays to use little land and much labor.

In an actual chemical combination the various elements have to be combined, apparently, in fixed proportions, without any variation whatever. This is known as the law of definite proportions. But in order to induce a given chemical combination, different substances have sometimes to be mixed in considerable masses. This gives rise to another law, which is probably as well understood as the law of definite proportions. It is of special importance in economics.

The law of variable proportions. Take, for instance, the juvenile experiment of mixing vinegar and baking soda for the purpose of producing a fizz. The actual combination of molecules which produces the gas that makes the bubbles doubtless follows the law of definite proportions. But not all the materials in the mixture will be thus instantly combined. At the end of a definite period of time, say a minute, some of the acid and some of the soda will remain uncombined, probably because a certain number of molecules of each never happened to come in chemical contact with the requisite molecules of the other. The greater the quantity of vinegar in proportion to the soda, the greater the probability that each molecule of the soda will come in chemical contact with a molecule of acid. Therefore the greater the proportion of vinegar to soda, the greater the proportion of the molecules of soda that will be used in the formation of gas and, conversely, for the same reason, the smaller the proportion of the molecules of acid that will be used. Increase the soda and decrease the vinegar, and the opposite would follow, for the same reason.

Many factors at work in combination. There are, of course, other factors in the problem, such as the size and shape of the receptacle in which the mixture is placed, the temperature of the mixture, the amount of shaking or stirring to which it is subjected, as well as the time allowed for the combination to take place. Leaving all the other factors unchanged except the one selected for experimentation, we get a result similar to that which we obtain in some of the larger economic combinations, such as the application of labor to land. In fact, we are here in contact with a universal law which applies to mixtures of chemicals, as distinct from chemical combinations, to the mixture of fertilizers in the soil, and to every other combination, including that of various forms of human talent in the promotion of national greatness.

The manufacture of ether. In the manufacture of ethers, alcohol is combined with acids much as soda is combined with vinegar in the experiment referred to above. After the mixing has taken place, only a limited proportion of the original ingredients is actually combined. Since alcohol is expensive and the acids are cheap, it is found economical to use large quantities of acids in order to force as much of the alcohol as possible to combine. The acid is literally massed in its attack upon the alcohol, in order that no molecule of the latter may escape. In fact, this phenomenon is explained by the so-called mass law. If alcohol were cheap and acid expensive it would be desirable to force every molecule of the acid to combine. In order that as few as possible might escape, it would be necessary to mass the alcohol in its attack upon the acid. An economist might not improperly call this an intensive use of acid and an extensive use of alcohol. Conversely, the rule actually followed of massing the acid upon the alcohol might be called an intensive use of alcohol and an extensive use of acid. It is certainly analogous to massing large quantities of labor and capital upon small areas of land in order to get the maximum product out of the land, even though a relatively small product per unit of labor and capital is secured.