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7. Factors of Production: Convertibility and Valuation
Factors of production are valued in accordance with their anticipated contribution in the eventual production of consumers’ goods. Factors, however, differ in the degree of their specifity, i.e., the variety of consumers’ goods in the production of which they can be of service. Certain goods are completely specific—are useful in producing only one consumers’ good. Thus, when, in past ages, extracts from the mandrake weed were considered useful in healing ills, the mandrake weed was a completely specific factor of production—it was useful purely for this purpose. When the ideas of people changed, and the mandrake was considered worthless, the weed lost its value completely. Other producers’ goods may be relatively nonspecific and capable of being used in a wide variety of employments. They could never be perfectly nonspecific—equally useful in all production of consumers’ goods—for in that case they would be general conditions of welfare available in unlimited abundance for all purposes. There would be no need to economize them. Scarce factors, however, including the relatively nonspecific ones, must be employed in their most urgent uses. Just as a supply of consumers’ goods will go first toward satisfying the most urgent wants, then to the next most urgent wants, etc., so a supply of factors will be allocated by actors first to the most urgent uses in producing consumers’ goods, then to the next most urgent uses, etc. The loss of a unit of a supply of a factor will entail the loss of the least urgent of the presently satisfied uses.
The less specific a factor is, the more convertible it is from one use to another. The mandrake weed lost its value because it could not be converted to other uses. Factors such as iron or wood, however, are convertible into a wide variety of uses. If one type of consumers’ good falls into disuse, iron output can be shifted from that to another line of production. On the other hand, once the iron ore has been transformed into a machine, it becomes less easily convertible and often completely specific to the product. When factors lose a large part of their value as a result of a decline in the value of the consumers’ good, they will, if possible, be converted to another use of greater value. If, despite the decline in the value of the product, there is no better use to which the factor can be converted, it will stay in that line of product or cease being used altogether if the consumers’ good no longer has value.
For example, suppose that cigars suddenly lose their value as consumers’ goods; they are no longer desired. Those cigar machines which are not usable in any other capacity will become, valueless. Tobacco leaves, however, will lose some of their value, but may be convertible to uses such as cigarette production with little loss of value. (A loss of all desire for tobacco, however, will result in a far wider loss in the value of the factors, although part of the land may be salvaged by shifting from tobacco to the production of cotton.)
Suppose, on the other hand, that some time after cigars lose their value this commodity returns to public favor and regains its former value. The cigar machines, which had been rendered valueless, now recoup their great loss in value. On the other hand, the tobacco leaves, land, etc., which had shifted from cigars to other uses will reshift into the production of cigars. These factors will gain in value, but their gain, as was their previous loss, will be less than the gain of the completely specific factor. These are examples of a general law that a change in the value of the product causes a greater change in the value of the specific factors than in that of the relatively nonspecific factors.
To further illustrate the relation between convertibility and valuation, let us assume that complementary factors 10X, 5Y, and 8Z produce a supply of 20P. First, suppose that each of these factors is completely specific and that none of the supply of the factors can be replaced by other units. Then, if the supply of one of the factors is lost (say 10X), the entire product is lost, and the other factors become valueless. In that case, the supply of that factor which must be given up or lost equals in value the value of the entire product—20P, while the other factors have a zero value. An example of production with purely specific factors is a pair of shoes; the prospect of a loss of one shoe is valued at the value of the entire pair, while the other shoe becomes valueless in case of a loss. Thus, jointly, factors 10X, 5Y, and 8Z produce a product that is valued, say, as rank 11 on the actor's value scale. Lose the supply of one of the factors, and the other complementary factors become completely valueless.
Now, let us assume, secondly, that each of the factors is nonspecific: that 10X can be used in another line of production that will yield a product, say, ranked 21st on the value scale; that 5Y in another use will yield a product ranked 15th on the actor's value scale; and that 8Z can be used to yield a product ranked 30th. In that case, the loss of 10X would mean that instead of satisfying a want of rank 11, the units of Y and Z would be shifted to their next most valuable use, and wants ranked 15th and 30th would be satisfied instead. We know that the actor preferred the satisfaction of a want ranked 11th to the satisfaction of wants ranked 15th and 30th; otherwise the factors would not have been engaged in producing P in the first place. But now the loss of value is far from total, since the other factors can still yield a return in other uses.
Convertible factors will be allocated among different lines of production according to the same principles as consumers’ goods are allocated among the ends they can serve. Each unit of supply will be allocated to satisfy the most urgent of the not yet satisfied wants, i.e., where the value of its marginal product is the highest. A loss of a unit of the factor will deprive the actor of only the least important of the presently satisfied uses, i.e., that use in which the value of the marginal product is the lowest. This choice is analogous to that involved in previous examples comparing the marginal utility of one good with the marginal utility of another. This lowest-ranked marginal product may be considered the value of the marginal product of any unit of the factor, with all uses taken into account. Thus, in the above case, suppose that X is a convertible factor in a myriad of different uses. If one unit of X has a marginal product of say, 3P, a marginal product in another use of 2Q, 5R, etc., the actor ranks the values of these marginal products of X on his value scale. Suppose that he ranks them in this order: 4S, 3P, 2Q, 5R. In that case, suppose he is faced with the loss of one unit of X. He will give up the use of a unit of X in production of R, where the marginal product is ranked lowest. Even if the loss takes place in the production of P, he will not give up 3P, but shift a unit of X from the less valuable use R and give up 5R. Thus, just as the actor gave up the use of a horse in pleasure riding and not in wagon-pulling by shifting from the former to the latter use, so the actor who (for example) loses a cord of wood intended for building a house will give up a cord intended for a service less valuable to him—say, building a sled. Thus, the value of the marginal product of a unit of a factor will be equal to its value in its marginal use, i.e., that use served by the stock of the factor whose marginal product is ranked lowest on his value scale.
We now can see further why, in cases where products are made with specific and convertible factors, the general law holds that the value of convertible factors changes less than that of specific factors in response to a change in the value of P or in the conditions of its production. The value of a unit of a convertible factor is set, not by the conditions of its employment in one type of product, but by the value of its marginal product when all its uses are taken into consideration. Since a specific factor is usable in only one line of production, its unit value is set as equal to the value of the marginal product in that line of production alone. Hence, in the process of valuation, the specific factors are far more responsive to conditions in any given process of production than are the nonspecific factors.26
As with the problem of optimum proportions, the process of value imputation from consumers’ good to factors raises a great many problems which will be discussed in later chapters. Since one product cannot be measured against other products, and units of different factors cannot be compared with one another, how can value be imputed when, as in a modern economy, the structure of production is very complex, with myriads of products and with convertible and inconvertible factors? It will be seen that value imputation is easy for isolated Crusoe-type actors, but that special conditions are needed to enable the value-imputing process, as well as the factor-allocating process, to take place in a complex economy. In particular, the various units of products and factors (not the values, of course) must be made commensurable and comparable.
- 26. For further reading on this subject, see Böhm-Bawerk, Positive Theory of Capital, pp. 170–88; and Hayek, Counter-Revolution of Science, pp. 32–33.