2. Stocks and Flows

CHAPTER TWO

STOCKS AND FLOWS

Despite the controversies surrounding the definition of capital, there seems, Haavelmo found, “to be at least one aspect of capital which is not very controversial: That capital must have the dimensions of a stock concept, something at a point of time, t, and not something per unit of time.”[1] As Haavelmo points out, here the agreement on definition ends. Nonetheless the concept of capital as a stock as distinct from other economic variables, that are flows, has played a more important role in some approaches to the capital notion than it has in others. This chapter is particularly concerned with these approaches, and will appraise them from the vantage point of the capital concept developed in the preceding chapter.

Our concept of capital too, it will have been observed, sees it as a stock, not a flow. However, the stock of capital is, on our view, seen as the planned outcome of a series of past activities (“flows”) and, at the same time, is seen as the basis of plans already (at least partly) formulated for a future series of activities (“flows”). One of the characteristics of some of the alternative approaches which stress the “stock” character of capital, is that they employ this “stock” character to permit the analysis of the role of capital in static economic models. In other words, because capital itself is not something per unit of time, it is seen as being able to be assimilated into models of the economic system in which no time is permitted to elapse, or at least in which time-subscripts do not matter.[2] It is the “timeless” character thus attributed to capital which has enabled these writers to deal with the problem that Hicks has recently described as: “how is capital to be fitted in to a static theory?”[3]

The “Presence” of Capital Stocks

What is characteristic of these latter approaches is that they admit capital goods into the production function by viewing production as depending simultaneously on two kinds of inputs, flow inputs and stock inputs. Output results, in this view, from the application of service flows, in the presence of stocks of capital. Capital contributes to the process of production by its presence. Vernon Smith sees the “distinguishing characteristic of capital goods” to be “simply that their presence, in the form of physical stocks, is required if production is to take place.”[4] Haavelmo, dwelling on the stock character of capital, draws from it the “fundamental conclusion” that the influence of capital on output is “due to capital being present in the process and not to the fact that certain parts of it are used up in the process.”[5] This way of looking at things, Haavelmo believes, removes “the mystery of stored-up land and labor from the definition of instruments of production.”[6] (Enke, going even further, insists on the possibility of treating production functions as “instantaneous relations” in which all inputs are treated as stocks.[7])

In this approach, it will be observed, it is the durability of capital goods that is being emphasized. Other inputs, it is being pointed out, contribute to production by being “used up.” The essence of capital goods, on the other hand, is seen in their remaining extant even after their “presence” has enabled the “flow” inputs to be transformed into output. The capital goods have, through their presence, provided “services” (without themselves losing any of their potential to provide such services in the future). These “services” may be viewed as flowing, as being “used up,” but these services are provided by the mere presence of something that is itself not used up by their creation.

It is to be noted that this way of looking at the productive role of capital goods represents, not so much an application of their “stock” character, as a (rather dubious) extension of this feature. It is one thing to notice that capital goods exist at a point in time. It is quite another thing to see the productive usefulness of these goods as consisting in their mere existence. The view that sees the role of capital goods as consisting in their mere presence, implies not only that capital goods exist, but that their continued existence over time is completely unaffected by the productive contribution which they make. If, as it may be claimed in its defense, this view of the role of capital goods depends on exclusive concentration upon a given instant, then it has been secured at the price of all the important insights that the recognition of multi-period planning can confer. The crux of the matter seems to depend, we will attempt to show, on the way one looks at the production function.

A production function can be looked at “positively”. As such it represents simply a set of technological relationships. On the other hand, a production function can be looked at as representing opportunities, from among which a human being is able to make a choice. Clearly an economics in which market events are seen as the results of deliberately planned actions, ought to view production possibilities, in this second way, as alternatives from among which planned courses of action may be constructed.[8]

Now, on the first view on the production function, (i.e., from a purely technological point of view), there is nothing to deter us from considering thinner and thinner slices of time. We can observe the inputs fed into a process of production during any short period of time, and observe the outputs yielded during this interval. By choosing a sufficiently short interval we can certainly arrive at short processes of production in which, as far as can be observed, part of the yield is to be ascribed merely to the “presence” of certain things, which emerge at the end of the interval in apparently the same form in which they entered the process.

But if we look at a production function from a “planning” or “decision-making” point of view, matters are quite different. We are no longer at liberty to select arbitrarily any interval of time we choose, and to consider it entirely on its own. We are forced to recognize that the plans that men make are multi-period plans. If we select arbitrarily a slice out of the overall span of time envisaged for a multi-period plan, we must be prepared to concede that this slice represents only a portion of a plan. What has been planned for this slice of time cannot be understood unless taken within the context of the particular overall multi-period plan that is relevant.

It follows, then, on this “decision-making” view of the production function, that to treat capital goods as if they were permanent goods, when in fact they have been constructed as part of a plan in which they are to be ultimately used up, is a distortion that ought not to win acceptance merely because a sufficiently short period of time is being considered. What may be acceptable as a technological description of what goes on in a selected short period of time, is grossly unsatisfactory as an economic description—that is, as a description of the course of events in terms of relevant human decisions that have been made.

This difference between what may be acceptable as a technological description, and what is required for the economic description, can be perceived perhaps more clearly by considering a succession of thin slices of time taken together. Let us suppose that the aggregate interval of time is long enough for a capital good to have reached the end of its working life and to have been replaced by another. Now from the positive, technological viewpoint, there can be no objection to a description of the process as having merely required at all times the “presence” of the capital good. And, taking in aggregate the above technological descriptions of what takes place in each of the thin time-slices, this is in fact the total picture obtained. And yet, from the point of view of the decision maker, what has taken place is far more complicated. Originally the capital good was acquired, in full awareness of its prospective working life, as well as the associated maintenance and operating costs on the one hand, and annual output on the other hand. The capital good was acquired with the intention of “using it up” over its life time, in the production of output. Clearly the economic descriptions of what takes place during the various thin time-slices must be capable, at least, of being pieced together into an overall story that does not run in flat contradiction to the economic facts. To do otherwise is to force the description of economic events into a mould no longer suited for economic analysis, i.e. a mould in which events are perceived, not as parts of plans, but as arbitrarily-cut slices of history “positively” considered.

Stock Demand and Flow Demand

Nothing that has been written in these pages should, it is hoped, be understood as necessarily implying criticism of the distinction frequently drawn between “stock demand” and “flow demand,” in respect to capital goods. This latter distinction is invoked in analyses of the market forces operating upon the prices of capital goods. It is argued that capital goods involve two kinds of market situation. On the one hand, the stock of capital goods at a given date is a datum, and can be expected to be altered only gradually. This characterizes the market for existing capital goods as one for a good that is virtually not able to be produced nor destroyed at all, so that its supply curve is perfectly inelastic. On the other hand, given sufficient time, new capital goods can be produced, and existing ones depleted through current use. So that alongside the market forces relevant to capital goods treated as a given stock, there are operative the market forces relevant to these goods treated as flows. Recognition of these two sets of interacting forces, it is claimed, provides insight into the process of capital goods accumulation and pricing.[9]

Now this Clower approach, like those discussed in the preceding section, depends on the notion of a given size of stock of capital goods, at a given time. Moreover, this approach is able to integrate these two sets of market forces pertaining to capital goods only by assuming that the “flows” of capital goods during a single short time period are small enough to permit the analysis of the price of existing capital goods just as if this stock was, in fact, unaltered in size during the period. In other words, this approach, like the approaches criticized in the preceding section, assumes (at least at one level of discussion) that capital goods are not “used up” during small periods of time. Nonetheless the criticisms of the preceding section do not apply to this approach.

One may indeed entertain doubts concerning an analysis in which the simultaneous critical assumptions are that the stock of capital goods is, and that it is not, constant during the passage of a period of time.[10] But we can find little to quarrel with in the assumption of an unchanging capital stock itself, in this context. What the Clower approach is saying is merely that two kinds of (interacting) adjustments are taking place on the capital goods market: (a) adjustments primarily affecting the prices of given goods, and (b) adjustments in the flows of these goods into and out of the sphere of production. Clower chooses to polarize these two kinds of adjustment by talking as if the first kind of adjustment was able to be carried on as if there were no second kind of adjustment at all. The assumed constancy of the capital stock is thus a simplifying one, that does not affect the essence of what is being discussed. It does not imply that capital goods are not used up during the processes of production to which they contribute, (after all the whole purpose of the analysis was to integrate the theory of capital goods being used up, with that of the stock of existing goods). On the other hand, the approaches criticized in the preceding section, emphasize the constancy of the capital stock because, on these approaches, it is of the essence of capital goods that their contribution to production leave these good intact; capital goods are not used up in production.

Are Capital Goods “Used Up” in Production?

We have seen that the Smith-Haavelmo approach to short run analysis is to treat capital as if it were, unlike other inputs, not “used up” during production. For some capital theorists such a treatment would be to rob capital of one of its essential features. For Hayek, for example, a definition of capital must exclude “permanent resources” from the capital category. It is for Hayek of the essence of capital that it is comprised of resources that have limited life.[11] On the other hand for Lachmann the capital category is broad enough to include resources that never become used up,[12] although, even for short run, this property is certainly not seen as the crucial capital criterion. For the approach outlined in the preceding chapter, again, whether or not resources are “permanent” is not of first importance; but, on the other hand, where a multi-period plan of production does envisage the using up of resources over time, then, as we have seen, this approach insists that this aspect of the plan not be suppressed. The differences between these various approaches to the question of handling the using up of capital goods during production, is brought out very sharply in the various treatments accorded to the notion of depreciation.

Haavelmo cites the views that the “input” from a capital good is simply its rate of depreciation. For Haavelmo this idea is “very dangerous and misleading,” and, from the point of view of production theory, “hopeless.”[13] Elsewhere he describes this idea more mildly as not perhaps “entirely hopeless” in itself, “but as unnecessarily complicated from a technological point of view.”[14] It results, Haavelmo thinks, from a natural tendency to ask what it is that “goes in” in order that the additional product made possible by capital goods should “come out.” And, as we have seen, this is, for Haavelmo, an inappropriate question with respect to capital goods. Capital goods play a role in production by merely being present and yielding a flow of “services” during each period of time. There are many processes of production in which depreciation is very slight indeed in comparison to output. This suggests, Haavelmo argues, that for something to “come out” of a capital-using process of production it is not really necessary at all for anything of the capital to “go in”. Additional output may be technologically attainable merely by adding the presence of a catalyst, in the form of capital goods. So that even if depreciation of these goods does occur during the course of a process of production, it is wrong to consider this depreciation as the relevant “input.” Thus for Haavelmo an isoquant map describing a capital-using process may not be assigned an axis measuring the physical deterioration of capital as one of the inputs.

Enke, too, insists on using a production function in which the presence of capital goods, (not their physical deterioration), is relevant to the level of output. However, Enke demands that, for the determination of the optimum mix of capital goods and other factors of production, the cost of capital goods include, besides the interest or rental charge involved, also an item for what he labels “time depreciation.” “Time depreciation” during a period of time, is a function of the stock of real capital employed, in contrast to “use deterioration” which is a function of output quantity. Use deterioration of capital goods does not affect the cost of using larger or smaller stocks of capital, and hence does not effect the marginal choice between capital and other (non-capital) means of production.[15] In fact, for Enke, use deterioration, while a genuine input, has really nothing to do with the “capitalistic” aspect of a production process at all; use deterioration is a flow input, capital is stocked. On the other hand the presence of capital stocks does involve time depreciation, and this does affect the optimum combination of capital goods and other means of production. Enke is thus able to define capital in such a way as to distinguish sharply between the employment of capital stocks on the one hand, and the non-capital flow input constituted by the use-deterioration of stocked capital goods on the other. While treating capital goods as means of production by virtue of their presence (as Haavelmo does), Enke yet insists that the cost of the presence of these goods include an item to cover their time depreciation.

Enke’s argument insisting on the need to allow for time depreciation in the cost calculations involved in the determination of the optimum capital-labor mix, affords a further useful opportunity to notice the two ways of looking at the production function, that were mentioned earlier. A production function can be seen as a positive statement of technological relationships, or it can be seen as presenting a set of opportunities relevant to prospective planning. Corresponding to these two views on the production function are two ways of looking at the optimum factor combination obtained by comparing an isoquant map with an isocost line. We have seen that, on the second, “planning” view of the production function, this function must be constructed within an explicit time framework relevant to multi-period planning. On the other hand, we found, on the “positive” view, a production function can be constructed in principle for arbitrarily-cut slices of time, no matter how thin. Now, on the latter “positive” view, the minimization of cost that is required for the optimum factor combination must involve those items of cost that seem technologically relevant to that portion of the process of production under consideration during the arbitrarily thin slice of time. Since the time-slice may not be relevant to any plan whatsoever, the “cost” (associated with the corresponding portion of the process of production) may not be in the nature of an opportunity cost altogether. If no plan is relevant, there can be no question of foregone alternatives, of genuine economic cost. All that is possible is a technological concept of cost, for the determination of which the accountant will seek to assign a value to what has been used up during the time slice. It is for this reason that for Enke the deterioration in capital stocks that has occurred during this time slice (purely as a result of the passage of time) must be charged as part of the cost of commanding the productive “presence” of these stocks during this time.

But on the “planning” view of the production function this treatment is not at all appropriate. The optimum factor combination, on this view, represents one particular course of action (out of the many courses of action that make up the production function), that appears optimal to the producer planning his future activities. For the producer who is contemplating alternative multi-period courses of action, therefore, an optimum factor combination can exist only in the context of a production function that is itself multi-period in scope. One can ask what the optimum capital-labor combination is, only at times when the producer is able to vary their combination, i.e. when he is forced to decide which combination to adopt in his production plan. If, for example, the producer has already invested in particular specific and immobile capital goods, then the search for the optimum capital-labor mix does not have to take account of the cost of these capital goods, insofar as they represent sunk, irretrievable investment. For a producer in this position, therefore, time-depreciation is quite irrelevant; in fact, interest charges on the investment will be equally irrelevant. (Insofar as varying intensity of use affects the durability of the capital goods, of course, then “user cost” will certainly be relevant, but this is different from depreciation.) On the other hand, if the capital goods have not yet been acquired, then of course time depreciation is a relevant cost; but the entire picture is now one in which the term “depreciation” hardly has a place. If we consider the decision maker before he has acquired capital goods then his decision involves a comparison between alternative multi-period projects. A relevant aspect of any such project will of course be the rate at which capital stocks will deteriorate, and will require maintenance and/or replacement expenses in order to be maintained intact. (In this “long-run” context, indeed, the sharp distinction drawn by Enke between use deterioration and time depreciation, seems quite unimportant.)

Similar considerations apply to Haavelmo’s refusal to consider the input of capital goods as consisting of their depreciation. To the economist “input” refers to what the producer must plan to apply to a process of production. From the multi-period planning viewpoint it hardly makes sense to focus attention separately upon one out of a large number of future periods of time. Certainly, if this one period is one for which the process of production will have been already irrevocably fixed by earlier multi-period decisions, there is little that can be said about it that is relevant to economic (as distinct from technological) considerations. On the other hand, on viewing prospectively a large number of such periods of time in succession, the “input” that is represented by particular capital goods certainly does appear as the investment that will be consumed over the lifetime of the goods, if their life is limited. In other words, for the “short run” Haavelmo would be right to ignore depreciation, but wrong in discussing a capital using production function involving capital as an input, as if it were relevant to economic decision-making. On the other hand for the longer run, for which decisions with respect to capital goods are feasible, Haavelmo would be wrong to view the production process as one in which these goods are not used up, if in fact they are used up (and if this fact is taken into account by the long-run decision-makers). Only if capital goods were completely non-specific and perfectly mobile, would decision-making for the immediately following slice of time, however thin, be relevant at all times (during the course of a multi-period process of production) to the capital goods employed; only then would the Haavelmo-Enke arguments be genuinely relevant.

Hicks and the Stock-Flow Production Function: A Digression

Our discussion of the Smith-Haavelmo use of stock-flow production functions, (in which the inputs are flows of labor services in the presence of stocks of capital goods) and our criticism of this notion, makes it of interest to digress briefly to consider a different kind of stock-flow production function that has been employed by Professor Hicks.[16]

Hicks explicitly attempts to construct a production function that should correspond to production processes that take time. To do this he considers a period of time, and notices that at the beginning of the period there exists an initial capital stock, while at the end of the period a closing stock of capital is left over. During the period there are applied flow inputs, and there emerges a flow output. The relevant inputs, argues Hicks, are thus the initial stock of capital and the flow inputs applied during the period. The outputs are the flows emerging during the period, and the stock of capital remaining over at the end. Between these four items (flow inputs, stock inputs, flow outputs, stock outputs) there will exist, with given technique, a production relation that can be expressed as the production function.

It is apparent that Hicks’ stocks of capital play a quite different role in his stock-flow production functions than do those of Smith or of Haavelmo. For the latter the importance of treating capital as a stock consists in that this enables the process of production to be viewed as one in which capital goods contribute to production without being themselves used up. For Hicks this is not at all the case. On the contrary, he sees the change that occurs in the stock of capital goods between the start and the close of the period as an important aspect of the production process, treating the initial stock as an input, and the closing stock as an output. For Hicks the stock character of capital is relevant merely because a “balance sheet” is drawn up at the start and at the close of the period. At given dates there exist particular stocks of capital; during the intervening period flows of inputs and outputs occur. Hicks’ time-conscious production function embraces both sets of elements.

In fact Hicks’ production function is vastly superior to that of Smith and Haavelmo precisely in its attempt to represent the period of time that a production process requires. It might even at first glance appear that Hicks’ production function is identical with that which we have called for in this chapter in order that the function be relevant to multi-period planning. The decision-maker contemplating a particular multi-period plan is contemplating, just as Hicks describes, the application of an initial stock of resources in conjunction with subsequent additional applications of inputs. It might seem that Hicks has provided us with just the tool that we have been asking for.

This, however, is not the case; Hicks’ production function, while not an “instantaneous” function (and thus certainly superior to the Smith-Haavelmo apparatus), is easily seen to be cast on what we have termed “positive” (rather than economic) lines. This is apparent when Hicks discusses the time-shapes of the flow inputs and outputs during the period of the production process. Hicks shows little compunction in principle to slicing up time into thinner and thinner slices; it is apparently of little moment that the resulting production processes, despite their taking up time, are nonetheless merely arbitrary segments of the process as a whole (that is relevant to multi-period planning).[17]

Capital Stocks and Income Flows

Any discussion of capital in which its “stock” character is emphasized, must sooner or later come to deal with the distinctive concept of capital that is associated with Knight and his followers. Professor Knight’s theory of capital will be of particular concern to us in the succeeding chapter; in the present chapter we refer to this theory only insofar as it impinges directly on the stock concept that has been associated with capital.

Knight’s view of the economic process is well-known. Of prime importance to this view is the sharp distinction that is drawn between agencies that render service, and the services so rendered. “What is in fact consumed in economic life is exclusively services, and accordingly, the primary meaning of production is the rendering of service.”[18] Unlike the agencies that render service, services themselves do not “exist” apart from their flow in time. Capital goods are simply the sources of streams of service. The latter have existence only as flows in time; capital goods exist at particular points in time. Capital goods are stocks, service streams are flows.

Moreover, by viewing capital goods as sources of flows of services, Knight is able to focus attention on an element common to all such goods (and to Knight both land and labor are to be included along with productive instruments, as capital). The element that is common to all agents of production is that they constitute “sources” of future service flows. Capitalization of the yield of a source of future service flows provides us with the value of the source.

By paying especial attention to the case in which a “source” yields a perpetual steady flow of services (after deducting an amount sufficient to maintain the source itself at all times), Knight is able to go even further. Any instrument of production is perceived as a “fund” of capital, a fund from which there is able to flow such a perpetual steady flow of services. Productive plant “is measured by the perpetual service income which it can be counted upon to yield. In other words, plant itself, in its quantitative aspect, is perpetual (regardless of changes in physical form), except for a possible net disinvestment in society as a whole. . . . Quantitatively speaking, any two pieces or items of wealth are to be compared as perpetual incomes. . . .”[19]

It is important to notice the distinctive features in Knight’s conception of capital as a stock, (as opposed to a flow). These features set Knight’s approach apart from that of Haavelmo and Smith discussed earlier (despite some superficial similarities); they set Knight’s approach completely apart from that developed in the first chapter of this essay; in fact the distinction that exists for Knight between stock and flow is quite different from all the other means by which stocks and flows are kept separate by writers on capital theory.

For Haavelmo and Smith capital was stocked in the sense that producers required the presence of capital goods without necessarily using them up, in order to raise the output obtainable from the application of flow inputs. For the approach outlined in the first chapter of this essay, capital goods are a stock, because they are what is found when the state of an unfinished project is appraised as of a particular date. Similarly for Hicks, as cited in the preceding section, capital goods are a stock because they are found when a balance sheet of an economic system (or a segment thereof) is drawn as of a particular date. For Fisher or for Fraser, discussing the possibility of defining capital, as Knight himself in fact does, so broadly that all items of wealth may be part of capital, capital is yet not the same as wealth: capital is wealth looked at from a particular point of view; it is the fund of wealth available at a given moment, as opposed to the flow of wealth produced and consumed during a given period.[20] The distinction between fund and flow that is for Knight of first importance in the theory of capital, is quite different from those relevant to these various points of view.

For Knight a special significance attaches to exchange transactions in which a perpetual flow of service is exchanged for an agency which is able (through judicious earmarking, out of the gross yield, of maintenance and replacement reserves) to act as a source of such a perpetual flow. The capital market has the function of ensuring a tendency for such transactions to be carried out on terms in which the rate of discount equates the capitalized values of the future streams of services to the costs of production of the agencies. In a perfect capital market any stream of services of whatever time-shape can be exchanged for a perpetual steady stream at the equilibrium rate of discounting. So that, as already observed, each instrument of production can be viewed as embodying the power to generate a particular perpetual service flow. It is this relationship between agencies, or sources, of perpetual steady service flows, on the one hand, and these service flows themselves on the other hand, that represents for Knight the relevant aspect of the stock-flow dichotomy. The economic world at any given time consists of a stock of “things” each of which is to be viewed as a potential source of a perpetual steady flow of services to be consumed. As of different dates an economy will possess different sizes of capital stocks, as a result of investment or disinvestment. At any one date the potential perpetual flows of future services are represented by the existence of the sources capable of yielding these flows. Capital is the fund from which an endless stream of future income can be drawn.

Knight and the Permanence of Capital

It will be observed that an essential element in the foregoing capital-income scheme is the postulated permanence of capital. Despite the fact that individual instruments of production have only finite productive lives, the capital that is embodied in these instruments is conceived of as permanent: when an instrument “dies” the capital that was embodied in it continues to have existence in the instruments that replace it (these replacements being made possible by the accumulated depreciation allowances set aside from the gross yield of the first instrument). It is only this notion of the permanence of capital that enables a particular instrument of production to be viewed as the source of a perpetual steady flow of services.

The permanence of capital as viewed by Knight is, however, not to be confused with the treatment of capital goods at the hands of Smith or of Haavelmo. The latter choose to look upon capital goods as not being used up in production; they are referring to particular instruments of production, and they find it convenient to treat them, when thin time slices are being considered, as if their contribution to processes of production left them in unaltered condition. Knight is not referring at all to particular instruments of production when he asserts the permanence of capital; he is referring to the abstract capital embodied in these particular instruments. Nonetheless, the Smith-Haavelmo approach does possess aspects of similarity to that of Knight. Some of these aspects are of relevance to the matters to be discussed in the succeeding chapter of this essay. Insofar as the present chapter is concerned, the significant similarity is that both approaches look upon capital goods as sources of service flows. For the Smith-Haavelmo view it is convenient to imagine that particular instruments of production are capable (at least for short periods) of rendering services without themselves being used up. For Knight the capital embodied in a particular instrument of production is capable of generating an income flow indefinitely without impairing its capacity to generate further income, because adequate “maintenance” (under which category Knight includes what is generally considered “re-placement”) can indefinitely “prolong the life” of the agent. (While expositions of Knightian capital theory are sometimes couched in language suggesting that particular agents themselves are permanent in the sense of not being used up in production, this is merely a loose way of referring to the permanence of the abstract capital which, in the Knightian view, is embodied in particular instruments.)

Knight’s emphasis on this permanence of capital has been repeatedly attacked as “mystical” or as involving “mythology.”[21] In a famous paper[22] Hayek, especially, has attacked the notion of a homogeneous fund of abstract capital represented by the particular heterogeneous non-permanent resources available at a given date, and the idea that such a “fund” can be transformed from one concrete form into another. Fraser has written of the pure mysticism of Knight’s view that the capital invested in particular non-permanent instruments of production is “a kind of substance or vital spark” that lives on after they are used up or disposed of.[23]

Some of the “mysticism” of the Knightian position has been removed by recognizing its assertion of the permanence of capital to be no more than a figure of speech suggested by the economics of the case Knight considers to be typical. In Kaldor’s words, “investing in 30 houses, one of which falls due for replacement and is planned to be replaced every year ad infinitum, is the same thing as investing in a house which lasts forever, while a certain sum has to be paid out each year to keep it in repair.”[24] Or, as Dorfman puts it, the Knightian position merely asserts tautologously “that under stationary conditions every capital item entails an obligation for perpetual replacement.”[25]

The purpose of employing this figure of speech is clearly that of being able to focus attention on the source-flow dichotomy noticed in the previous pages. So long, the Knightian position would maintain, as economists allow themselves to be preoccupied with the petty problems associated with the limited lives of particular bits of equipment, they cannot hope to be able to stand back and glimpse the underlying long run economic relationships that transcend the lives of these specific pieces of equipment. For the Knightian position the important feature associated with the holding of a piece of productive equipment is that possession now of this “thing,” confers command of a perpetual flow of services; this piece of equipment can be seen as the source of a never-ending stream. This insight is reinforced by the cultivation of a manner of speech in which attention is. withdrawn from the concrete, short-lived bit of equipment itself, and turned instead on the abstract “capital” which it may be considered to represent—a capital which, in the above figurative sense, can be viewed as permanent.

The Knightian position thus views the world, and the continuing course of economic events in this world, in a very special way in which the stock-flow dichotomy plays a decisive role. At any given time the world consists of a collection of things. As time proceeds men draw streams of output by virtue of their possession and judicious maintenance of these things (such maintenance being made possible by the streams of gross output themselves). Nothing is required for the enjoyment of these streams of output except the maintenance of these things. No flows of input have to be applied from outside the system; all possible flows of input, including labor, are seen as emanating from “things” that are possessed and maintained within the system. What an economy may consume over time depends merely on the collection of things that exists and is maintained. It is as if the course of economic events flowed automatically and effortlessly from the stock of things possessed—the only demand made on human decision-making being the requirement that at all times attention be given to allocating a sufficient fraction of the output flow for the maintenance of the capital stock. For an increase to occur in the stream of output, it is necessary to set aside a larger portion of current output for the creation of new resources.

We are not directly concerned in this essay with Knight’s productivity theory of interest (nor, for that matter, with any interest theory), but it is of significance to notice how the Knightian view of capital has built into itself the notion of a productivity rate. With all output being considered to flow automatically from the existing collection of resources, we have immediately the notion of a definite rate of flow of output in relation to the existing capital stock. In Knight’s view this rate depends on the aggregate stock of capital held at a particular time. The market process is relied upon to guarantee a tendency towards individual producers investing their capital in those ways that will exploit for each of them individually the productivity rate relevant to the economy at a particular time.[26] By these assumptions the Knightian position is thus able to look on each particular resource as a source for a future output stream that will flow at the universal productivity rate. The essence of capital theory, in this view, is the analysis of the way these relationships work themselves out through the market, determining interest rates, capital accumulation, the organization of production, and so on.

A Critique of the Knightian View

From the point of view of the present essay the fundamental objection to the Knightian way of looking at things is a very simple one. It has already been stated by Hayek in a footnote to his essay on the subject, cited in the previous section.[27] Hayek points out that an investment (through the sacrifice of a short segment of income flow) yields in the first place only another limited segment of income flow (of different time shape); and that “this limited income stream which is the result of the first investment becomes a permanent income stream only by an infinite series of further decisions when the opportunity of consuming more now and less in the future has to be considered every time. By jumping directly to the desired result, the permanent income stream, Professor Knight slurs over so much that is essential for an understanding of the process that any use of his concept of capital for an analysis of the rôle of this capital in the course of further changes becomes quite impossible.” This presents the objection admirably. The present section will dwell on this objection and attempt to relate it to the conceptual framework advanced in the first chapter of this essay.

It will be recalled that in that chapter the case was presented for a treatment of capital goods that should relate them specifically to a relevant system of production plans. Capital goods should be recognized in the first place as the interim result of as yet incompletely fulfilled plans of production formulated in the past. In the second place they should be recognized as playing a decisive role in any new production plans that may be formulated now (including under this heading the possible modification of the later stages of earlier plans not yet completely carried out). It was argued that the theory of the market proceeds by the analysis of individual decision-making and of the way in which individual plans have mutual impact upon one another. The appropriate way to study the role of capital in the economic process, it was therefore maintained, must be found in the similar analysis of the multi-period plans made in the market. Any concept of capital goods which fails to relate them to multi-period planning in the manner described, is thus of severely limited value for the explicit extension of the theory of the market to the course of economic events over time.

In conjunction with these principles it was also pointed out in the same chapter that the desired recognition of the planned character of capital goods might, nonetheless, lead to error. The assignment of function to particular capital goods (by making reference to the use which had originally been planned for these goods) might lead to overlooking the necessity for additional decision-making in the future. It might thus lead to a view that the presence of a good automatically guarantees the flow of services for the sake of which that good was originally produced. It was pointed out that where a steady level of production is maintained continuously for some time there exists a temptation to view the current maintenance of the stock of capital goods as input required for the production of current output. In other words there is a temptation to ignore the planned character of capital goods maintenance, to overlook the fact that capital goods maintenance is undertaken as part of a series of plans being made for the future—even if only to ensure that future output does not fall below current output. A failure to withstand this kind of temptation involves acceptance of the notion that the future will take care of itself so long as the present “sources” of future output flows are appropriately maintained. These kinds of temptations, it was further pointed out, become even more difficult to resist in a system where monetary calculation can be employed. The Knightian approach reflects perfectly the way in which this misleading and unhelpful notion of “automaticity” has been developed into a fully articulated and self-contained theory of capital.

In the Knightian view, indeed, the future course of production is completely determined by the present state of affairs. The instruments of production possessed now are the sources of future flows of output. Because all future inputs flows can, in this view, be seen as represented now by something (or some person) that serves as the source of these future flows, and because maintenance of these sources is seen as somehow a matter of mere routine calling for no particular decision-making, we are presented with a picture of the world in which the future is entirely capable of taking care of itself. The future flows automatically from or “grows” out of, the present. Professor Knight has himself given us a description of the simplified situation which, it seems, most faithfully mirrors the essential features of the real capital-using world as Knight sees it. Knight draws a picture of an economy, “Crusonia,” in which all that is consumed is obtained from “the natural growth of some perennial which grows indefinitely at a constant (geometric) rate, except as new tissue is cut away for consumption.”[28] This picture represents a number of abstractions from the real world. What is, from the point of view of the present essay, the most arresting and most objectionable of these abstractions, is that which portrays the flows of consumption “goods” in the model as forthcoming automatically (“growing”) from the capital stock on hand. No room is left for planning, for human decision-making, at the production level. All that is left subject to human decision is how much is to be consumed in each period. Once this has been decided, the future course of events inexorably follows.

What the Knightian view has chosen to do is thus to see the essential elements of the economic process that are relevant to a theory of capital as consisting in those aspects of the problem that do not involve multi-period planning at the level of production. For the purpose of the analysis which the Knightian theory of capital is designed to contribute we are asked to assume that the appropriate relevant plans will somehow be made. We are told in effect that these plans do not have to be explained; that once we have explained the present state of affairs, we have explained all that demands explanation in connection with the entire future course of events. From the point of view of the present essay, it is clear, the Knightian approach has, by this procedure, simply renounced claim to being able to offer an explanation of the course of economic events in a capital-using world. To repeat Hayek’s remark once again this concept of capital slurs “over so much that is essential for an undertaking of the process that any use of [it] for an analysis of the rôle of this capital in the course of further changes becomes quite impossible.”

Capital and Income

Our discussion of the Knightian view of capital as sources of perpetual service flows, leads us to reflect on the more general capital-income dichotomy. None of the criticisms leveled at the Knightian approach have any application, of course, to the validity of the capital-income concept as an accounting tool. A distinction between capital and income does not imply that the economic process in fact resembles an everlasting tree that spontaneously yields fruit every year (as the Knightian view chooses to imagine) but merely that someone wishes to distinguish between “the fund of wealth available at a given moment,” on the one hand, and “the flow of wealth produced and consumed during a given period” on the other hand.[29] The Knightian view has, in fact, illegitimately transferred these (superficially) smooth accounting concepts to a realm of discussion where they do not belong and where their use hides rather than reveals the true chains of cause and effect. Nonetheless critical attention from a capital theory perspective deserves to be paid to the capital-income dichotomy, especially from the point of view presented in this essay. We will discover that this will raise still further problems for the Knightian approach.

Economists have long struggled to formulate acceptable criteria for the distinction between capital and income.[30] Fisher chose to define income as equivalent to consumption. Of the gross output that rolls off the assembly lines during a given period, only that portion which is consumed during the current period should, Fisher argues, be termed current income. All the rest of the gross output consists of goods that will yield consumption services in future periods of time. They should be kept apart from current consumption. Fisher chooses to reserve the term “income” to denote only this latter category.

It is to be noted that both “gross output” and “consumption” are magnitudes that correspond to definite economic entities. It is true that neither the magnitude of gross output nor that of consumption can be known in advance (merely from a knowledge of the initial stock of capital goods) until the appropriate production and consumption decisions have been made. (And, indeed, critics have objected to the use of these magnitudes as measures of current welfare possibilities on the grounds that each of them depends somehow arbitrarily on the pattern of human decisions. Thus Kaldor objects to Fisher’s definition of income that it makes income depend on the saving-consumption decision.[31] Similarly Samuelson argues that gross output does not offer a measure of the current welfare possibilities created by production, because gross output is not a definite figure, it depends on the intensity with which one wishes to utilize the existing stock of capital goods.[32]) Nonetheless, at least ex post, both gross output and consumption have unambiguous economic meaning.

It is of interest, then, that neither of these two magnitudes has been generally accepted as an income concept. Gross output has been rejected because of the desire for a “net” concept, in the sense to be discussed below.[33] On the other hand, Fisher’s insistence on consumption as the appropriate income magnitude has not found favor because, as noted above, it does not provide a measure of the potential volume of consumption attainable (in the absence of a decision to save). Instead of these two unambiguous economic entities economists have generally searched for a definition of income that should equal “net output”. Most of the difficulties surrounding this search have to do with just what is wished to be intended by the “netness” of this latter term. We will discover that net output is a magnitude that corresponds to no well-defined economic category at all, but is imposed artificially upon an account of the actual course of economic events in order to fulfil a specific accounting motive that many people hold to be important.

Matters will be made clearest by referring to the Hicks-Hayek definition of income. This identifies income as the “level of consumption flow permanently attainable.”[34] It is the maximum amount one can consume during a period without making it impossible to maintain this level of consumption indefinitely. Gross output is rejected as the income category because if all of it were to be consumed this would mean that the capital goods that contributed to the production of this year’s gross output would no longer exist in intact form for next year’s process of production; next year’s output will be smaller. Consumption is similarly excluded, because a decision to consume very little will mean that one is consuming less than all that could be consumed without diminishing future consumption; such a case constitutes, in some sense which these writers are attempting to make precise, living below the standard set by one’s income. What is sought is a criterion by which to separate, out of a period’s gross output, that amount which must be ploughed back into the production process (if current production possibilities are to be maintained indefinitively) from the portion of gross output that can be consumed (without affecting the continued availability of current production possibilities).

The portion of gross output that is not net output in this sense, is thus that portion of it necessary to restore (or replace) depreciated equipment to their original quality, (so that next year’s initial stock of capital goods be not smaller in any way than that of the current year). Intact maintenance of capital requires that this difference between gross and net output, not be consumed. Consumption of any portion of this difference must be considered consumption of capital, not consumption of income. Such consumption of capital constitutes “living beyond one’s income;” one is consuming now at the expense of being able to maintain a steady level of consumption over future periods of time.

Useful as such a net output, or income, concept undoubtedly is, it is for the purposes of this essay important to point out that there is no natural economic magnitude that emerges from the description of the economic process which can be identified with the concept. Net output, or income, does not constitute a well-defined economic pie in its own right, (such as gross output is, or as consumption is), it is an arbitrarily-cut slice of a larger pie.

Economists have long noted the arbitrariness of the capital-income distinction. There is nothing that makes it more natural to seek to maintain a steady income than to seek an income stream of different time shape. So that there is no particular a priori importance that is attached to the accounting criterion for the determination of the size of the portion of gross output necessary to maintain capital.[35] But there is still a further difficulty that, from the point of view of this essay, calls for special emphasis.

This difficulty has to do with the notion of “constant income” Hayek alludes to some of the difficulties involved. In order “to give the concept of a constant income stream an objective meaning,” he observes, it is necessary “to postulate identity of tastes at successive moments.”[36] This is required not only in the sense that relative preferences remain comparable from year to year, but also in the sense that the absolute satisfaction derived from one year’s income is the same as that derived from that of any other year. It is not enough to say that an income stream is constant if, looking forward to it ex ante from a given date, one feels indifferent as to the sequence of the component elements of the stream. Such a statement has to do with time preference, it does not have relevance to the concept of an income flow that should enable “the level of total satisfaction . . . to be maintained constant throughout.”[37] What is looked for is a criterion that should enable one to say that someone is rendered as well-off by this year’s income as he was by last year’s. We have somehow to compare the actual satisfaction derived this year from this year’s income with that derived last year from last year’s.

This raises what appear to be insuperable difficulties. Economic analysis is never couched in terms that involve the comparison of satisfactions between which an individual is not free to choose. An individual may be free to choose today between prospective income flows of different time shapes. He is never in a position to choose, in any but a prospective manner, between a satisfaction on one date and a second satisfaction at a different date. (It is this circumstance that creates the problems associated with welfare comparisons over time, during which relative tastes have undergone alteration.)[38] To compare the satisfaction derived this year from this year’s income, with that derived last year from last year’s income, is to attempt the same task as to compare A’s satisfaction from a steak dinner with B’s. Intertemporal utility comparisons, like interpersonal ones, can be made only on an absolute basis; this is outside the province of economic analysis.

It follows that economic analysis can never be invoked in order to describe a particular flow of income over time as being a constant one. Such a description can be made only arbitrarily; we may describe income as constant in money terms of some other arbitrarily selected criterion, but we cannot do so in any absolute sense. All this does not, of course, render the capital-income dichotomy invalid. We may still continue to use the Hicks-Hayek “permanently-attainable-level-of-consumption” definition of income. We are merely forced to recognize that these concepts can be applied only arbitrarily by individuals choosing to do so. For such individuals the application of these concepts may provide criteria for accounting operations in which they may be intensely interested. The capital-income relationship provides such a criterion. Important as this relationship unquestionably is for most of us, it must not be elevated into a tool of economic analysis.[39] It represents an accounting convention, not merely because many people may not be interested in such a distinction at all, but because, in addition, a person can set up the capital-income dichotomy only by making arbitrary judgements of what constitutes for him an unchanged level of satisfaction over time.

The implications of these observations for the Knightian view on capital should be fairly clear. From an accounting point of view there can, as we have seen, be no objection to making the distinction between capital and income. And from the point of view of the person concerned with maintaining what he (arbitrarily) judges to be a constant income flow, a very special significance does indeed come to be attached to his stock of capital. This stock is an entity which must be maintained intact if the desired constant income level is to be continuously assured. Given this stock of capital the individual is assured of this perpetual income flow; diminish the stock in any way and the individual can no longer look forward to such a flow. The individual may, then, quite justifiably look upon his stock of capital as somehow being the “source” of the prospective perpetual income flow.

But, as we have seen, all this has meaning only from the viewpoint of the individual interested in setting up for himself the capital-income dichotomy. He may reasonably consider his capital stock as merely the source of a prospective perpetual income flow. He may do this by choosing to assume that the capital stock will in fact be appropriately utilized to this end, and by arbitrarily choosing a relevant concept of constant income for his purposes. But all this cannot be done, in a non-arbitrary way, by outsiders. The outsider can observe objectively the size and composition of an individual’s stock of capital. He may describe all the possible time shapes of output and consumption flows that may, under different circumstances, be secured by utilization of this stock of capital. But he is unable to single out one particular time shape of flow out of the other flows, and pronounce this flow to be a constant income flow of which the original capital stock is to be considered the source. He cannot do this, in the first place, because, as discussed in the previous section, he has no right to assume in advance that the whole series of decisions necessary to secure any one particular output and consumption flow, will in fact be made. The discussion in the present section has shown that he cannot do so for yet an additional reason. As an outsider he is unable to determine which of the possible output and consumption flows represents, in the arbitrary judgment of the individual concerned, a level of constant income. And, as we have seen, the constant income concept, and with it the capital as-a-source-of-perpetual-income-concept, are meaningless from any other than an arbitrary point of view.

We must conclude, then, that the Knightian capital concept is wholly unhelpful. It represents an extension of the capital-income dichotomy from a realm of discourse in which the essential arbitrariness of the distinction does not matter, to a realm of discourse where it does matter. What was acceptable at the level of accounting, turns out to be wholly unacceptable at the level of economic analysis. And with the recognition of the arbitrariness of the capital-income dichotomy must come realization that a capital concept based on this dichotomy cannot be looked to as a tool in economic analysis.

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[1] Haavelmo (1960) p. 43 (and see also p. 91). See also Fraser (1937) p. 250; Kendrick (1961) p. 102 (“Most economists have continued to view capital as a stock.”) For further background on the stock concept of capital see also Schumpeter (1954) pp. 627f. See also Lerner (1953) p. 545.

[2] For a survey, of the characteristics distinguishing “static” from “dynamic” systems see Baumol (1959) Ch. 1.

[3] Hicks (1963) p. 343.

[4] Smith (1961) p. 64. (Italics in original).

[5] Haavelmo (1960) p. 91. (Italics in original). For a similar opinion see Kendrick (1961) p. 103.

[6] Haavelmo (1950) pp. 70–80.

[7] Enke (1962) pp. 372, 375. While Enke (pp. 369, n.1, 375, n.23) cites Haavelmo’s book in support of his conception of the production function as an “instantaneous relation,” there appears reason to question the full justice of this claim.

[8] Current practice generally (and, as it seems to us, unfortunately) follows the “technological” view. This is especially the case with respect to aggregate models. The paragraphs following in the text explain why this practice is especially unfortunate in the capital theory context.

[9] On this see Clower (1954). See also Witte (1963); Thalberg (1961).

[10] As Clower (1956) p. 68 recognizes, his assumptions are strikingly parallel to those basic to the perfectly competitive model.

[11] Hayek (1941) Chapter V.

[12] Lachmann (1956) p. 12.

[13] Haavelmo (1960) p. 79.

[14] Haavelmo (1960) p. 93.

[15] Enke (1962) p. 377.

[16] Hicks (1961) pp. 23ff.

[17] Hicks (1961) p. 27.

[18] Knight (1956) p. 43. For expository discussions of the Knightian view of capital see especially Kaldor (1937) and Weston (1951).

[19] Knight (1956) p. 47.

[20] Fisher (1906) p. 52; Fraser (1937) p. 250.

[21] The terms were used by Böhm-Bawerk (1907) p. 282 and (1894–5) p. 127 in his criticisms of J. B. Clark, and then applied by Hayek (1936) against Knight. See also Kaldor (1937) p. 198, Stigler (1941) p. 309, Mises (1949) p. 512; cf. also Haavelmo (1960) p. 91.

[22] Hayek (1936).

[23] Fraser (1937) p. 302.

[24] Kaldor (1937) p. 165. See also Stigler (1941) pp. 309f.

[25] Dorfman (1959) p. 358.

[26] See e.g. Conard (1959) p. 80.

[27] Hayek (1936) p. 363, n.17. See also op. cit. p. 370: “. . . it has no meaning, in economic analysis, to say that apart from the human decision, which we have yet to explain, the aggregate of all the non-permanent resources becomes some permanent entity.” It is to be noted that Hayek does not, however, give this objection central attention. This is especially the case for his The Pure Theory of Capital (1941).

[28] Knight (1944) p. 30. See also Dewey (1963) p. 134 for the opinion that this model contains all that is essential for the theory of capital.

[29] Fraser (1937) p. 250.

[30] The classic survey of the attempts has become Kaldor (1955) Appendix to Chapter 1.

[31] Kaldor (1955) pp. 56–57.

[32] Samuelson (1961) p. 34.

[33] Cf. also Hicks (1963) p. 347.

[34] Cf. Samuelson (1961) p. 45, n.1; See Hicks (1939) Ch. 14; Hayek (1935); Kaldor (1955) pp. 64–67.

[35] See Hayek (1941) pp. 298–299, 335–336; Mises (1949) p. 511.

[36] Hayek (1941) p. 159n.

[37] Hayek op. cit. p. 158.

[38] See Rothenberg (1961) Appendix to Chapter 2; Weckstein (1962).

[39] The discussion in the text has been carried on at the level of the individual; it applies even more critically at the macro-accounting level.