The imputation approach: Menger, Wieser, Walras

Even less satisfactory is the treatment of capital by the authors who start from marginal utility and adopt an “imputation” approach in the sense that the market imputes to factor services the value of what they produce.

Carl Menger conceives production as a “downward” flow of services from inputs “of higher order”, that is, employed earlier, toward goods of “lower order”, and he insists that the value of the inputs derives from the value - the utility - of their final product; but hating mathematics and lacking the notion of marginal productivity he is unable to perform the derivation when there is more than one input; therefore his approach to income distribution remains disconcertingly vague. Understandably, he is also unable to reach a determination of the rate of interest: in 1888, at the end of a verbose and inconclusive article on what “capital” can mean, Menger states that a satisfactory theory of the yield of capital is still to come and expresses the hope that Bohm-Bawerk may soon redress the situation (so as better to counter the socialist propaganda, he explicitly writes).

Wieser eschews mathematics too, and proposes verbally an imputation method amounting to a system of equations, one for each consumption good, where technical coefficients are given, the values of consumption goods are given, the imputed rewards of factors are the unknowns to be determined, and for each consumption good the sum of the rewards imputed to its inputs equals its value. Besides problems of over- or under­determination of the system of equations, the method needs given values of the con­sumption goods so it remains incomplete. Furthermore capital, measured as an amount of value, is one of the factors in the imputation, and Wieser admits that this creates a problem, because the value of capital should derive from the imputation process, but if it is not known one does not know how much capital each process employs; the solution is clearly unsatisfactory: at each moment, Wieser argues, the value of capital can be taken as given (by previous calculations of economic agents).

When Wieser writes (his first contribution is in 1888), Walras has already (in the first edition of his Elements, 1877, pt II) completed the “imputation” approach via a general equilibrium of production and exchange with fixed coefficients, with all factors physi­cally specified and income distribution determined by the indirect factor substitution mechanism. In the Preface to the fourth edition, Walras summarizes: “the formula of the English school, in any case the school of Ricardo and Mill, must be reversed, for the prices of productive services are determined by the prices of their products and not the other way round”. However, he too is unable to insert capital satisfactorily in the approach. Unique among the founders of the marginalist approach, Walras never glimpses the possibility of treating the several capital goods as “embodying” a single factor capital of variable “form”; he treats them as so many distinct factors, each one with its given endowment. Yet his conception of equilibrium fully belongs to the traditional method of normal positions. The equilibrium is described as: (1) a centre of gravitation to which the economy tends through slow adjustments (Walras 1954: 380); (2) persistent, allowing the treatment of equilibrium relative prices as if constant (for example, Walras determines the purchase price of land by dividing the land rental by the rate of interest, as if both variables could be assumed constant for ever); and (3) characterized by a uniform rate of return on the supply price of capital goods (URRSP), such as the classical natural prices or Wicksell’s equilibrium prices. This clearly requires an endogenous determination of the composition of capital; but up to the third edition (1896) of his Elements Walras appears not to be clear about the fact that his specification of the capital endowment prevents it. He argues that URRSP is reached by variations of the composition of invest­ment because, if production of a new capital good rises owing to a higher-than-average rate of return on supply price, the increased production will significantly reduce its rental; but this can only be due to the increase of its endowment, which however Walras cannot admit because he treats the equilibrium’s capital endowments as given. This contradictory view of URRSP as brought about by a process incompatible with the specification of the equilibrium’s data reveals a confusion but it also reveals the origin of Walras’s acceptance of URRSP in the traditional argument (explicitly accepted in one passage, 1954: 271) that URRSP is brought about by changes in the relative quantities

in existence of the several capital goods.

With the fourth edition (1900), evidently having become clearer that he is taking the capital endowments’ vector as arbitrarily given and not as adjusting, Walras introduces three changes whose importance is first stressed by Garegnani (1960). A first change (the only one Walras announces in the Preface) concerns the tatonnement, which in the previous editions involved a repetition of actual productions and exchanges. Now Walras extends to the complete model the assumption he had until then restricted to pure exchange, that the adjustment toward equilibrium excludes actual disequilibrium productions and exchanges: it operates by means of provisional “bons” and production only starts when equilibrium is reached. Clearly, he has become conscious that he cannot allow disequilibrium productions to alter the endowments of capital goods. A second change reveals he has realized the mistake of his previous argument on what process achieves URRSP. Now the process relies only on the effect on the costs of production of new capital goods (the increase in the production of a capital good, Walras argues, raises the rentals of the factors more intensively utilized in that industry, so the cost of production rises relative to the rental - now assumed little affected - of that capital good). However, in a multiproduct economy changes in the quantity produced of a single product cannot greatly affect its cost of production; evidently having realized this fact, Walras introduces a third change: without modifying the equations, he inserts two new sentences (1954: 294, 308) where he states that URRSP is not always achievable and the capital goods unable to yield the same rate of return as the other ones will not be pro­duced, which requires eliminating the equations imposing URRSP for these unproduced capital goods.

Another little discussed aspect of Walras’s approach to capital deserves mention. He distinguishes “capital proper”, that is, durable capital goods, from raw materials, seed, and other circulating capital, and no endowments of the latter inputs appear among the data of equilibrium (1954: 238-41). He makes circulating capital disappear from the equations of equilibrium by replacing, in the equations determining the cost of produc­tion of goods, the cost of the raw materials and so on with the cost of the services of land, labour and “capital proper” that produced them. This is consistent only if production - imagining it to be in yearly cycles, with the equilibrium describing one cycle - is as follows: at the beginning of the year production starts with no circulating capital at all, only labour, land and durable capital goods; intermediate goods appear and are then totally used up during the productive process, so at the end of the year gross output consists only of consumption goods and new durable capital goods. The need for endow­ments of many circulating capital goods, for example, seeds, at the beginning of the year disappears from sight. Only with the fourth edition circulating capital is admitted, and only in a not very clear Part VI, but the picture of production of the earlier Parts influ­ences later authors, contributing to a frequent erroneous identification of capital with only durable capital goods.