Highly fertile soil located close to a city market and devoted to truck farming yields high returns, and its value per acre is correspondingly high. Nearness to the railroad affects materially the values of farm lands in the wheat, corn, cotton and live-stock regions. Accessibility, convenience, and cheapness of transportation on the side of location are just as important in valuing farm lands as are quality and richness of the soil on the side of fertility.

The Margin of Substitution.-The same piece of land may be used for various purposes, and consequently there are forces regulating the amount of land which shall be devoted to each kind of use. The prin

ciple of substitution explains this selective process. We may define this principle as the tendency to substitute one use for another whenever such a change is necessary to put the land to that use where its products and services are worth the most.

A few miles out of Chicago there is a region of truck farms. Some are profitable, some not so profitable. The less profitable farms are on the margin of substitution. If their yield per acre were any less, it would pay to change from truck to wheat farming. Let us assume that wheat will yield a net return of eight dollars per acre. As soon as truck land yields any less than that amount, it will be shifted to wheat growing. The marginal acre of truck land is the acre which earns just barely enough to keep the land from being shifted to wheat growing. But let us assume further that an acre of land will yield a net return of four dollars for grazing purposes. The same acre yields slightly over four dollars for wheat growing. This is the marginal acre of wheat land, or the acre which earns just barely enough to keep the land from being shifted to grazing. Finally, let us assume that the poorer grades of grazing lands earn just enough per acre to cover the bare expenses of production. There is no net income. Consequently there is no rent. This is the marginal acre of grazing land, or the acre which earns just barely enough to keep the land from lying idle.

But many better grade truck farms earn high returns, and are far above the margin of substitution. If an acre of truck land earns twenty dollars, and the same acre used for wheat growing would yield only eight dollars, the truck land enjoys a marked differential of surplus returns. If in a different location an acre of wheat land yields eight dollars, and the same acre used for grazing would yield only four dollars, the wheat land enjoys a marked differential of surplus returns. If in another location an acre of grazing land yields four dollars, its yield is that much above the no-rent marginal acre of grazing land, and consequently the grazing land shows a differential of surplus returns. The marginal acre of land for each use is above the margin for some less gainful use to which it might be applied. Above the marginal acre of land for each use are acres which yield surplus gains. What is marginal at a given use is marginal simply with respect to the next lower use. What is surplus returns at a lower use is merely marginal for the next grade higher use. Within each particular kind of use, there are many

unequal rates of returns, some at the margin for that use, others at varying scales above the margin. Hence, to study the process of choosing the best uses of land, we proceed from the fact of unequal grades of fertility and location to the fact of unequal returns, and apply the principle of substitution by showing the marginal and differential gains which are purely relative to next lower and higher grades of uses.

The same explanation applies to urban and other kinds of land. Some retail shops earn more per front foot of space than others. As the shops grow poorer they still yield more per front foot than the land. is worth for residence purposes. Finally, there come the marginal shops, which yield barely enough to keep the land from being shifted to residential uses. When shops earn less per front foot than the land is worth for homes, the substitution of uses will occur. But the value of residential sites will in turn show wide variations. At the outskirts of the city will be found land which earns just barely enough as building space to keep it from being turned to truck farming. Each kind of use has a marginal fringe, with respect to the next lower use to which the land may be put. Each kind of use has many plots of land which yield more than the marginal fringe, but their surplus gains are still not high enough to take other land away from yet higher uses to which it may be applied. Each use of land is sandwiched between higher and lower uses, with many degrees of differential surplus gains on individual plots within these limits.

It is at the margin of substitution that the changes in uses of land are taking place which profoundly affect economic life. When factories or shops drive out homes, when truck lands drive out wheat farms, when pasturage drives out tillage of the soil, when congested building sites drive out gardens, changes take place of the utmost consequence to economic and social life.

Since these changes are of such fundamental importance, it is imperative to have in mind the principle of substitution which regulates the amount of land that will be put to each particular use. This principle may be summarized in the following manner: From the standpoint of any single use of land, the size of returns may be classified as either marginal, super-marginal, or sub-marginal. For purposes of illustration, we may take the use of wheat land. Returns are marginal when they are just barely sufficient to keep the land from being changed to grazing or to some other use. Returns are super-marginal when they consist not merely of the marginal earnings sufficient to keep wheat land from being changed to grazing, but in addition consist of a surplus or differential return due to superior fertility or superior location for wheat growing purposes. Returns are sub-marginal on wheat land when the land could be used more profitably for other products. Consequently, when returns on wheat land are marginal, they are just enough to avert the substitution of grazing for wheat growing. When returns on wheat land are super-marginal, they are considerably more than enough to avert the substitution. When returns on wheat land are sub-marginal, they are

not enough to avert the substitution. It should further be observed that the super-marginal wheat land tends to reach a point where it coincides with marginal truck lands. When the marginal acre of truck lands yields just barely enough to keep the land from being changed to wheat farming, the given piece of truck land is at its margin of substitution. Thus, the marginal acre of the more profitable use of land tends to reach the super-marginal acre of the next less profitable use of land. Where the respective layers of uses meet is the margin of substitution. By combining our analysis of the differential aspect of land returns with the principle of substitution, we arrive at an explanation of the forces which constantly tend to place land in that use where it will yield the largest net returns.

The Principle of Diminishing Returns.-The principle of diminishing returns is not limited to land, although it was first worked out as an analysis of land returns. The principle applies to all forms of capitalistic production, and in applying it to land we are simply dealing with the special form of the principle which throws most light upon land production. The general principle may be stated as follows: As the use of any factor in production is increased, there comes a point where output does not increase in proportion to the increased use of that factor. As applied to land in particular, this principle may be stated as follows: As the use of labor or capital is increased on a given piece of land, there comes a point where the output from the land does not increase in proportion to the increased use of labor or capital. The point of diminishing returns is the point beyond which returns grow less and less in proportion to additions of labor and capital.

The principle may be illustrated by a study of the effect of increasing applications of fertilizer upon farm land. The following data are the result of experiments in cotton growing.3

The returns increased in proportion to added units of fertilizer capital until more than $7.00 worth of capital per acre was added. Beyond that point, production still increased, but not in proportion to the added outlay of capital. Before the point of diminishing returns was reached, an added $2.00 of capital increased the yield 51 pounds. After the point of diminishing returns was reached, an added $2.00 of capital increased the yield only 4 pounds.

3 U. S. Department of Agriculture, Bulletin 651, p. 14.

The principle of diminishing returns may be illustrated with respect to labor by the following hypothetical example:

The point of diminishing returns is reached when more than forty hours of labor are applied per acre. Thereafter, the added yield bears a smaller and smaller proportion to the added outlay of capital. The product will not be increased in proportion as the labor is increased.

Several qualifications of the principle of diminishing returns as here illustrated may be noted. First, it is assumed that the efficiency of capital and labor remains constant. If improved machinery or more efficient labor be added, the old point of diminishing returns may be transformed into increasing returns. The new point of diminishing returns would be pushed farther back. Whenever the technology of production changes, due allowance must be made in applying the principle of diminishing return. Second, the law states a relationship merely and only between added units of labor or capital and added units of yield. The problem is: to obtain an added bushel, how many hours of labor or units of capital must be added. Will the added hours required to increase the yield one bushel be more or less than the hours required to produce the last bushel? If the last bushel required 5 units of capital to produce, will the next bushel require more than 5 units? If so, diminishing returns are in effect.

Third, diminishing returns are usually accompanied by increased total returns. There is not an absolute decrease of returns, but merely a diminishing rate of increase. If to double the bushels per acre requires four times the labor and capital, returns are still increasing, but not as fast as the increased expenditure of labor and capital. Diminishing returns are a diminishing rate of increase. To restrict the meaning of diminishing returns in this manner many writers prefer to use the phrase, "diminishing increment," or the phrase, "diminishing productivity."

The law of diminishing returns has traditionally been stated in terms of physical units. Product has been stated in terms of bushels or pounds, labor in hours or days, capital in physical quantities. But this traditional terminology places certain limitations upon the use of the principle when attempt is made to apply it to the modern money economy. Agriculture has come fully under the pecuniary régime, and has accepted

the methods of business. Farming has been thoroughly incorporated into the price system. Consequently, modern conditions call for a statement of the principle of diminishing returns in terms of money and price. Product is measured in terms of its money value. Capital is measured in terms of its money value. Labor is measured in terms of its money value. The unit of measurement of all factors is the dollar, or other money unit.

The following hypothetical examples illustrate possible forms of stating the pecuniary principle of diminishing returns. Let us assume that on a given acre of land, $25.00 of labor yields $50.00 worth of product. The farmer seeks to discover the amount of additional labor required to produce $10.00 additional crop. The calculations may be assumed somewhat as follows:

First $10.00 increase of product requires $4.00 additional labor

Second
Third

66

In each step of this calculation, more and more labor is required to produce an additional $10.00 in value of crop. Diminishing returns are in effect.

The calculation might also be made in the following terms:

First $5.00 additional labor will increase the product $10.00

The same amount of additional installments of labor yield less and less value of product. The law of diminishing returns is in effect.*

Even the foregoing pecuniary statement of the principle of diminishing returns is inadequate for the needs of the money economy. To make practical application of the principle to the business of agriculture, it is advantageous to shift the statement from returns to unit costs. By taking unit costs, we inquire the cost of each factor, land, labor, and capital, per unit of output, and we inquire the total cost of all these factors per unit of output. Unit costs have been found the most expedient method of calculation in this field by modern accountancy. Unit costs are a device of accounting, aimed to serve the purpose of a statistical tool. Expressed in terms of unit costs, then, a condition of diminishing returns is one in which the average cost per unit of product increases as labor or capital is added to the use of the land. Let us assume that the unit of output is $100 worth of product. The conditions of cost

4 In economic literature, a great variety of forms of statement of the law of diminishing returns appears. To exhaust the list of different forms in this treatment would be tedious and confusing. The attempt here made is chiefly to state the more common and simple form of the law. But no pretense is made that these explanations cover all possible forms of statement.