# Popular Science Monthly/Volume 77/November 1910/Professor Norton's Law of Progress

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* PROFESSOR NORTON'S LAW OF PROGRESS
By Professor T. N. CARVER
HARVARD UNIVERSITY
PROFESSOR J. PEASE NORTON'S recent article on "The Cause of Social Progress and of the Rate of Interest" contains a notable contribution to economic theory. His analysis of the way in which other factors contribute to the value of the work of the genius is most acute, and his reasoning is, up to a certain point, entirely sound. It is, however, merely a part of the universal law of diminishing returns, and not, as he seems to think, a refutation of that law. Of two factors, $X$ and $Y$, combined for the production of a given result, if one factor, $Y$, increases, that increase adds, within limits, to the effectiveness of each unit of $X$, but correspondingly detracts from the effectiveness of each unit of $Y$. If, for example, one man, cultivating ten acres of corn, can produce a thousand bushels, he can, ordinarily, if given twenty acres of the same kind of land, produce more than a thousand bushels, say sixteen hundred bushels. Give him the use of still another ten acres, making thirty acres in all, and he can produce still more corn, say two thousand bushels, and so on, until a point is reached when additional land would be of no use at all to him. Up to this point, while every added increment of land adds to the crop produced per unit of labor, at the same time it reduces the crop produced per acre of land. This is a case similar in certain respects to that assumed by Professor Norton, of a genius who makes a labor-saving invention by means of which there is an increase of two dollars per capita in the product of the community. The larger the population the greater the product of this man's labor, or, which amounts to the same thing, the greater the value of the invention. Professor Norton assumes, however, that the product, or the value, of this invention would increase in exact ratio with the population. This he has no right to assume. In fact, inasmuch as the universal opinion of economists is to the contrary, he is under some obligation to support his assumption by definite and positive proofs. It is probably true, at least some economists would agree, that if the population and the land and natural resources, and the capital as well, all increase with the population, this joint increase of all productive agents would bring an exactly proportionate increase to the value of the invention. But if the population alone increases, while the land and capital remain fixed in quantity, then the value of the invention, while it may increase, will certainly not increase as fast as the population increases. The twine binder, for example, undoubtedly increased the productive power of labor. Let us assume that at the time of its invention it added two dollars to the product of every person in the civilized world. If the population doubled and the available ​wheat land also doubled, there is no reason to doubt that the value of that invention would also be doubled; that is, it would add two dollars to the productivity of twice as many people as before. Something like this has probably taken place since the twine binder was invented. But suppose the population had doubled without any increase whatever in the available wheat land. Would that invention still have been capable of adding two dollars to the product of every person, or only a dollar and a half? Or, let the population go on doubling and quadrupling generation after generation, without any increase in the available wheat land, would the twine binder continue indefinitely increasing every person's productivity by two dollars, or only one dollar, a half dollar, etc.? If there is no more wheat land to gather harvests from, is it certain that any more twine binders would be needed with a dense than with a sparse population, or that the value of the invention would increase at all? Has not Professor Norton erred in thinking of labor as the sole factor of production, omitting to think of land as even furnishing a necessary condition of efficient production?
Let us present the argument in another form. An agricultural invention might easily reduce by two dollars the cost of cultivating every acre of land under tillage, thus increasing the efficiency of labor. Obviously then, other things being equal, the more acres there are under tillage the greater will be the total saving effected by the invention. If labor and capital increase in proportion as the land under tillage increases, there is no reason to doubt that the total saving would increase in exact proportion as the land under tillage increased; that is, it would continue to amount to two dollars multiplied by the number of acres. But suppose the labor and capital to remain stationary, while more and more land is brought under tillage, would the saving continue to be two dollars per acre, or would it fall lower and lower? This illustration is given merely to show the necessity of considering all the factors in a problem of this kind, and not a part only.
So long as there are new acres of land being made available, and new funds of capital coming into being, all the results which Professor Norton posits may actually happen. But what does it signify to say that a large population using large areas of land may be quite as well off as a small population using small areas of land, and that an increasing population may be better and better off provided it not only has more and more land but is improving the arts of production at the same time? This, it will be observed, is quite different from saying that we "arrive at the conclusion that the comfort and prosperity of a population tends to increase more rapidly than the population upon which it depends." Until it is shown that this is true, however small the area of land or the supply of capital, it is no refutation of the Malthusian theory, and it is not even a criticism of the law of diminishing returns.
​As an attack on the Malthusian theory, Professor Norton's argument is of the same character as that which reasons that since big fish eat little fish, and since, as a consequence, every time a big fish is caught the lives of a great many little fish are saved and they are thus allowed to grow to maturity, therefore the more people there are catching and eating big fish the more abundant will fish become, because, for every big fish which is caught, a large number of little fish will be enabled to grow to bigness. ∴ If we will all become ichthopophagi, an inconceivable number of people can subsist and we need not concern ourselves with the law of Malthus.—Q. E. D.
The real conclusions to be drawn from Professor Norton's preliminary analysis, which is really a valuable piece of work if he had not spoiled it by trying to base false conclusions upon it, are as follows: (1) An increasing population may, by reason of the enhancing value of every productive improvement, increase in general prosperity and well-being, provided it is not hindered by too great a scarcity of the other necessary factors of production, such as land and capital. (2) In spite of such scarcity, and the consequent operation of the law of diminishing returns, the prosperity may increase, provided the arts of production improve rapidly enough to more than counterbalance these disadvantages.
The facts cited by Professor Norton regarding interest rates can all be accounted for without calling in this supposititious "law of progress." A time of rapid invention is naturally a time of great demand for new capital, because an invention is a new opportunity for the use of capital. Therefore, men who see these new opportunities bid high to get possession of capital. This, however, is not a complete explanation of interest. Professor Norton would have difficulty in explaining why an appliance embodying one of these new inventions would sell for less than its anticipated product, without recourse to some of the "agio theories" which he dismisses so slightingly. In new countries, where land is abundant and opportunities are many, there is likely to be an increase of population, because men like to go to such countries. Such countries also furnish abundant opportunities for the use of capital, and men bid high for it in order to attract it. In old and worn-out countries, where opportunities for both men and capital are few, there are likely to be a stationary or decreasing population and low rates of interest.
In conclusion let me say that, though these criticisms seem severe, they are aimed at some of the conclusions which Professor Norton bases upon his analysis rather than upon the analysis itself, which is, let me repeat, an admirable piece of work and destined to increase the already high esteem in which Professor Norton is held by students of economics everywhere.