CHAPTER 4 Capital in Historical Perspective Introduction: The History of Capital Theory is Relevant

Considerations involving capital are as old as economics itself. And, perhaps more than any other field in economics, current capital theory bears the stamp of its history. Modern discussions are very heavily influenced by the categories developed by capital theorists since Adam Smith, and by the contexts in which they wrote. The history of capital theory is a history of complex, often esoteric, intellectual battles. And more often than not, these theoretical debates about abstruse technical issues mask the underlying ideological differences that are the real issues. But there is one thing that many of the protagonists have in common: their adherence to a framework in which equilibrium, in some significant sense, prevails. In this chapter we shall examine some aspects of the various approaches to capital that have characterized the history of capital theory. In doing so we shall seek (a) to clarify the significance, or lack thereof, of the insights gained from the high points in the development of capital theory, (b) to remove the ambiguity that has surrounded key terms like “profit,” “rent,” and “interest,” and (c) to clear the way for a consideration of capital in situations of disequilibrium where, it will be seen, many of the traditional issues are rendered moot.

The Questions

Market economies are sometimes referred to as “capitalist” economies, suggesting the presence of a phenomenon called “capital” that is in some way responsible for the character of the economy and for its mode of production in particular. At a general level we may want to say that capital is “that which makes production possible.” Its origins can be traced to the idea of a fund of purchasing power (owned by “capitalists”) which, when made available, allows for indirect methods of production, methods that involve production (or “capital”) goods. This can be explained further as follows.

All production can be traced logically to the input of labor services and natural resources, what we may call original inputs. These inputs can be used to produce useful outputs or they may be used to produce other inputs. These other inputs, which are produced means of production, are thus logically called capital goods. They facilitate production. And since producing useful outputs using capital goods necessarily takes more time than producing outputs using only original inputs (from the vantage point of a moment in time when the capital goods are not yet produced), the capitalists’ fund is very important in allowing these (advantageous) indirect methods to be adopted. (Defenders of the market system, against those who seek justification for the earnings of these apparently “unproductive,” “non-working” capitalists, have often pointed to the necessity to reward the capitalists for parting with their wealth in order to facilitate these “roundabout” methods of production. Capitalists who own the capital goods directly may be thought of as lending the money to themselves.)

Capital, then, originates from the idea of a fund of money that facilitates the time-consuming use of production goods. But is it the fund or the goods, or both, that facilitate production? Can it be said that while the capitalists’ fund facilitates the use of production goods under social arrangements where such goods are privately owned, it is the production goods and not the fund that are truly productive? If so, it seems logical to differentiate between a capital fund, which is just an accident of particular historical social arrangements, and capital proper which refers to the technologically necessary instruments of production. It seems natural from this perspective to think of capital as a “factor of production” along with the original “factors of production”—labor and land. In modern economics it is thus this physical capital that is now implied when no qualifiers are used. It must be recognized, though, that individual capital goods can accomplish nothing on their own. It is together with other capital goods and with labor and land that they may be seen to be (jointly) productive. How, then, are we to account separately for the contributions of the individual capital goods to the value that they help to produce? And if “capital in general” is to be thought of as a factor of production, it seems necessary that a relationship should be established between the notion of “capital in the aggregate” and the individual capital goods involved in the production process. The latter are diverse and heterogeneous in nature and it is not immediately obvious how one should proceed to add them together. A logical method is in terms of their values, their prices. But, as we shall see, it is only in equilibrium that such prices have the meaning that we seek, and even then will not be free of contentious ambiguity.

Thus investigations in capital theory often return repeatedly to the same fundamental questions:

• What is capital?

• Is it a separate factor of production?

• Is it a fund?

• Or is it a physical stock?

• How is capital to be measured?

• What is the nature of the earnings of capital?

• How is this related to interest?

• How are capital’s earnings determined and justified?

• What determines capital’s earnings in relation to earnings in general, that is, how does capital feature in the distribution of income and wealth generally?

These questions are related to the historical development of capital theory. We illustrate this with a brief impressionistic historical outline.¹

Adam Smith’s Corn Economy

Adam Smith was interested in the causes of economic progress. There is a natural and important connection between capital and economic growth and development. Growth theory had obviously not yet become the technical abstract specialization that it is today. Yet there is a “model” implicit in his work (Hicks 1965:36–42; Kregel 1976:20–23; Lachmann 1996:130–132).² Smith’s world was still largely an agrarian society, but his implicit model survived the circumstances of his time. As we shall see, Ricardo in particular tried to extend Smith’s insights into a world to which it was much less suited. This had significant consequences for the development of capital theory. Most modern economists working in the area are influenced (whether they know it or not) by Ricardo’s agenda.

We concentrate on those aspects of Smith’s work that arise out of his way of looking at capital in a predominantly agricultural society (Lachmann 1996:130), although, of course, he was aware of, and said much about, the implications of the rapid industrialization that was occurring. An agrarian economy (we may designate it as a “corn economy”) depends largely on harvests. Next year’s harvest depends, to a large extent, on how much of this year’s harvest is plowed back in seeds and, even more, on how much corn there is this year. This year’s harvest has three possible uses: to keep the working population alive and perhaps growing, to feed the animals used in production, and to use as seed for production. Thus, this year’s harvest may be seen as a type of capital stock. In a modern economy it is natural to see elements of the capital stock at any time that are not being used, as a result of obsolescence or incomplete adjustment to new conditions. In a corn economy, by contrast, all capital is used, is homogeneous, and is turned over regularly once a year. So we have an initial harvest, a working population of certain size, and the possibility of a harvest next year that is dependent on labor and its productivity. It is not clear what Smith thought about the determination of wage rates. It is easiest to assume that he took it to be determined by subsistence or convention (ibid.:131).

We may formalize Smith’s model in a rather simple way (Hicks 1965:36–42, Lachmann 1996:130–142). There is a crucial relationship between this year’s harvest and next year’s harvest. This year’s output Y_t—our capital stock for this year—is divided up into seed corn, fodder, and food production. In the simplest formulation, the whole of the corn that the laborers uses for their (and their animals’) consumption plus their planting may as well be counted as their “wage.” The capital stock then comprises a “wage fund” necessary to keep society going until the arrival of the next harvest. Then if N is the number of laborers, the (average) wage rate w = Y_t/N or:

Y_t = Nw ; w = real wages per worker

Growth in the corn economy will thus depend on the number of workers N and on productivity p, the amount of corn produced (on average) by each worker.

Y_t+1= pN = pY_t/w or Y_t+1/Y_t = p/w

Thus the rate of growth is equal to p/w - 1. This growth rate varies inversely with the wage rate and directly with average productivity. If p rises faster than population, the wage rate can rise.

This model neglects to account for all sections of the economy, for example, the towns and the landowners. If we assume that k < 1 of any year’s output is set aside each year to feed the non-agrarian classes, then the wage rate must be kY_t/N = w. The capital stock is now not Y_t but rather kY_t = K_t = Nw. So Y_t+1 = (p/w)K_t = k(p/w)Y_t, and the rate of growth is k(p/w) - 1. Obviously, as formulated, k is a measure of the “drag” on economic growth imposed by the “nonproductive” elements of society. This conclusion is a result of formulating output as consisting solely of corn and gives rise to some obvious objections. This aspect of Smith’s model is of less concern to us at this point, however, than at some others.

Smith did not think of p, w, and k as constants. Economic growth means that the wage fund grows ahead of population. Smith believed that p would increase over time as a result of the division of labor, thus causing a rise in w. Thus p and w would grow together, though not necessarily at the same rate. Economic growth and capital accumulation in turn made the division of labor possible.

The annual produce of the land and labor of any nation can be increased in its value by no other means, but by increasing either the number of its productive laborers, or the productive powers of those laborers who had before been employed. The number of productive laborers, it is evident, can never be much increased, but in consequence of an increase of capital, or of the funds destined for maintaining them. The productive powers of the same number of laborers cannot be increased, but in consequence either of some addition and improvement to those machines and instruments which facilitate and abridge labor; or of a more proper division and distribution of employment. In either case the additional capital is almost always required. It is by means of an additional capital only that the undertaker of any work can either provide his workmen with better machinery, or make a more proper distribution of employment among them.³

(Smith 1982:343)

Thus Smith regarded saving as necessary for the achievement of economic growth, and the earning of profit consequent not simply upon the accumulation of capital but significantly upon the fruits of the division of labor. In modern terms, Smith sees accumulation and technical progress as being tied together. And although he seems to identify a type of diminishing returns, this is clearly not in the form of a declining rate of return to investment in a given mode of production, but rather refers to the eventual possible exhaustion of investment opportunities for extending the division of labor (that is, for the discovery and introduction of new and improved production methods) and this leads naturally to reliance on foreign markets.

Smith’s corn economy is obviously a special case that raises a number of questions. It is not clear, for example, whether he thinks of machines, buildings, etc., as capital and how their accumulation is to be treated.⁴ However, it is an instructive special case. In this economy, since capital is homogeneous and is identical to output, there is no problem concerning the valuation (absolutely or relatively) of either. Thus the rate of yield or of growth can likewise be measured unambiguously. It is a one-commodity, subsistence fund economy in equilibrium where the capital stock uniformly lasts one period. Durability of capital thus plays no role. There is no question about the appropriate composition or durability of the capital stock (although Smith was aware of the changing shape of productive equipment) and past mistakes have limited influence. There are no individual differences in expectations regarding the type of product to be expected nor the date at which it is to arrive (although of course there may be some short-term uncertainty regarding the harvest). Thus, although production takes time, time does not feature in the valuation of capital and output, except in so far as future output may be discounted.⁵ Neither labor units nor time units need to be used to value the capital stock. When we turn to Ricardo we see how special these conditions really are.

Ricardo’s Uniform Rate of Profit

In the more industrialized economy of 1815 it was no longer tolerable, even as an approximation, to assume that all capital was circulating capital; nor that, even in a metaphysical sense, all capital was “corn.” The self-containedness of the single period was nevertheless so powerful an instrument, and so much depended upon it, that Herculean efforts had to be made to retain it. What Ricardo did, in his efforts to retain it, can now be understood (thanks to Mr. Sraffa). . . . Homogeneity was to be retained by reducing capital to its labor content (the labor theory of value); fixed capital was to be reduced to circulating by consideration of periods of production (in the manner to be worked out more fully, decades later, by Jevons and Böhm-Bawerk). But all the power of these devices. . . could not save the self-containedness. It is apparent from Ricardo’s own work that even in his hands the static method is already confining itself to its proper place—to the comparison of static equilibria, even of stationary states; it cannot extend to the analysis of a dynamic process. In the light of the subsequent developments there is nothing surprising about that.

(Hicks 1965:47)

As mentioned, Smith’s model was essentially a subsistence fund theory. There is a stock of food to maintain workers from one harvest to the next. What capital does for the owner is to facilitate the employment of a certain number of workers for the production of a certain output. All economic considerations are such that one never has to look beyond this one-year horizon. This makes the application of the static method possible and largely excludes the consideration of expectations.

Ricardo had to face problems that Smith was able to avoid. Once machinery played a large part in the economy, Smith’s assumption of a homogeneous capital stock was no longer defensible. The labor theory of value served to bring all economic goods within a common denominator. Ricardo used the “labor hour” as a unit of measurement; labor time is the common standard of comparison. Machines, corn, and cattle all cost labor and are seen to be comparable in those terms. If we have a stock of circulating capital (for example, a stock of corn), we can ask how many hours of labor it took to produce it and get a value for the input. But if we have a machine lasting fifteen years, although we can say its production took labor hours, the total input is not used up in one year and enters successively into the output of fifteen years. Ricardo deals with this by regarding fixed capital, like machinery, as circulating capital that circulates more slowly. Some part of the machine gets used up in each of the fifteen years. Fundamentally there is no difference. All capital stocks rotate, it is only a matter of degree. It thus becomes possible to calculate the value of the inputs of any capital item that matures in any given year and to compare it with the value of its output in that year, thus being able to calculate a rate of return.

Ricardo’s main concern was with the distribution of income between the various categories of inputs and their owners. It was in order to give an account of the earnings of capital that he had to find some way to reduce the heterogeneous capital items to some common measure. His basic argument concerns the tendency for rates of return on various capital investments to become equal. This tendency provides a mechanism for determining flows of capital to various types of production. In long-run equilibrium a capitalistic economy establishes a uniform rate of profit. This is what explains the distribution of wealth. In equilibrium all capital ventures earn the same rate of profit. Ricardo thus started the now common practice of using what would be the state of affairs in a hypothetical situation of long-run equilibrium, a situation that is an end state of an indefinite number of interactions in an essentially unchanging environment, as if it were the everyday state of affairs. This is the equilibrium method of explanation. We speak of the rate of profit on capital as though it were a parameter.

Ricardo’s concerns reflected his preoccupation with the future of capitalistic economies. The event of the Napoleonic blockade and the consequent rise in food prices led him to wonder about the long-term trend of an economy in which the population was rising. How would the population get fed? He seemed to accept Malthus’s idea that the population would grow in such a way as to keep the wage rate at the bare level of subsistence. But if the population was growing, this would lead to the use of land of progressively inferior fertility. So with the wage rate fixed at subsistence level and the margin of production being extended to inferior land, the earnings (rent) of the landowners on the infra-marginal land would tend to rise. This means that the rate of profit is bound to fall. Pushed to its logical conclusion, the rate of profit would fall to zero, at which point capital accumulation would stop. A stationary state would have been reached. There could be no such thing as permanent growth. The only possible exception to this result is in “improvements in machinery connected with the production of necessaries,” “discoveries in the science of agriculture,” and international trade (Ricardo 1973:120; Kregel 1976:24).

These exceptions notwithstanding, Ricardo’s emphasis and his legacy are his method of concentration on the hypothetical long run. It is this that prompts Lachmann to label both the Cambridge England neo-Ricardians and the neoclassical growth theorists as Ricardians (Lachmann 1973). They share the method of comparative static equilibrium analysis that derives from Ricardo and his interest in accounting for the “laws” of distribution. In this way the focus is clearly on the mechanisms of social development and away from aspects of human action and decision. If human planning features at all in the capital accumulation process, it is in a mechanical and implied way. Action is relied on implicitly to bring about the equilibrium that is assumed. If some capital venture were to become unprofitable, capital would be withdrawn and invested elsewhere. But where capital is durable, it can only be withdrawn very slowly. Thus we must assume that no changes occur while capital is in the (long) process of being shifted from areas of low profitability to areas of high profitability. And we are not permitted to ask how it is known which are the areas of low and high profitability. Somehow the economy is envisioned to grope its way soon enough to a configuration of capital items on which the rate of profit is uniform and the maximum possible. Reflecting on the discussion of the previous chapter, we realize that in a world of continuous unexpected change, flows of capital will not be able to keep up, and equalization will never occur. Prices of the various capital goods will be such that the original labor value invested in them has no enduring meaning and the whole Ricardian basis would seem to be of dubious relevance. Relevance rather than realism is the key, and evidently relevance is often “in the eye of the beholder.” Ricardo’s long-run equilibrium method, we shall see, continues to command many adherents.

In his discussion of the distinction between circulating and fixed capital, Ricardo was forced to consider the role of time in production. His labor theory of value contains the elements of what was to become a particular approach to dealing with the time dimension in capital theory. In a world of heterogeneous capital items, time is of the essence. A very different approach to dealing with it was provided by Carl Menger.

Menger’s Time Structure of Production

Menger’s pioneering approach is responsible for our thinking of capital in terms of a time structure, reflecting the structure of capital goods employed in the production process. There is no attempt in Menger to reduce the variety of goods and services available at various dates to a single dimension. At any moment in time some goods are useful for immediate consumption, and some are only useful in so far as they contribute to the production of goods available for immediate consumption. And since production takes time, a time element is already implicit in the contemplation of a set of economic goods at any single moment in time.

Menger thus characterizes production as a sequential process in which goods of higher order (capital goods) become transformed into goods of lower order (consumption goods). Capital goods are varied in nature but can be classified by where they fit, along a time continuum, into the production process. The lowest or first-order goods are, as noted above, consumption goods. The lowest-order capital goods are second order. The next highest are third order, and so on. With this model, he makes clear that the element of time is inseparable from the concept of capital. Any theory that treats the process of production as instantaneous necessarily misrepresents reality in an important way.

The transformation of goods of higher order into goods of lower order takes place, as does every other process of change, in time. The times at which men will obtain command of goods of first order from the goods of higher order in their present possession will be more distant the higher the order of these goods.

(Menger 1976:152)

And the rewards to saving result only if more time-consuming methods of production are adopted.

[B]y making progress in the employment of goods of higher orders for the satisfaction of their needs, economizing men can most assuredly increase the consumption goods available to them accordingly—but only on condition that they lengthen the periods of time over which their activity is to extend in the same degree that they progress to goods of higher order.

(Menger 1976:153, italics added)

The higher-order goods that people come to own must allow greater production if there is to be progress. That is, they must (in combination with other goods) be able to produce a greater volume of consumption goods in the future or, in other words, they must be able to extend consumption further into the future. It is interesting to note that, while Böhm-Bawerk’s later discussion of the greater productivity of more “roundabout” methods of production is clearly drawn from Menger, the latter was clear that there is nothing mechanical about the relationship between saving (diverting consumption from the present to the future) and productivity. Saving may be necessary but it is not sufficient for economic progress. He envisaged the time-consuming creation of specific capital goods to be a necessary condition for achieving economic progress.

Menger first introduces these ideas in connection with processes in nature. People find the fruits of nature valuable. But at an early stage in the development of civilization they learn that they can do more than simply “gather those goods of lowest order that happen to be offered by nature” (Menger 1976:75). By intervening in the natural processes, individuals can have an effect on the quantity and quality of the subsequent yield.

To understand the objectives of the “producers” is to understand that the earlier a producer intervenes, the greater are the opportunities to tailor the production process to suit his own purposes. This provides an intuitive basis for the notion that the more “roundabout processes” tend to have a greater yield in value terms.

(Garrison 1985:165)

It is important to realize the role of subjective value in Menger’s capital theory. The value attributed to any capital good is prospective, not backward looking as with Ricardo. “There is no necessary and direct connection between the value of a good and whether or in what quantities, labor and other goods of higher order were applied to its production” (Menger 1976:146). At any point in time there is a capital structure characterized by capital goods of various orders whose value is determined by the values attributed by consumers to the consumption goods they are expected to produce. “The value of goods of higher order is always and without exception determined by the prospective value of the goods of lower order in whose production they serve” (Menger 1976:150). These values manifest in the market as prices. As long as these prices remain (and are expected to remain) constant and as long as there are no technical changes in methods of production, the capital structure will remain constant. But if there should be a permanent change in the price of even one consumption good, this will almost always imply the need to change the capital structure in some way. Changes and substitutions will occur in response to the perceived changes in prospective output values.

The level and pattern of the employment of resources (including labor) and their earnings is determined and thus depends on the strong link between the structure of consumption and the structure of production. Changes in the demand for one (or some) consumption good(s) (relative to others) cause changes in the evaluation and use of particular capital goods, and in employment. The implication in Menger is that the market can accomplish this smoothly.

Time is inevitably involved in the notion of capital. Since the value of higher-order (capital) goods depends on the prospective value of the consumer goods they are expected to produce, the elapse of time, and with it the arrival of unexpected events, implies that some production plans are bound to be disappointed and thus the value of specific capital goods will be affected. The economic consequences of human error are implicit in Menger’s view of capital.

Menger and Ricardo thus present contrasting and really irreconcilable visions. Adopting Menger’s perspective, one cannot lose sight of the variety of goods and services and individual activities and choices. There is no suggestion of a uniform rate of profit. And yet there is an inescapable order within the variety provided by our understanding of the purposes of these individuals. “The process of transforming goods of higher order into goods of lower order, . . . must always be planned and conducted, with some economic purpose in view, by an economizing individual” (Menger 1976:159–160). We see here the need to consider aspects of intertemporal planning discussed above in Chapter 3. No such need was suggested in our analysis of Ricardo’s approach.

Böhm-Bawerk: Interest and the Average Period of Production

Introduction

Böhm-Bawerk is probably the economist most often cited in connection with the development of capital theory. He is thought of as the “father” of Austrian capital theory and credited with being the first to introduce the element of time and its implications clearly into considerations of capital (Hennings 1987d:233). This conception neglects the contribution of Menger. Böhm-Bawerk’s work on capital was a conscious extension of Menger’s. His departures from Menger are not seen universally as being an advance.⁶ As we shall see, some of the later Austrians had reason to regret aspects of Böhm-Bawerk’s work on capital and, even more so, the interpretations to which it gave rise. Whereas Menger produced hardly more than twenty-odd pages on capital theory (in spite of which it may be said that he laid the groundwork for a comprehensive theory of capital), Böhm-Bawerk produced three large volumes and some shorter works. It was a major part of his life’s work. It is to be expected, then, that the scope for various and differing interpretations might be quite large. Austrian, Ricardian, and neoclassical capital theorists all find much with which they can agree in Böhm-Bawerk, albeit much also to disagree with. A reading of Böhm-Bawerk reveals an uneasy amalgam of the ideas of Menger and Ricardo. Capital theorists in general have chosen to emphasize the Ricardian elements.⁷ The Mengerian elements might just as easily have been emphasized, had capital theory developed differently. As it is, modern capital theory, with its reliance on “production function” reasoning, can, with some justification, be traced back to Böhm-Bawerk (along with Wicksteed and some others). Much of the ambiguity surrounding the assessment of his contributions relates to his use of a theoretical device designed to provide a physical measure of the capital stock—the average period of production.

The Advantages and Disadvantages of Capitalistic Production

Böhm-Bawerk’s characterization of a capital-using economy is very similar to Menger’s. Production is a process involving time. Original factors are transformed, with the aid of produced means of production, into consumption goods. Like Menger, he too conceived of capital goods as being related to one another in terms of the stage of the production process that they occupy. And, like Menger, he conceived an increase in capital to involve a change in the time structure of production (not his term) in some way. It is not simply an augmenting of each type of capital good at each level of maturity (each stage of production), but a change in the internal structural relationships. Like Menger, he held that capital goods derived their value from their usefulness in the production of consumption goods; their value was to be derived from the value to consumers of the goods they produced. All durable capital goods are valued by the present value of their services using a subjective rate of discount (to be discussed below, see Hennings 1997:132). He emphasized the heterogeneity and specificity of individual capital goods and denied that they could be aggregated into some physical measure of the capital stock. Hennings quotes Böhm-Bawerk as follows:

A nation’s capital is the sum of heterogeneous concrete capital goods. To aggregate them one needs a common denominator. This common denominator cannot be found in the number of capital goods . . . nor their length or width or volume or weight or any other physical unit of measurement. . . . The only measuring rod that does not lead to contradictions . . . is the value [of these capital goods].

(Hennings 1997:132, his translation of Böhm-Bawerk 1959)

Böhm-Bawerk denies that capital goods are individually or intrinsically productive and insisted that the production processes that they make possible are the sources of any increases in value that arise. But since these processes can be characterized by a series of stages of production successively further back from the ultimate consumption goods in which they culminate, he perceived a connection between the number of such stages and the amount of value added. That is, there is a strong intuition connecting the length of production, indicated by the number of stages involved (the degree of “roundaboutness”), and the degree of productiveness that results.

There are two concomitants of the adoption of the capitalist methods of production. . . . One is advantageous, the other disadvantageous. We are already familiar with the advantage. With an equal expenditure of the two originary productive forces, labor and valuable forces of nature, it is possible by well chosen roundabout capitalist methods to produce more or better goods than would have been possible by the direct noncapitalist method. It is a truism well corroborated by empirical evidence.

(Böhm-Bawerk 1959: Book II, 82–83, footnote references crediting Lauderdale and Jevons omitted)

[O]ne thing that can be stated with a reasonable degree of certainty is the proposition . . . that as a general rule a wisely selected extension of the roundabout way of production does result in an increase in the magnitude of the product. It can be confidently maintained that there is no area of production which could not materially increase its product over the result obtained by its present method.

(ibid.:84–85)

Böhm-Bawerk felt that a more “time-consuming” process of production would not be chosen unless it was more productive in this sense, unless it added sufficiently more value to compensate for the longer “waiting” required. “The disadvantage which attends the capitalist method of production consists in a sacrifice of time. Capitalist roundaboutness is productive but time consuming. It yields better consumption goods, but not until a later time” (ibid.:82). Thus by wisely selecting more roundabout methods of production, increases in value can be obtained and these have to be weighed against the “cost” of waiting. In addition, however, it is apparent that the returns to greater degrees of roundaboutness must eventually diminish. In summary:

All consumption goods which man produces come into existence through the cooperation of human powers with the forces of nature, which are in part of economic character, in part free natural powers. Man can produce the consumption goods he desires through those elemental productive powers. He does so either directly, or indirectly through the agency of intermediate products which are called capital goods. The indirect method entails a sacrifice of time but gains the advantage of an increase in the quantity of the product. Successive prolongations of the roundabout method of production yield further quantitative increases though in diminishing proportions.

(ibid.:88)

Roundaboutness and the Average Period of Production

Böhm-Bawerk’s lengthy exposition is generally imprecise. His discussions can be read as suggesting informal general properties of real capitalist economies. Capital accumulation involves judicious changes in the time structure of production that furnish greater output value. And output value is increased not only by augmenting existing products, but also by producing “better goods.” Both output and input undergo “qualitative” change as opposed to simply quantitatively augmenting existing processes (even though he seems to be assuming a given technology). And this interpretation is strengthened by his connecting the fruits of roundabout production to the division of labor.

Our modern system of specialized occupations does, of course, give the intrinsically unified process of production the extrinsic appearance of a heterogeneous mass of apparently independent units. But the theorist who makes any pretensions to understanding the extrinsic workings of the production process in all its vital relationships must not be deceived by appearances. His mind must restore the unity of the production process which has had its true picture obscured by the division of labor.

(ibid.:85)

Yet, perhaps in order to deal with a variety of criticisms, for example as to the precise meaning of roundaboutness, in the very next paragraph Böhm-Bawerk now attempts to make his observations more formal and precise. An attempt to capture the degree of roundaboutness by measuring a period of production from the original factors to the emergent consumption good would be impossible and misleading in the modern world with its vast array of inherited capital goods. One could not, as it were, trace production back “to the moment when the first finger is stirred in the making of the first intermediate product that was later used in the production of the good in question, and as continuing until its final completion” (ibid.:86). And so he introduces the average period of production.

It is more important, as well as correct, to consider the average time interval occurring between each expenditure of originary productive forces and the final completion of the ultimate consumption good. A production method evinces a higher or lower degree of capitalist character, according to whether, on the average, there is a longer or shorter period of waiting for the remuneration of the expenditure of the originary productive forces, labor and uses of land.

(ibid.:86)

And he proceeds to define arithmetically the average period of production, which we may succinctly express as follows:

where T is the average period of production for a production process lasting n calendar periods; t, going from 1 to n, is an index of each sub-period; l_t is the amount of labor expended in sub-period t and N =l_t is the unweighted labor sum (the total amount of labor time expended). Thus T is a weighted average that measures the time on average that a unit of labor l is “locked up” in the production process. The weights (n - t) are the distances from final output. T depends positively on n, the calendar length of the project, and on the relation of the time pattern of labor applied (the points in time t at which labor inputs occur) to the total amount of labor invested N.⁸ Since this formula is in units of time it may be added across various processes to yield an overall measure of roundaboutness. In this way Böhm-Bawerk hoped to have solved the problem of measuring roundaboutness.

It is highly probable . . . that some fraction of a working day will have been expended centuries ago. But because of its minuteness it would be a magnitude which would influence the average so little, that it can almost always simply and safely be disregarded.

(ibid.:87)

And he seemed to place a high reliance on this formulation.

Wherever I have spoken in this or preceding chapters of a prolonging of the roundabout method of production, and of the degree of capitalist character, I would have it understood that I mean this in the sense just set forth [the average period of production] . . . [T]he measure must be the mean duration of the process, and that mean must be computed by averaging units, each of which represents a period of time. . . . For want of a better term, I shall use “average period of production” to distinguish it from the absolute production period.

(ibid.:87)

In this way Böhm-Bawerk’s lengthy, intuitive discussion of the nature of capitalist production as an increasing reliance on produced means of production in specialized production processes became associated with this rather specific and limited formula. Though in actuality a small part of his work as a whole, and arguably an aberration in his breadth of vision, it became the focus for many prolonged and energetic debates in capital theory.

Criticizing the Average Period of Production

Some obvious observations can immediately be made. The formula is crucially dependent on being able to identify the stages of production. It is assumed that the process begins at stage 1 and ends at stage n. In this way any kind of “looping” (coal is used in the production of iron and vice versa), where the output of one stage becomes available as an input of an earlier stage, is ruled out. Second, if the output is a flow (as it usually is), then we must also have some way to connect inputs that occur at time periods n – t with precisely that output that arrives at time period n and separate them from those that need to be connected to outputs occurring at time periods n+j where j is an index of time periods occurring after n. In other words, if the production process is a flow input–flow output process, a set of inputs are used to produce jointly a set of outputs occurring over time and the measuring of T becomes more problematic. Similarly, we must be able to identify the amount of labor time l that is used. This obviously presumes that it is possible to reduce any labor heterogeneity to comparable terms, like efficiency units, and then to measure the number of such units supplied per period of time. Also, as it is formalized, the services of land are omitted, although verbally they are definitely considered to be part of the process. Böhm-Bawerk adds parenthetically, “Let us ignore the cooperating uses of land, just for the sake of simplicity” (ibid.:86). Including the services of land, while mathematically simple, would raise the practical prospect of accounting for the varying productivities of each unit of land used per period of time.⁹

Traditionally Böhm-Bawerk’s average period of production construct, though widely criticized, has been popularly used (particularly in mathematical models, where it is easily converted to a continuous time formulation (see Faber 1979; Orosel 1987)) as a purely labor-time formulation, with land neglected. Thus it has come to seem that time itself plays a role in the creation of value, and not the contingent activities (of humans or nature) that must necessarily occur in time if value is to be created. Or alternatively it could, ironically, be read as an expression of the labor theory of value, as suggesting that the essence of any value is the labor time that went into it. The average period of production construct thus gave rise to a vision of production quite out of character with Böhm-Bawerk’s vision. His general characterization of a capital-using economy is in no way dependent on being able to measure, practically or conceptually, the degree of roundaboutness by the average period of production or any other measure. But, in using it in the way that he did, Böhm-Bawerk (inadvertently) encouraged the interpreting of his work as suggesting a type of mechanical production function, in which production time could be used as a measure of capital itself, and, therefore, of “capital intensity.” The pivotal ingredient for the internal consistency of this approach is the presence or absence of (Hayekian) equilibrium. This can be seen by considering the criticism leveled by Clark (and in slightly different form a generation later by Knight against Hayek).

Böhm-Bawerk had attempted to incorporate Menger’s vision of time in the production process using a quantifiable concept. Clark (1893) (and later Knight) attacked this concept as meaningless and indefensible, and, in the process, suggested a view of capital in which time as we know it seemed to play no real part at all. We have seen that the average period of production can only be calculated when the production process is describable in a very particular way. A favorite example in the literature is the case of wood production from a forest in which a fixed number of young trees are planted while the same number of trees are cut down each period. It should be clear that it is possible to say that, since production and consumption go on steadily each period,¹⁰ they are in effect simultaneous.¹¹ Production and consumption are synchronized and occur together all the time (Clark 1893:313, 1988:14–18; see also Hayek 1941:114–145, 181, 195). In this case, it is possible to calculate the period of production. It is the time that it takes, on average, for a tree to grow from a seedling into a mature tree ready to be cut. If we assume that this time is the same for each tree, we have an even clearer measure. Clark’s criticism can be understood to say that this time period is irrelevant since the forest is, after all, a permanent source of wood. Since production and consumption are in effect simultaneous, the relevant period of production is zero. This is the kind of vision that one is offering in suggesting that capital should be thought of as a “permanent” fund yielding a flow of income. A “capitalist” economy is then one in which capital plays this role.

According to Knight (1936), the period of production, as applied to the economy as a whole, is always infinite or always zero, depending on the perspective that one adopts. In the former case, there is no such thing as an origin to the period of production. The infrastructure of capital goods dates back to Adam and Eve. There must always have been production with the help of some capital goods, and part of gross output was always used to maintain current capital goods and produce others. Output is a continuous flow that never ends. All social production is continuous. In the second case (where T = 0), time intervals are seen as irrelevant. In other words, we can either think of the production process as stretching back from the beginnings of human history and forward into the unending future, or we can think of the production process as essentially timeless, since production occurs simultaneously with consumption. Thus, Clark and Knight argued that it is quite wrong to say that there are time intervals in production. Consumption and investment take place at the same time—the two are concurrent, simultaneous. The whole thing is a misconception.

It is clear, however, that this view is valid only for an economy that has reached a state of stationary equilibrium—a situation in which the capital stock has been built up, is suitably maintained, and yields a continuous income (net of maintenance cost). It is a world where unexpected change is absent and all production techniques are unambiguously known. This implies that all production plans are consistent with one another. In terms of the forest example, the forest is already grown and yielding a steady output when our analysis begins. It tells us nothing about the decisions to grow the forest in the first place, when questions relating to the “period of production” must have been important. Production and consumption only appear to be simultaneous to the observer who does not care about the production plans that gave rise to the production process in the first place. One plants seedlings today not in order to cut trees today but in order to cut trees some years from now. One cuts trees today only because one planted seedlings some years ago. One cannot ignore the time element. Where the capital structure and the array of consumption goods is continually changing, production and consumption frequently do not even appear to be simultaneous. Even where we have a simultaneous and perfectly synchronized production process, considerations of the time structure and the decisions related to it must still enter. “The posited simultaneity of inputs and outputs literally leaves no time for an equilibrating process to take [or have taken] place” (Garrison 1985:129).

Clark’s (and after him Knight’s) emphasis on the technical and logical aspects of “period of production” concepts had the effect of making capital debates appear to be about abstract technical issues rather than about real economic issues. To concentrate on Böhm-Bawerk’s (and later Hayek’s) way of measuring production periods was to divert attention away from his (and Menger’s) vision of the capital structure as involving time in the decisions made by producers. It is these decisions that are the roots of the changes in the capital structure. The period of production that is relevant is that which is perceived by every producer individually in the process of making a decision. Time enters into decisions through producers’ subjective evaluations of the constraints and possibilities. The period of production as an objective construct is inherently problematic, but this is irrelevant for understanding the importance of time, of the fact that different consumption goods are or were available at different times. The capital structure implies a time structure of production. Böhm-Bawerk, following Menger, understood this even though the Ricardian aspects of his work pointed in a different direction.

Böhm-Bawerk as Neoclassical and Ricardian

Modern reformulations of Böhm-Bawerk, focusing on his average period of production, have shown how a connection can be made between his “model” and a classical and neoclassical approach (Dorfman 1959; see also Lachmann 1996:135–140). If a measure exists for the capital stock and the rate of flow of output, then the average period of production can be measured as K/ f, where K is the capital stock and f is the output emerging from the production process in each period. (Alternatively, if the average period of production, T, is known or can be computed by reducing all inputs to labor time, the value of the capital stock, K, can be calculated as we shall see below). Dorfman uses the example of a reservoir in a stationary situation, where the inflow equals the outflow, implying a constant water level. Clearly the quantity of water can be expressed in terms of time. For example, with 100 million gallons of water, 2 million per day flowing in and out, this would imply that the average drop of water was in the reservoir for five days. The ratio of stock to outflow is 5, which is the period of retention of each drop. The same basic logic can then be applied to the capital stock.

In terms of the labor theory of value, f will be equal to the value of the labor expended to produce it. Using the same notation introduced for Smith’s corn model above, we have f = Nw, and the average period of production T = K/Nw or

K/N=Tw

According to Lutz, interpreting Böhm-Bawerk, “An increase in capital per worker in the process of production [is] identical with the adoption of a longer, more roundabout method” (Lutz 1967:9). So, in modern terminology, the capital-labor ratio is very simply related to the average period of production and the wage rate. In a neoclassical framework, where capital and labor can be continuously substituted for one another, changes in r and T must be in opposite directions for any level of output. K is a direct function of T (T is a proxy for K), and r (the rate of profit on K) diminishes with K. So K/N = Φ(w/r), with the first derivative positive. Implicit in this approach is a “production function” where output Q is a diminishing function of the average period of production T,Q = φ(T) (see Hayek 1941:140–141,189, 208). So Böhm-Bawerk can be seen as part of the neoclassical tradition leading directly to modern growth theory, to be explored below. (See also Hennings 1997:144–148.)

Alternatively in a classical world, with a given capital stock and a given number of workers, if the wage rate rises, the average period of production will fall. If w falls, it becomes possible to extend the period of production. Given the subsistence fund K and given the technique of production, the shorter the period, the less productive it is. As long as K and N increase proportionately nothing will change. T and w will not be affected. But if K, for example, increases relatively to N, T or w or both will rise. Thus capital accumulation puts upward pressure on the level of wages and the average period of production. In this way, Böhm-Bawerk can be seen to have added a new dimension, a time dimension, to Ricardo’s theory of distribution. If T is taken to be constant (as with Smith and Ricardo), a datum of the constant technique of production, then the classical conclusion of an inverse variation between the wage and profit rates and the earnings of labor and capital follows.

Further Considerations: Value, Labor, and Equilibrium

Consideration of Böhm-Bawerk’s work as reducible to symbolic, quantitative representation illuminates some further interesting aspects of period-of-production analysis. Although he previously denied that this was possible, Böhm-Bawerk has been interpreted as proposing the average period of production construct in order to provide a purely physical measure of capital. As we have noted, this involves finessing the qualitative aspects of labor and land. But it also ignores the heterogeneity of outputs. Essentially it assumes either that the mix of outputs is fixed, or that production techniques for the different commodities are identical and fixed, or that only one output is produced. Whichever it is, since these assumptions violate the essence of an economy where exchange plays a role in determining value, these considerations suggest (1) the impossibility of a purely physical measure of capital, (2) the lack of validity of the labor theory of value, and (3) the limitations of equilibrium analysis.

1. The impossibility of a purely physical measure of capital. Actually, at an early stage Böhm-Bawerk’s critics pointed out that, even in his simple case of one output and one input (labor), it is impossible to obtain a purely physical measure when the role of implicit interest is considered. Böhm-Bawerk purportedly showed that if output is produced by homogeneous labor time over a period of time in a continuous and unchanging fashion, then the accumulated value of that output can be calculated as a weighted average of that labor time. Implicit in this is the idea that capital acts as a subsistence fund which has the appropriate time structure to feed the necessary labor. That is, the “right” amount of subsistence is available at exactly the right time to sustain the labor necessary at each moment in time. Now, if there are alternative uses for this subsistence fund, we must conceive of it earning at least a return equal to its next best use. That is to say, the subsistence fund can be imagined to be earning interest over time. When this interest is calculated as simple interest, accruing only once every period, it can be easily shown that it cancels out of the formula for T, but when it is accrued continuously, as compound interest, as it should be, then the formula for T depends on the rate of interest (see, for example, Lutz 1967:20–21).¹² Since Böhm-Bawerk used the size of the capital stock as a determinant of the rate of interest, showing that the former depended on the latter seemed to involve catching Böhm-Bawerk in a hopeless circularity. The unsurprising truth is that the search for a purely physical measure of the capital stock was hopeless from the beginning. This was to be belabored later by the Cambridge (England) capital theorists who pointed to the fact that (in part) the distribution of wealth determined the relative prices of outputs, and particularly determined the level of wages relative to profits. So if the rate of profit equals the rate of interest which enters into the value of the capital stock, then the latter is not independent of the distribution of wealth. Thus the same physical quantities of various capital goods will not have a unique value. And, according to the Cambridge neo-Ricardians, since capital thus cannot be measured in purely physical terms, the notion of its marginal product is meaningless and its earnings are thus left unexplained. We shall consider this further in due course.

2. The lack of validity of the labor theory of value. This question, having been dealt with adequately in the literature, need not detain us too long (see, for example, Hausman 1981:17–20). Significant for our purposes is the role of time. If two processes of production have identical labor inputs at identical moments in time, but one must be allowed some extra time to “mature” (like glue drying, or wine aging), how can we say that nevertheless they have the same value? If resources other than labor, for example, physical space, are needed over time, and these resources have alternative uses, then the extra time taken will mean that the output requiring more “pure time” will command a higher value in the market if it is to be produced. Time itself does nothing, but production that occurs over time (naturally or with the aid of original non-labor resources) has a value unaccounted for by the labor theory of value. This criticism could perhaps be deflected by a reformulation in which all original inputs are “suitably” valued. As such it amounts to offering a “cost of production” theory of value and goes to the heart not only of issues of prime concern to capital, but also of issues of the entire corpus of economic theory. For our purposes we merely note that “cost of production” can only be said to “determine” value in some sense when equilibrium exists, that is, when the value of the output in the market is (as expected) exactly equal to all the payments to the inputs. There can be no capital gains and losses. This brings us then to our third observation.

3. The limitations of equilibrium analysis. The symbolic representation of Böhm-Bawerkian analysis and the criticisms that surround it only make sense in an equilibrium context. By this we mean a context in which production occurs in a continuous and unchanging fashion over time. There can be no disappointments regarding the production process. Production plans must be explicit and must dovetail. If this were not the case—if producers, for example, had different conceptions of what constituted the “correct” method of production—we could not speak sensibly of an average period of production to be computed from a consideration of input requirements. At the very least there would be as many such average periods as there were opinions. Similarly, and even more relevant, there can be no innovations in production methods that render resources obsolete (in whole or in part). Every such innovation changes the pattern of inputs and the average period of production implicit in the equilibrium situation appropriate to it. We may wonder what relevance this retains in a world in which a large part of the process of capital accumulation is associated with technological innovation. This is something that will occupy us at some length.

Conclusion: The Many Faces of Austrian (Böhm-Bawerkian) Capital Theory

Austrian capital theory has become synonymous in the literature with Böhm-Bawerkian capital theory. Ricardians, neoclassicals, and modern Austrians find much with which they can agree and from which they can draw in Böhm-Bawerk. But they are not the same things. Both the Ricardians and neoclassicals focus on some of the technical questions that surround Böhm-Bawerk’s empirical insights on the greater productivity of roundabout methods of production. And they interpret these within an equilibrium framework. The modern Austrian (market process) theorists, following Mises, Hayek, Lachmann, Kirzner, and Rothbard (and also Fetter), focus on some of Böhm-Bawerk’s less formal pronouncements and draw some crucial insights from them. In particular these involve the role of time in production and the nature of profits and interest. We shall examine this below. But first we must take note of some developments arising out of these various interpretations of Böhm-Bawerk, notably growth theory and neo-Ricardian distribution theory.

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¹This is obviously not meant as a detailed or complete history of thought in capital theory. Such a project would require a separate, and probably much longer, work. What follows here is simply a highlighting of certain ideas in their historical context.

²This “model,” described below, is derived by Hicks from Smith’s Wealth of Nations, (1982) book II, ch. III, “Of the Accumulation of Capital, or of Productive and Unproductive Labor.”

³“It is worth emphasizing . . . that Smith’s concern with economic growth takes us back in a sense to the oldest part of the edifice, namely his treatment of the division of labor, the point being that the increasing size of the market gives greater scope to this institution, thus enhancing the possibilities for expansion, which are further stimulated by technical change in the shape of the flow of invention” (general introduction in Smith 1982:31).

⁴But see Ahiakpor (1997).

⁵Smith’s discussion of interest (book II, ch. IV) makes it clear that he considers interest to be something different from profits. We shall return to this question below.

⁶This statement relates to Böhm-Bawerk’s work on capital. His work on interest theory was clearly an advance and marks the beginning of the pure time preference theory of interest to be dealt with below.

⁷“However much he denied any adherence to classical cost theories of value, his view of production and the role of capital and time bear the mark of the Ricardian tradition” (Hennings 1987a:104; also Hennings 1987c). See also Hennings (1987b:114–115) and Hennings (1997:ch. 8). Yet consider this same theorist’s capsule assessment:

A leading member of the Austrian School, he was one of the main propagators of neoclassical economic theory and did much to help it attain its dominance over classical economic theory. His name is primarily associated with the Austrian theory of capital and a particular theory of interest. But his prime achievement is the formulation of an intertemporal theory of value.

(Hennings 1987a:97, italics added)

Says Kregel (1976:28–29), “Böhm-Bawerk’s role in the Austrian theory was to combine the Ricardian approach to capital in terms of labor and time with the ‘new’ marginal approach to pricing through utility.”

⁸In the special case where there is an even flow on inputs so that the same amount of labor time, l₀, is applied in each period, (n - t)l_t = (1/2) n (n + 1) l₀ and l_t = nl₀ and therefore T =n/2 + 1/2 or simply n/2 (when n is large enough so that the 1/2 can be ignored, or when T is expressed in continuous time where it is absent). So, when inputs occur at the same rate over time, each unit is “locked up” on average for half the length of the production period.

⁹It should also be clear that this formula does not allow for a unique or monotonic expression of “roundaboutness.” In other words, (a) this measure may yield a number that is consistent with an infinite number of input patterns, different amounts of labor time occurring sooner or later in the process, and (b) when considerations involving interest are included, this measure may not rise or fall uniformly in any ranking of roundaboutness as we add labor-time units at various points; it may change direction (in its ranking) at some points under certain conditions if we change the inputs at various points in the production process. These types of considerations played an important role in later criticisms of any attempt to measure capital in physical terms in the Cambridge debates which we will examine below.

¹⁰In this case, as in many others, “production” consists in harnessing the processes of natural biological growth for economic purposes. These were the first, and in some ways are the most fundamental, capital processes. Consequently much economic theorizing about capital proceeds from these first cases to argue by extension and, more often, by analogy to other, more complex cases.

¹¹In this example “consumption” is equated with the harvesting of trees. Of course, in reality, trees are inputs for further production processes that result in consumption at a later date; for example, the manufacture of pencils. The essential point, however, is that the woodlot example above provides a case of perfectly synchronized inputs and outputs that, in principle, could characterize other processes where inputs lead ultimately to consumption. Once such a process is completely established and becomes “permanent,” an endless and unchanging succession of inputs and outputs results, making it appear that production and consumption are indeed simultaneous. As explained in the text, however, this way of looking at the world is superficially valid only as long as there are no changes in the patterns of consumption and production. At any point of time, in any real capital-using economy, the capital structure that exists will be only partially adapted to the ever changing pattern of consumption.

¹²This can be easily seen as follows. If l units of productive inputs are applied in the first and the second periods and if only simple interest is considered, then we may use the equation 2l(1 + Tr) = l(1 + 2r) + l(1 + r) where r is the rate of interest to solve for the unknown average period of production T. This gives 1.5 units, which is the same value as yielded by Böhm-Bawerk’s formula, (1 + 2l) / 2l. Using compound interest, however, the equation changes to 2l(1 + r)^T = l(1 + r)² + l(1 + r). If we solve this for T we get T = (ln(2+3r+r²)-ln2)/ln(l+r) which contains the rate of interest, r (Lutz 1967:20–21).