Front Page Titles (by Subject) CHAPTER 12: THE PRINCIPLE OF PROPORTIONALITY - Economics, vol. 1: Economic Principles
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CHAPTER 12: THE PRINCIPLE OF PROPORTIONALITY - Frank A. Fetter, Economics, vol. 1: Economic Principles 
Economics, vol. 1: Economic Principles, (New York: The Century Co., 1915).
Part of: Economics, 2 vols.
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THE PRINCIPLE OF PROPORTIONALITY
§ 1. The principle of proportionality; its general nature. § 2. Cost and sacrifice defined. § 3. Sacrifice of effort a matter of proportion. § 4. Sacrifice involved in common use by several users. § 5. Gross and net uses. § 6. The doctrine of separable uses. § 7. More intensive utilization. § 8. More extensive utilization. § 9. Application of complementary agents at the two margins. § 10. The principle of proportionality in agriculture. § 11. Intensive use of ground space. § 12. Intensive use of tools and machinery. § 13. Intensive development of water power. § 14. Bearings of the principle.
§ 1. The principle of proportionality; its general nature. In what has been said in regard to scarcity as an element in value (Chapter 2) it was implied that value involves, in the simplest case of direct or immediately enjoyable goods, a certain proportionality between goods and the desires of men. The more abundant are goods, relative to the desire for them, the less is their value. Similarly, in connection with the principle of evaluation (Chapter 4), we encountered, in the relations between the stimuli and the reactions of the nervous system, a certain quantitative relation, or principle of proportionality. In the whole process of trade, also (Chapter 5, Trade by Barter), which is the adjusting of a ratio between two or more goods in a group of traders seeking to buy and sell, an element of proportionality is plainly involved. And still later (in the last three chapters, 9-11) in discussing the improvement of productive processes we have touched upon the important problem of proportionality in the use and development of indirect agents. We saw that the development of new inventions, new processes, etc., was largely a matter of bringing things together in the most effective way—that is, in the best proportions for the accomplishment of certain physical, mechanical, chemical, or other desired technical results.
§ 2. Cost and sacrifice defined. In our evaluations there are usually certain negative items variously referred to as cost or as sacrifice. In its broadest sense cost may be defined as that which must be given up to get another thing. This is its original, and still general, meaning. This would include, on the one hand, sacrifices of a purely psychic nature—disappointments, regrets, etc., caused by doing or by giving up a thing; and, on the other hand, the prices of things—whether expressed in money or in other goods. Usually, however, in business the word cost is given a more specialized meaning, and we shall take this in order to distinguish it from price in general on the one hand, and from sacrifice on the other. In this narrower connotation cost means the outlay (considered as a business expense and expressed in money terms) which a person must make in order to obtain a certain product from goods. Sacrifice may be defined as that less definitely measured, psychic, alternative good (whether of enjoyment or of freedom from effort) which must be given up to get another good. Finally, price is the good surrendered in a trade with another person.
Sacrifice is involved in every choice and in every price in barter or sale; but cost, in this business man’s sense, only when the outlay for a good up to date is compared with its value or with its selling price.
§ 3. Sacrifice of effort a matter of proportion. In the case of complementary agents (see Chapter 4, section 5) the valuation of each in any particular use is constantly affected by the valuation of the other. This always involves a problem of proportionality. The simplest case is presented by the use of one’s time and labor in getting enjoyment from a direct good. The sacrifice of time and labor are outlays which have to be balanced against the gross or total advantage afforded by the good. It is a sort of offset or deduction, and the real or net service or psychic income is the resultant of the action of the two complementary goods, the man’s effort and the material object. A piano is capable of being played upon steadily for twenty-four hours a day, but the player becomes weary after two or three hours, and values the uses of the piano for the rest of the day at zero. These uses must go for nothing if the piano is not played, but they are to be realized at too great a sacrifice. A case of this kind is presented whenever any durable agent in the owner’s hands is capable of affording additional uses which as a matter of fact are not availed of. Such uses lie beyond the boundary of economic utilization, for the owner has not the time to use them—or the energy, or the present desire.
Riches and poverty affect the estimate of sacrifice involved in the use of goods. The more highly the person is able to value his own time, because of his riches, income, etc., the more highly he values the earlier uses of duplicates to save his time, and the less highly he values the later uses of goods which tax his time. Each article in the scanty belongings of the poor is used a great deal; each article in the abundant belongings of the rich is used very little, and the goods of the middle class occupy positions ranging between these extremes.
§ 4. Sacrifice involved in common use by several users. It often may happen that the further uses contained in goods may be taken by another person, possibly by several, each of whom may bring to the use his freshest powers. This may enhance the usefulness of the good, but again sacrifice may result from the inconvenience of common use, and sooner or later the outlay-value exceeds the gross income-value of the uses thus secured. A book stands many hours untouched on the shelves of the library; it has potential uses for some one during every minute of the twenty-four hours but they can be secured only with inconvenience. When, as often happens, two or more persons wish to use the book at the same hour, time and energy are wasted. The greatest net uses, therefore, are seen to be to the first user and in the first hour, for these uses cost the least time and trouble. If the members of a family will take turns, one chair will serve for all of them; but if all are to be able to sit down together, a chair must be provided for each. Often it will happen that only one chair is in use, the other nine chairs being valued only for their potential uses. I knew two young men who owned a dress-coat in partnership, and as they had different evenings free from business all went well until both were invited to a reception which both were very eager to attend. In tenement houses there are sometimes let to lodgers beds or bunks that are never allowed to get cold, men working in the day occupying them by night, and men working by night sleeping in them by day.
§ 5. Gross and net uses. In cases of this kind each use of the chair, or the book, etc., is technically the same as every other use, but economically these uses must be looked upon as a series of unlike valuation-magnitudes. The value of each use is a net amount resulting from subtracting the outlay from the income-value. Even if the income-values remained undiminished by bringing in new uses, the outlay-values would be increasing, and the net use-value correspondingly lessening. A point is reached where the net value of the use falls to zero. Thus in Figure 20 if on the line BB7 be represented the height of successive gross uses and on the line CB7 the height of the successive outlays, net uses are B1C1, B2C2, etc., until at B7 there is no further net use.
§ 6. The doctrine of separable uses. We may think of the use of an object not as one undivided whole, but as a group of uses, separable each from the other. Likewise any one of these uses is separable from the use-bearer considered as a concrete object. Every economic good, the use of which can be spread throughout a period of time, may be looked upon as consisting of groups of uses. The simplest case of this results from mere physical divisibility. A basketful of peaches is eaten piece by piece; each peach may be counted as one use. In this case the use is consumptive: it is not separable from the using up of the use-bearer itself.
The truly separable use, however, is found in the case of a durable agent which continues through a period of time to render a series of durative uses. A very perfect example is a diamond necklace, the sparkle and charm of which is a use which is absolutely without detriment to the use-bearer (i.e., the necklace, tho perhaps not to the wearer). Many agents have this enduring quality more or less fully (see Chapter 11 on Consumption and Duration), and in all such cases the durative use may be treated practically and theoretically in economics as something separable from the use-bearer, in matters of valuation, of trade, and of price. The peaches may be gathered without harming the fitness of the trees to produce another crop. Shelter is furnished, once the house is built, without destroying the house more than disuse would, if it stood tenantless. The horse is the better if driven moderately each day, and the carriage lasts for years. In every such case, the use is something different from the “using up” of a limited number of goods, for there is left in the use-bearer the power to go on yielding indefinitely some more of the same product or use if it is kept in repair.
Some of the uses contained in a use-bearer may be actual or realized; others may be and may remain merely potential. Or they may all be realized in the course of a period of time, at the end of which the good is entirely consumed or worn out. The uses of a suit of clothes, for example, may be realized only day by day for a considerable period. Some men go on wearing a suit until it is almost completely worn out before discarding it; others discard clothing while there are still many possibilities of use in it. It may perhaps be safely asserted that the great majority of things have potentialities of which the owner for one reason or another does not avail himself. As already indicated, it does not pay to squeeze all possible uses out of a good. Uses 8, 9, etc. (beyond 7 in Figure 20), are quite possible of realization, but the attendant inconvenience or sacrifice is so great that they are valueless, and they will be ignored. The owner will not forego his sleep because he dislikes to have the piano go unused through the hours of the night.
In the case of a durable good circumstances may warrant a very slight utilization at one time and a very much more complete utilization at another. The factory which has been running on half-time may later be operated day and night to meet a great increase in demand.
§ 7. More intensive utilization. The uses of a good at a given time are actual or realized up to a point, limit, or margin beyond which further uses would not be worth the outlay of effort or of other goods. This point in the utilization is called the intensive margin. Using the thing more and more, while uniting other things with it, is using it more intensively. Getting more use out of the book by effort, out of the farm by applying more fertilizer, out of the factory by employing two or three shifts and working longer hours, out of the house by putting more people in it, is intensive utilization. The superior uses come easily, naturally; the inferior ones are to be secured only with increasing difficulty. When some change comes—such as an increase in demand for the product of an agent—which causes that agent to be more intensively utilized, this change is said to have lowered the (intensive) margin of utilization. The inferior grades of uses are being resorted to.
§ 8. More extensive utilization. This same change of demand may, however, bring about a simultaneous change of a different sort. If there are various agents of different degrees of excellence, and only the better grades are being used to meet this particular demand, then an increase in the demand is likly to result not only in a more intensive utilization of the superior agents, but also in the calling of some of the inferior agents into use. The best agents that are available at the time are used first, but as they are more intensively used, there is increasing inconvenience. This may be relieved by using either physical duplicates of the better agents or by using inferior agents. If there is more than one of a certain kind of agents, the duplicates are distributed so as to be where most valued by the owner. A man having two umbrellas keeps one at his office and the other at home; a student having two books of the same kind keeps one at his room and the other at the university; a farmer having two hoes keeps one at the barn and the other in a distant field, and by this method the additional units have higher uses than if they were used in the same way or at the same place as the earlier units.
It may finally be necessary to have recourse to agents which as a whole are inferior to the other agents, but whose first uses are better than the remaining intensive uses of the better grades of agents. This employment of inferior agents is also called lowering the margin of utilization. But it is a different margin with which we have to do—the margin between superior and inferior agents. It is the extensive margin. At the same time that an increase in demand causes the use of double shifts in the efficient factory, another factory, of inferior efficiency, which has been completely idle, may be brought into use, tho possibly not to its full capacity. There has then occurred a change or lowering of both margins. At the same time that the cultivation becomes more intensive on the better fields, it becomes more extensive if there are other areas which have just come to have valuable uses. The intensive margin of use is in the particular thing; the extensive margin is the line between the superior and the inferior good. The inferior agent which is not utilized is spoken of as “below” or “beyond” or “outside of” the (extensive) margin of utilization. The interrelations between the two margins are shown in the diagram.
Intensiveness and extensiveness of utilization are relative terms. The utilization of one machine or of one piece of land is more or less intensive as compared with another when more of other agents (e.g., labor) is used with or upon it; or the utilization of an agent becomes more or less intensive than it was before if more or less complementary agents are used than before. One might say that the use of an agent is intensive in one place as compared with another (e.g., land in New Jersey compared with that in Kansas), yet extensive as compared with still another place (with that in western Europe). In the same way extensive utilization is relative.
§ 9. Application of complementary agents at the two margins. It is not our purpose at this point1 to emphasize the fact (important as it is) that changes of demand occur, and that these changes cause the best economic proportion to change. Rather we use illustrations of change to make clear that in any given set of conditions there is a best proportion in which to combine agents. There is a right degree of economic utilization in that particular situation. Where this best proportion is attained, is a point of economic equilibrium, in the sense that there is in the situation itself (and until some other conditions change, as invention, increased demand, etc.) no motive to change the proportion. In such a case the effort is made to repeat the process, to maintain just that proportion which has been found to be on the whole best. If either of two complementary agents is used in greater or less amount than this best proportion, a loss results, something less than the possible maximum of value is obtained.
Now the case of the two margins always occurs when one of the complementary agents is present in more than one quality or grade, as respects stuff, form, or place. Then the supply of the complementary agent is distributed over the different grades of uses, now to the lower uses in the better agent, now to the upper uses of the poorer grades. In this way the effectiveness of each unit of the complementary agent is kept equal on the intensive and on the extensive margins of utilization of goods. As the value of the added product in the more intensive use of a particular agent decreases, a point finally is reached where it is better to transfer the outlay to another agent, to shift from the intensive to the extensive margin, by going over to the use of another field or of another machine not so good. As the effectiveness of the labor, of the machinery, of the lands, of complementary agents of every kind, that men have to apply to two grades of another agent is being compared constantly, the uses of the complementary agents are distributed along the two margins. The margin of utilization is marked by a line of uses valued at zero. When used to that point the total value obtainable from the agent is at its maximum. If utilization is less intensive the value of the last possible use is lost, and if it is more intensive there is a net loss on the outlay.
§ 10. The principle of proportionality in agriculture. The principle of proportionality applies to the use of agents in all kinds of business and determines the degree of their economic utilization. This general principle was first formulated in reference to land in agriculture, and for a long time was supposed to be peculiar to the use of that class of agents.2
The use of land in agriculture is conditioned on the presence of a top-soil of suitable mineral elements and texture, and on a proper surface, exposed to light, air, and sun, with the necessary climatic influences of temperature, moisture, etc. It was long ago seen that on such a piece of land a crop larger than usual could be obtained only with greater effort or expenditure.3
It is obvious to every farmer and gardener that he cannot indefinitely increase his crop, that two men cannot always produce twice as much as one man on a fixed area of land, and that in general the product does not vary either up or down in proportion to the labor and materials applied. Instead of 20 bushels to the acre, 25 or 30 bushels might be raised, but it would require more plowing, labor, seed, fertilizer, and other expenses, in value greater than the addition to the value of the crop. On the other hand a moderate degree of thoroness of cultivation is necessary to get any results worth while; and, besides, if a small crop is raised, the value of most of the uses of the land for that season would be entirely thrown away. Only 5 or 10 bushels per acre might be raised with less expense per bushel merely for labor and material, but there would be left no remainder to apply to the value of the land-uses. Between the wastefully small crop of 1 bushel and the wastefully large crop of 100 bushels an acre, there lies a point, more or less correctly ascertained by experience, where the largest net result is obtained, a point where by aiming to raise either less or more the man in charge gets a smaller net return (surplus of total price over expenses).
§ 11. Intensive use of ground space. The principle of proportionality applies to ground-space in all industries. Some space is needed for any activity, even for mere existence, and a limited area cannot afford an unlimited number of uses. If a large library is accumulated in one small room, a point is reached where there is scarcely room to stand, and much energy is wasted in trying to find the books. In a university the psychical product, education, may be limited by the need of space. School-rooms, laboratories, and college class-rooms, if used all day and all night, would accommodate several times as many students as they do; but the “wee sma’ hours” would not be popular; and, therefore, as students increase, buildings must be added. One cannot conveniently increase the business of a lumber-yard without a larger yard-space, or of a factory without a larger floor-space. But the added space may be gotten by spreading horizontally or piling up vertically. Even in agriculture vertical addition is possible by the use of greenhouses in which mushrooms are grown below the tables and tomatoes above, and where artificial heat gives a more intensive utilization throughout the winter. Therefore, with more space and also more time a single foot of ground can be made to yield half a dozen crops in the year. In the production of food, however, on account of the need of sun, light, and air, the limits of space are more quickly felt, and are less elastic than in most other industries; the difference, however, is one of degree, and not of kind. In mercantile, commercial, and manufacturing businesses 10 acres or 60 acres of usable floor-space may be had by putting a building of that number of stories upon an acre of land, and installing elevators and moving stairways, parcel carriers, and telephones. Not only is the initial cost high, but the cost of maintenance likewise, and it is economically warranted only when land-space is very high priced. Business adapts itself to this law, but does not escape its operation. Neither the law of gravitation nor the principle (or law) of proportionality is violated or broken when materials are lifted to build the upper stories. Both “laws” are at work, even when the building is rising from the ground.
§ 12. Intensive use of tools and implements. All the implements used in agriculture are subject to the limitation of the principle of proportionality. Why will not one hoe, one rake, one plow, one scythe, one horse, one wagon, do for all the farmers of a neighborhood? It might, in many cases, but it would be with much labor and time in carrying the things back and forth and in waiting for others to get through using them; it would require work to be continued all night, on Sundays and on holidays, and even then the plowing, hoeing, harvesting, and other farm operations could not be performed when most needed. Even now there is much loss in just these ways because, tho every farmer has at least one, and some have many, of these tools, there are brief periods when there are not tools enough. Why, then, not have more tools? Because they cost. Between the extremes of no tools and a multitude a balance is struck at a point where the last additional tool adds to the price of the crop at least as much as the tool costs. The mode of estimating these costs we have later to study more closely.
In manufacture, whether by hand tools in small shops or by machinery, in transportation, whether by boat or railroad, there is, in the mind of the manager, the same ideal point of equilibrium between the price of the uses to be added and the price of the other agents (labor, tools, materials) that must be expended to secure the additional product. To do nothing with a tool, implement, machine, for the purpose of saving the things that would have to be used with it, is to lose the use of it.
§ 13. Intensive development of water-power. In the development of water-power it is possible to combine the original source of water-supply with various kinds of other agents to generate more or less power. A waterfall may be made to yield, perhaps, 25 horse-power daily with a crude undershot wheel, 75 more horse-power if a dam is constructed and an overshot wheel is used, 150 more horse-power if an iron turbine replaces the wooden wheel, and 500 more horse-power if a large reservoir is built a half mile distant and the water conducted under pressure to a reaction wheel at the foot of the fall. The last is technically the most efficient, but economically its large cost will not be warranted until there is a large demand for power at that place.
§ 14. Bearings of the principle. It is plain that this principle of proportionality must be taken account of in all practical affairs by those who are directing the processes of productive industry, whether on a large or on a small scale. Their problem is both technical and economic. They must make effective technical use of goods, and they must combine things in ways that will pay. To the student of economics a clear understanding of this most fundamental principle of proportionality is essential to the solution of the complex problems of valuation. Things are not valued in isolation from each other. The great mass of complementary agents act and react upon each other. The valuation put upon one agent is due in part to the presence in certain proportions of other agents. Many evidences of this truth will appear to us as our study proceeds.
[* ]The use a is the highest in the sense that it is the most easily obtained. Like results are to be had by the use of b to g successively only at greater costs; or less valuable results at the same costs.
[* ]The rectangles, M, N, O, P, Q, represent agents of various grades, each consisting of strata of uses. The best uses are a, b, and c, in M; but after M has been utilized intensively down to d, N will begin to be utilized at its highest point. When utilization goes down to f, O comes into use, and so on. Therefore it will be seen that until the intensive margin takes in d, M is on the extreme margin of utilization, and N is just outside it; when the intensive margin falls to g and h, P is inside the extensive margin, and Q is just outside.
[1 ]We are studying here the static problem. In Part VI, chs. 32-39 the dynamic problem is much more fully treated.
[2 ]Of this supposed peculiarity various explanations were given, such as the chemical qualities of the soil, and as the assumed durativeness of agricultural land, etc.
[3 ]Note the significance of the phrase “larger than usual.” Surely the crops may be larger some years than others, and especially large in those years when there is remarkably favorable union of rainfall, temperature, freedom from pests, etc. “Larger than usual” means larger than on the same, or on like, land under circumstances alike except in respect to intensiveness of cultivation.