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Capital and Interest
The Collected Works of F. A. Hayek: Volume XI
By Lawrence H. White The University of Chicago Press
Copyright © 2015 The Estate of F. A. Hayek
All rights reserved.
ISBN: 978-0-226-27490-4
CHAPTER 1
Some Observations on the Imputation Problem
1. The Concept of Economic Imputation and Its Origins
Whenever an economic good yields utility directly and in isolation, the theory of marginal utility enables us to establish a well-defined correspondence between its utility and its subjective value. Under these conditions, as is well-known, the value of a given amount of the good is determined by the smallest amount of utility that can be obtained from its use without foregoing a greater amount of utility that can be obtained elsewhere. However, this principle does not apply directly to goods that do not satisfy certain needs on their own, but can do so only in conjunction with other economic goods. According to Menger, these are called complementary goods. Under these circumstances, the utility obtained in each case is brought about and depends on several goods. Thus, several values must be derived from this utility, if value is still to be explained by utility. This raises a highly important issue, since the underlying relationship between value and utility is not limited to those cases where needs require several consumer goods for their satisfaction but includes those in which needs are met by a product and thus indirectly require a multiplicity of (producer) goods for their satisfaction. While the former case is usually disregarded as trivial, considerable attention has been paid in the literature to the problem of deriving the value of the individual producer goods from the utility jointly created by them. This problem, for which Wieser introduced the term Zurechnung (English: imputation; French: imputation; Italian: imputazione) in analogy to its use in jurisprudence, has been dealt with extensively by the so-called Austrian School in its elaboration of the theory of subjective value.
2. The Position of the Doctrine of Imputation in Modern Economic Theory
According to the modern theory of subjective value, the determination of prices is basically explained by individual valuation. At the same time, since Ricardo, it has been widely agreed that the objective of economic theory is to discover the determinants of income, primarily by investigating what determines the prices of the factors of production. Consequently, all economic theory rests on the explanation of the value of producer goods and hence on the theory of imputation. A satisfactory solution of the imputation problem is thus a precondition for a distribution theory based on the theory of subjective value. As subjective value, to be explained by this theory, is itself the cause of exchange and the determinant of price, the solution must proceed without recourse to exchange. It must therefore be based on that type of an economy guided by a single will that Wieser has called a simple economy. Unless otherwise specified, we will refer to the conditions of such a simple economy in our subsequent observations.
For a theory of distribution based on subjective value theory, the importance individuals attribute, under given conditions, to each of the factors of production must derive from the valuation of the utility of the product. As remains to be shown, this issue is intimately related to the question to what extent the production which requires the use of the good in question is to be economically expanded. It thus implies a question about man's use of goods as circumstances demand. In seeking to determine the value of a given quantity of consumer goods, although the answer found overcame the spurious contradiction between value and utility and simultaneously laid the groundwork for all value theory, the problem thus solved constitutes only a part of the problems of theoretical economics. The foundations for answering the question of the structure of the economy as a whole and hence for the problem of distribution are only addressed by the theory of imputation. If the imputation problem has not received due attention and has been ignored altogether in some systems of subjective economic theory, which moved directly from the explanation of the value of consumer goods to the explanation of prices and the forms of income, this is due to the mistaken belief that, by explaining the value of consumer goods, the problem of economic value as a whole has been solved. It thus has been overlooked that producer goods, to which altogether different conditions apply, require a separate explanation. It is not true that imputation theory is merely a special application of the general rules for determining value, as was believed in the early days of the marginal utility theory. In truth, it is the next and decisive step in the development of economic theory based on subjective value. We shall attempt to show in subsequent sections what strides have been made in that direction. If one holds the view that no fully satisfactory solution to the problem has yet been found, it cannot be excluded — as several younger authors claim — that the determinants for the prices of the factors of production exist only in an exchange economy and that for this reason an imputation of value is not possible. Yet this admission would be tantamount to abandoning subjective value theory as a satisfactory explanation for economic processes and would deprive these authors of the very basis for many of their analyses.
3. Older Formulations of the Problem
The imputation problem has often been formulated — not quite correctly — as asking which share of the utility attained by a product is attributable to specific producer goods used in its production. In this formulation, the problem coincides with a perennial problem of economics, namely, the relative productivity of the factors of production. In a wider sense, all attempts to answer this question, unclear as is its meaning, could be classified as imputation theories. There have always been some, J. St. Mill among them, who have insisted that the problem is inherently insoluble because each factor is an indispensable condition for the outcome as a whole, but over the years various efforts have also been made to solve the problem. Most of these efforts were doomed from the start, however, because of their underlying materialistic concept of productivity, based on ideas from physics, and the corresponding objective interpretation of value. In addition to the endeavors of the Physiocrats and the classical and socialist schools, which ascribe productivity exclusively to the "value-creating power" of land or human labor, the best-known attempt is J. B. Say's theory of productive services. However, these cannot be counted as imputation theories in the narrower sense, if for no other reason than that the systems of thought embodying them had not developed an independent measure of the economic outcome to be imputed, other than the actual expenses for producer goods.
As long as no adequate explanation for the expression of economic outcome, that is, value, had been found, all attempts to determine the participation of the factors of production in this outcome were bound to fail. Explanations had to be shifted to the field of technology until the relationship between the usefulness and the scarcity of goods became the point of departure for explaining all economic actions. It is true that Ricardo, as well as his predecessors and his successors, in the specific case of land rent correctly described one element in the relationship between the value of products and the value of one factor of production in their theory of differential rent. They thereby introduced into economic theory the idea of imputing part of the value of a product determined independently of the participation of the producer good. However, this idea could not be generalized because it lacked a theoretic framework for deriving a measure of economic outcome and for divorcing its magnitude from its physical causes. H. v. Thünen's more elaborate version of the rent theory came closest to being interpreted as a theory of imputation — its basic features were in fact subsequently developed specifically by American scholars along these lines (see Section 5). It too failed, however, for lack of an appropriate concept of value. Once the subjective value theory showed that the outcome of economic activity could be expressed in terms of value, independently of the activity itself, the problem of determining the participation of the individual production factors in this outcome could be tackled with some hope for success. The long neglected scholar H. H. Gossen, who first developed this theory, already fully recognized this fact and attempted to solve the problem in a way that is in principle analogous to Menger's and Böhm-Bawerk's later attempts. The systematic treatment of the theory of imputation, however, must be dated from the publication of Menger's Grundsätze der Volkswirtschaftslehre in 1871.
4. The Development of the Imputation Theory by the Marginal Utility School
The so-called principle of substitution, which had already been used successfully in explaining the value of consumer goods, underlay the first attempts at solving the imputation problem. Menger, like Gossen before him, made some tentative attempts in that direction, while Böhm-Bawerk later constructed a self-contained imputation theory on this foundation. The principle of substitution states that the value of a good disposed to a specific use equals the smallest utility to be attained not in this use but the smallest utility in any use whatsoever. According to Menger value is explained by the dependent utility of the good in question. His reasoning goes as follows: If a good originally disposed to a use with a higher utility ceases to be available, it will be replaced by the good that until that time was in the use with the lowest utility. Thus the loss of utility caused by the unavailability of the original good would ultimately manifest itself at the position vacated after this substitution. Menger applies the same reasoning to replaceable goods of higher order. For irreplaceable producer goods he supplemented it by the further consideration that the loss of utility due to the unavailability of such a producer good and the prevention of production caused by it is partially compensated by the utility achieved by the complementary goods in new uses. The final loss thus amounts only to the difference between the utility originally expected and that finally attained. However, if none of the complementary goods required for a specific purpose can be used elsewhere or replaced, the entire utility attained by the combination will be lost if any one of the goods is unavailable. Böhm-Bawerk summarizes the resulting rules for the imputation of value in the following three cases
1. If none of the required complementary goods can be replaced or used elsewhere, then considering the loss or acquisition of these goods the entire utility of the product can be imputed alternatively to each of the goods.
2. If a producer good can be used elsewhere, its value must correspond at least to the utility attainable in the alternative use and the difference between the total utility of the product and this value constitutes the upper limit to the value of the remaining complementary goods.
3. The value of replaceable goods must never exceed the utility that can be attained in their alternative use.
Within these limits, which may be quite narrow in the case of goods that have multiple uses, the value imputed to the individual goods will depend on the specific situation in which valuation takes place. When the acquisition or loss of a "final unit" is involved, whereas the availability of the remaining complementary goods is taken for granted, it should be attributed all that remains after deducting the minimal values for the other goods from the value of the product; on the other hand, according to the above rules, when the provision of the necessary complementary goods is not yet ensured, only the minimal value will then be imputed to the good, which has to be viewed as an isolated "splinter." In other words, if we are to apply the latter method to the valuation of all complementary goods, the undistributed residual will be attributed to the value of that good the lack of which would make production impossible. Generally speaking, to irreplaceable factors therefore the entire remaining amount over and above the minimum values of the other goods will be imputed, while goods that have no alternative uses only obtain the amount of value left over after the maximal value attainable by the complementary goods has been deducted. Therefore the results of the imputation will differ according to the stipulated situation. As a consequence, the sum of the various values ascribed to the individual factors may well either not exhaust or exceed the value of the product. This outcome is nevertheless consistent with the general theory of value held by the authors adhering to this interpretation, for whom the principle of marginal utility is only of alternating effectiveness in determining the value of the units of a given quantity of goods. It is also an unavoidable consequence of their defining value in terms of dependent utility. The method, however, fails in determining the values of a set of producer goods which must be used jointly to generate utility. Invoking substitutability or alternative uses of these goods only refers to cases which are as much in need of an explanation as the one in question. It is for cases like these that Wieser's attempted solution was intended.
Wieser's Ursprung und Hauptgesetze des wirtschaftlichen Wertes had closely examined the conditions relating to the value of producer goods even prior to the publication of Böhm-Bawerk's above-mentioned treatise. After offering a critique of Menger's and Böhm-Bawerk's attempted solutions, he presented his own fully developed solution to the imputation problem in a second work, published in 1889 under the title Der natürliche Wert. Wieser's second work remains the basic and most thorough treatment of the problem even today and can be viewed as the classical account of the theory of imputation as such, although it has been superseded and complemented to some extent by his comprehensive treatise on economic theory. Menger's and BöhmBawerk's attempts mainly consisted in extending to producer goods their successful explanation of the value of consumer goods by dependent utility. Wieser's solution, however, takes into account in a broader sense the specific conditions of production, which he has incorporated into the system of subjective value theory by his fundamental inquiry into the law of costs. At least at the outset of his inquiry he concentrates on the value of the products as the primary problem the solution of which will result in the solution of the problem of imputation. Just as the economic principle requires for consumer goods used for different purposes that the same margin of use is maintained in all these uses, producer goods, accordingly, should also be used in such a way that their share of the value of the product in none of its uses be smaller than the greatest value that might have been attained in any other use, but could not be accomplished for lack of a sufficient provision of these goods in arranging the production process. It follows that in a simple economy, production will be extended to the point where the individual producer goods have the same valuation in the various lines of production and the utility attained in each production is distributed fully among the various production factors. Only if this condition is fulfilled, will the available producer goods be put to the most advantageous use. Then it will be impossible to achieve a more advantageous use by shifting individual units of producer goods to the production of goods the utility of which exceeds the sum of the values of these producer goods or by withdrawing them from the production of goods where the reverse is true. The only exception is where a product's utility scale is discontinuous and thus prevents the extension of production up to this point. In this case the value of the product is determined by its "cost utility," that is, the sum of the values to be imputed to its factors in their marginal uses (law of costs).
(Continues...)
Excerpted from Capital and Interest by Lawrence H. White. Copyright © 2015 The Estate of F. A. Hayek. Excerpted by permission of The University of Chicago Press.
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