4. Measuring Capital

CHAPTER FOUR

MEASURING CAPITAL

The discussions of the preceding chapters have paved the way for a consideration of that knotty problem, the measurement of capital. There exists a sizeable literature attempting to grapple with this problem, some writers denying that capital measurement is possible even in principle, some claiming to have discovered the “right” method to achieve such measurement, some arguing that more than one measure is required, others arguing again that no measurement problems whatsoever exist with respect to capital other than those common to all resources. Here we will attempt to clarify the major issues involved, by a consistent application of the positive approach to the analysis of capitalistic production that has been endorsed in this essay. We commence with our own discussion of the capital measurement difficulties, to be followed in the second half of the chapter by a critical survey of the relevant literature.

A DISCUSSION OF THE PROBLEM OF CAPITAL MEASUREMENT

What Should a Measure of Capital Measure?

We consider a market economy at a given date. Each of the individual members of the economy owns some stock of capital goods. Each of these capital goods was produced during some past period of time with some definite process of production, its production having been undertaken in anticipation of and for the sake of its ability to advance subsequent stages of production. Each of these capital goods is now capable of making various contributions to alternative future processes of production including possibly (but not necessarily), the contributions envisaged at the time when these goods were produced. The stock of capital goods available today is the result of the production and consumption decisions made during past history. The future course of history depends on the decisions that will be made with respect to the utilization of resources services that can be expected to be available during the future, including the services of the existing stocks of capital goods.

Now, were the present stock of capital goods to be in some sense “smaller” than what it is, then the streams of output that can be expected from the future, would seem smaller, in some anticipated sense, than they actually do seem. One aspect of the capital measurement discussion has to do with attempts to render precise the “quantity” of capital involved in such a statement; this is the search for a “forward-looking” measure of capital.

On the other hand, we have observed that the existing stock of capital goods is the result of choices made in the past. In order to achieve the existing stock of capital goods, sacrifices were made, alternative uses of past resource services were foregone. Clearly if lesser sacrifices would have been made in the past, in some sense, the stock of capital goods existing today would in some sense be smaller than what it in fact is. Another aspect of the capital measurement discussion has to do with attempts to render precise the “quantity” of capital in this kind of statement; this is the search for a “backward-looking” measure of capital.[1]

Or again, the existing stock of capital goods may be considered apart from their past history, and from the future course of production to which they may make contribution. Attempts have been made to pin down some sense in which a quantity notion can be attached to the collection of sheer physical items that make up the capital stock. Sometimes “forward-looking” or “backward-looking” measures of capital have been used, not as being of prime interest in themselves, as for their ability to serve more or less appropriately as substitute measures for the stock of capital conceived of simply as a collection of physical items.

We will take these alternatives interpretations of the notion of a capital quantity (which by no means exhaust the full list of such interpretations), as the starting point in our discussion. We consider first the notion of a quantity of capital goods as it relates to the individual decision-maker; then we will take up the notion of the quantity of capital goods in the economy as a whole.

The Quantity of Capital Available to an Individual

Let us first dispose of the necessity to devise a measure of capital goods seen merely as a collection of physical items and nothing more. If one is indeed unconcerned with the economic history leading up to the present existence of the stock, and also not directly concerned with the contribution to future output that these items can make, then there can clearly be little immediate economic interest in any such measure. And even if one’s announced interest in the quantity of physical goods is for the purpose of eventually using this physical measure in decision making with respect to future production, or in the analysis of future production, it is difficult to perceive its usefulness. The truth is that the heterogeneity of the various physical items in the stock not only constitutes a well recognized barrier to the construction of such a measure, but represents at the same time the reason why such a measure can play no significant role at all in the analysis of decision making in the course of capitalistic production. The producer simply cannot afford to ignore the heterogeneity of the various items in the capital stock. The particular alternative combinations of resource services from among which he chooses all depend crucially on the special features possessed by each piece of capital equipment. To treat a given stock of heterogeneous capital goods as a homogeneous quantity must involve either the suppression of the differences that exist between the various items (in which case the resulting measure has no relevance for decision making in production) or else the assimilation of these differences into the measure, based on weights derived from the importance which decision-makers attach to these differences (in which case the measure is either “forward-looking” or “backward looking” and is no longer a bald physical measure at all.)[2]

Turning to backward-looking and forward-looking measures of capital we notice first of all the special case in which the most desirable prospective production processes are precisely those which were envisaged at the various dates at which construction of the currently-existing capital goods was undertaken. As was observed in the first chapter, this is the situation in which the earlier stages of the multi-period plans adopted in the past, have been carried through successfully without the discovery of anything calling for a revision in the later stages of these plans. A measure of the sacrifices made in the past in order to arrive at the present state of affairs measures at the same time the sacrifices that are rendered unnecessary by the availability of the capital stock—sacrifices which had in the past been considered justified by the anticipated usefulness of the capital goods. Or, to put it the other way around, a measure of the flow of productive services that the most efficient exploitation of the present stock of capital goods now promises to yield, measures at the same time the anticipated productive contribution for the sake of which the goods were constructed in the first place. In this special case the “present state of affairs” appears now merely as a cross-section of the even course of economic history. The sacrifices measured by a backward-looking view of the present state of affairs dovetail faultlessly with the prospective productive contributions made possible by the present state of affairs, as measured by a forward-looking view of this state of affairs. As was noticed in the first chapter, this situation is one in which only fleeting interest attaches to the “present state of affairs.” From the vantage point of later dates nothing that needs to be explained about the course of economic history will be seen to have depended importantly upon the state of affairs in such a situation. The case that is of interest for the theory of capital is the realistic one in which the forward-looking measures of the capital stock do not dovetail with the backward looking measures (e.g. in which the forward-looking measure of capital shows a quantity of it too small to have justified the past sacrifices indicated by the backward-looking measure of the same stock).

It follows, then, that for the cases that are of interest for a theory of capital, the notion of a quantity of capital goods must be spelled out either in terms of the past sacrifices that gave us the capital goods in question, or in terms of the future productive contribution these goods can be expected to make for the efficient producer. In general these two notices will not dovetail; the quantity of capital as measured by its prospective contribution to production will not be that quantity for the sake of which the past sacrifices were incurred. It will in general be illegitimate to use a backward-looking measure of capital as an index of its productive capacity, or a forward-looking measure as an index of the past sacrifices incurred.

Backward-Looking Measures of Capital: The Individual

Let us consider the requirements for a backward-looking measure of the capital goods owned by an individual. It will be simplest to consider this problem first in a Crusoe setting. The sacrifices made by Crusoe in the past in order to attain his present state consist of the best alternative uses to which each bit of past input could have been applied at the time when one of the decisions was made that contributed to the production of the capital goods now possessed. At each past date when input was applied towards capital goods production, some “next best” employment of the input was foregone. The aggregate of these sacrifices is what it is sought to measure for the purpose of the backward-looking measure of the now existing stock of capital goods. This seems clearcut enough; but it raises the obvious problem of heterogeneity in ways that are apparently not always obvious.

It is important to realize carefully wherein this heterogeneity problem exists and where it does not exist. Heterogeneity is a problem here not because of the heterogeneity of the existing capital goods themselves, since we are measuring the stock of these goods in terms not of the physical items making up the stock, but of the past sacrifices responsible for the stock. If past sacrifices were homogeneous in nature, then we would have no heterogeneity problem at all. But past sacrifices are in general not homogeneous, and this for two reasons.

First, the sacrifices involved in past inputs are in general of different kinds. While there is no objection in principle to a search for the “amount of past sacrifice” involved in a stock of heterogeneous capital goods, understanding “sacrifice” as a simple homogeneous quantity, the likelihood is that the alternative outputs foregone in the past were themselves of different kinds. Suppression of these differences (by collapsing all the different sacrifices into a single homogeneous sacrifice notion) may do no particular harm, as far as concerns our purposes in wishing to measure capital in this way, but it does require the solution of an index-number problem.

Second, the orifices involved in the production of the capital goods were, in general, made at different dates. This involves a heterogeneity problem, almost completely ignored in the literature, that is thrown into focus by an approach which emphasizes the decisions associated with the capital stock. A distinction is made in the literature[3] between “point-input” cases (where all the inputs responsible for capital goods were invested at one single date), and “continuous-input” cases (where the inputs responsible for the capital goods were invested continuously over a period of time). Now, in the case of continuous input, we can assume that capital goods must in general be ascribed to a series of decisions made at various dates. It follows, then, that even if the alternative outputs foregone at each of these past dates were to be identical in all observable respects, any attempt to add them together would involve a problem of heterogeneity. This is so (a) because the date at which an act of consumption takes place (or is foregone), is an important respect in which it differs economically from other acts of consumption, even when all the acts of consumption are appraised as of one particular date; and (b) because in the continuous input case each of the foregone possibilities of consumption was being valued at a different date.[4]

For Crusoe these difficulties must certainly appear insuperable. Even if a system of weights is able to be devised that could bring together all the different kinds of enjoyments (rejected during the process of producing the capital goods) into a single quantity of sacrifice, this could be done only with respect to Crusoe’s value scale as of one particular date. In a world in which tastes and expectations are in principle free to change there seems no theoretically valid way in which the sacrifices undertaken at various dates can be aggregated.[5] Of course it would still be possible in principle for Crusoe to appraise the aggregate of past sacrifices as they now appear to him in retrospect, but it is not clear in what sense this would be able to provide a useful measure of the capital stock. The rationale of the backward looking measure of capital as we have thus far described it rests on the assumption that where greater sacrifices have been undergone, they were accepted only in order to achieve “more capital” (as viewed in anticipation). This would require a measurement of the relevant sacrifices at the times at which they were under undertaken. If one could assume that a plan to construct the entire existing stock of capital goods had been adopted at one date (in advance of the times at which the actual sacrifices necessary would have to be undertaken) there would perhaps be some merit in measuring these sacrifices as of the date at which they were originally envisaged. But barring this special case, even this limited value must be denied to the Crusoe backward looking measure of capital.

Let us see whether these difficulties arise entirely out of the peculiarities of the Crusoe setting, and can be avoided by transferring the problem to a market economy. Can an individual in a market economy devise a backward-looking measure of his stock of capital goods, that should not founder on the heterogeneity problems we have discovered?

The advantage, for the purposes of measuring “economic quantities,” that is conferred by the existence of a market, arises out of the possibility of using market prices to overcome the heterogeneity problem by translating quantities of one physical commodity into value terms for comparison with quantities of other physical commodities. The immediate justification for this is that the market in fact permits easy conversion through commerce of a quantity of physical goods into other goods of equal market value.[6] Can we use market prices to measure the sacrifices undertaken during the past in order that the present stock of capital goods be brought into existence. Clearly the current market prices of the items making up the stock will not serve for this purpose. Current market prices reflect the present anticipations of the productive usefulness of the capital goods, and thus, we have already noticed, may be quite different from the corresponding expectations held at the time when the capital goods were produced.[7] Our first thought is to add up the market values of the inputs used in the past in the production of today’s stock of capital goods, making sure to allow compound interest to accrue at the respectively appropriate rates and for the respectively appropriate lengths of time.[8] (The “appropriate” rate of interest would here be that rate which could, at the time when input was applied in the past, have been obtained for a loan of funds for the relevant length of time, i.e. till the present date. It would be incorrect to use the rate or rates of interest that have in fact been ruling during this length of time, since we are concerned with the extent of the sacrifice undertaken at the time of input application.)

This way of calculating the “cost” of the capital stock would certainly overcome the heterogeneity problem that arose due to the different kinds of alternatives involved in the various applications of input. These would now be expressed in homogeneous terms of monetary value. A particular alternative enjoyment foregone at one date can be added to a particular alternative enjoyment foregone at a second date, because both enjoyments are expressed in monetary terms. Inclusion of accrued interest (as outlined in the preceding paragraph) enables one to compare sacrifices made in the distant past with those made in the immediately preceding past, since they are being measured by the amounts of money at the present date which these sacrifices could respectively have bought at the dates at which they were undertaken.

But reflection will convince us that we have not yet succeeded at all in obtaining the backward looking measure of capital which we have been seeking. Our purpose in seeking such a measure was to exploit our understanding of the past decisions which led to our existing capital stock. Knowing that larger sacrifices would have been undertaken only for the sake of a more desirable stock of capital, we sought to use a homogeneous measure of these sacrifices as an index of the size of our capital stock. But all we have succeeded in obtaining is the sum yielded by adding together all the quantities of present money that could have been owned today if, instead of applying inputs at various past dates, their market values in money had been loaned out at the going rates of interest up to the present date. This sum of money is indeed the present money equivalent of the production costs of the goods in our capital stock. But since this sum is composed of money values of costs incurred at different past dates, the sum itself is unable to serve as a measure of the “total sacrifice” incurred in the past for the sake of the present stock. The money equivalent of the input applied at one past date may serve as a measure of the sacrifice involved in its application, because the money was an alternative, available at the time, which was rejected for the sake of the capital stock. But since an individual is at no time able to choose between two alternatives the adoption of which require decisions to be made at different dates, it follows that sacrifices undertaken at different dates cannot be compared. (A person may pay x dollars in the summer to enjoy a cold shower, this shows he prefers the latter to the former; he may pay y dollars in the winter to enjoy a warm bath, this shows he prefers the bath to the y dollars. But even if y > x this does not prove that the winter bath is preferred to the summer shower. Even though we know that in the winter he prefers y dollars to x dollars, and so also in the summer, we have no decision possibility permitting him to choose simultaneously between summer and winter enjoyments. He may use the loan market to express his present preferences between x dollars in the winter and y dollars in the summer, but this, of course, is something different).

In brief, our individual seeking to measure the quantity of sacrifice involved in his present capital stock by using market values, still finds himself confronted with one of the heterogeneity problems that Crusoe found insuperable. The inputs applied at different dates correspond to sacrifices that can in principle not be compared or aggregated. To add the money values of these inputs is to add essentially heterogeneous items together and to delude oneself into believing that, because all the values are money values, the heterogeneity does not exist. The fact is that a dollar sacrificed at one date can no more be added to a dollar sacrificed at a different date, than a carrot can be added to a potato. The fact that the carrot and the potato are each called “vegetable” does nothing to alter the matter. Only in the every special case when all the past inputs that produced the current stock of capital were committed in one single irrevocable decision, (so that all that was sacrificed was valued as of a single date), can one hope to use the market value of inputs (as anticipated at the moment of decision), as a measure of the sacrifices undertaken. Only in this case can a backward looking measure of capital be conceivable.

We conclude that the attempt to measure the “quantity of capital” in an individual’s stock of capital goods, by measuring the past sacrifices involved, must be pronounced a failure. In a later section we will discover what additional difficulties stand in the way of constructing, even in principle, a backward-looking measure of the entire capital stock that exists in an economy as a whole. We turn first to consider the possibilities for a “forward-looking” measure of the capital stock of an individual.

Forward-Looking Measures of Capital: The Individual

The rationale of the forward-looking measure of capital is provided by the notion that a larger stock of capital goods ought to make a larger contribution to future output than a smaller stock. The purpose is then to measure the capital stock by the contribution to future production that it is able to make. Capital goods are in this context treated exactly like other resources, and involve no problems of measurement that are not shared in principle by other resources. Several problems present themselves in connection with the construction of such a resource measure. First there is the problem of reducing to a single quantity all the contributions to output that the stock of capital is able to make during many different future periods of time. Second there is the problem created by the many alternative ways in which the stock of capital can be used in future production—what precisely do we wish to mean by the “prospective productive contribution” that a capital good is able to make?

As far as the first of these problems is concerned there seems to be no great difficulty, at least for an individual in a market economy. Once the second problem has been solved, that is, once we have identified the particular future output flow which we consider as the prospective contribution to output of the capital goods, then we can simply find the present market value of this contribution by adding together the prospective market values of each bit of the future output flow, appropriately discounted down to the present date (at the relevant rates of interest now prevailing). This will give the individual an “objective” value of the productive capacity of his stock of capital. (Of course, the individual might be more interested in his own subjective valuation of this flow of output. This will permit him to gauge the desirability of the flow by reference to his own private tastes, including time preferences. In general this could lead only to an ordinal measure).

The real difficulty, it is clear, has to do with the second problem, that of identifying the contribution to future production that we wish to associate with a particular capital good or collection of capital goods. The difficulty is a result of two circumstances, (a) the versatility of capital goods, and (b) the possibilities of substitution between capital goods and other inputs. First, since capital goods may be used in the production of more than one kind of output, we are required to specify the particular product towards the output of which the stock of capital is, for our purposes, considered able to make contribution. Second, since in the production of many products there exists the possibility of using either relatively more capital with other inputs, or relatively less capital, and since future output depends sensitively on the particular ratio between inputs that is employed, it is necessary to specify the degree of capital intensity that we have in mind when we talk of “the productive contribution” of our capital goods.

The fact is, of course, that these difficulties arise from the necessity to make decisions with respect to the productive utilization of capital goods, as of other available resources. It is in many respects a misleading simplification to talk as if a given resource were unambiguously associated with a definite flow of output, in the sense that such an output flow is forthcoming automatically from the resource. Until a definite plan has been formulated that shall clearly mark out the part in the production process that a piece of capital equipment is to fill, it is not really meaningful to talk of its “potential contribution to production.” This is so not only because, as was stressed in earlier chapters, output does not emerge without decisions being made,[9] but also because as we have now seen, there are more than one use to which a resource can be put, and more than one technique by which it can be applied to a given use. We have already observed that it would be inappropriate to use, for this purpose, the original production plan envisaged at the time the capital was constructed; the essence of our attempt to measure capital in a forward-looking manner is to be able, where necessary, to ignore bygones. It appears, then, that the attempt to measure a stock of capital goods in terms of their potential contribution to future output must assume that all the decisions with respect to the utilization of the capital goods have already been made in the light of current conditions. This means, in addition, that the forward-looking measure of the capital stock is able to provide a measure of capital only against the background of given anticipated prices for other inputs and for products (since it is only with the knowledge of these prices that a production plan can be formulated). To measure the potential productive contribution that a stock of capital goods can render, in isolation from the consideration of other factors of production, appears to be an impossible task.

But, once the difficulties and qualifications surrounding a forward-looking measure of capital have been comprehended, it becomes likewise clear that such a measure is in fact obtainable, in principle, without the problems that frustrated the search for a backward-looking measure. The truth is that a capital good is measured—no matter what difficulties this task entails, and no matter how inaccurately it is performed, whenever an individual buys or sells the capital good, and whenever, possessing a capital good, he refrains from selling it at the going market price. And the measurement so made is certainly a forward-looking one. The highest price a person will pay for a capital good is set by his estimate of the present value to him of the addition to the future flow of output that the capital good can make possible, taking into account the particular production process in which he envisages the capital good to be applied, and the particular manner in which he envisages it to be used in this process. The fact that capital goods are bought and sold is evidence that individuals are indeed able to compare its productive usefulness with that of other resources, and with quantities of immediately consumable commodities.

Does this mean that an individual can measure the size of his stock of capital by simply finding out its current market value? Not quite. We have seen that a forward-looking measure of capital implies that one has in mind a definite plan for the productive utilization of the capital goods. Such a plan depends on one’s expectations concerning the future prices of the different possible products and of the different possible complementary inputs. An individual’s forward-looking measure of a given stock of capital goods is thus highly individualistic, depending crucially on his own subjective expectations concerning the future. The market price of a capital good expresses the quantity of capital that it represents to other individuals in the market (the marginal buyers and marginal sellers), based on their expectations. In the absence of an equilibrium situation there is not even a guarantee that the market price fully expresses the expectations of all potential market participants. And even if the market were to be in equilibrium, our individual cannot be sure that he shares the set of expectations upon which the market price is based. So that for an individual who has his own ideas as to the future, the market price does not provide the subjective measure in which he is interested. On the other hand, for an outside observer wishing to see how much capital the market ascribes to a particular capital good, the market price certainly gives him the information he wants provided he remember that those who do not trade at the going price clearly disagree with the rest of the market as to the size of the capital good’s prospective productive contribution.[10]

The Quantity of Capital Available to an Economy as a Whole

We turn now to consider the additional complications that attend the search for a measure of capital, when the capital sought to be measured is that of an entire economy, (or is the “average” capital available per head, a concept that implies the aggregation of all the capital available to the group). We will discover that our dissatisfaction with other treatments of this aspect of the capital measurement problem, stems more than ever from the prevalent disregard of the plan relevance of the capital concept.

Now, if our interest were in the stock of capital conceived as a collection of physical objects, then there would in principle be no especial difficulty with the construction of an aggregate measure of all the capital goods that exist in an economy. All that would be involved would be the addition of the machines that belong to A, to the machines that belong to B, and so on. But we have already shown that we are not very interested in the “size” of the stock of capital goods in physical terms, where this involves the suppression of the economic differences between heterogeneous goods. There seems no reason for our interest to be reawakened in such a concept merely as a result of the widening of the focus of attention to embrace an entire economy.[11] Our interest, then, must still be in the economic aspects of the nation’s stock of capital goods, and this raises serious questions concerning the meaningfulness of aggregation in this context altogether.

Supposing, for the sake of argument, that each of the individuals in the economy had succeeded in devising a valid “backward-looking” measure of the capital stock that he possesses. In other words, each individual has a clear quantitative notion of the sacrifice undertaken in the past for the sake of the capital goods he now possesses. Is there any meaningful way of adding these measures of capital together in order to measure the aggregate stock of capital? Clearly there loom formidable theoretical obstacles in the way of adding together the “sacrifices” undertaken by different individuals. The sacrifices we are concerned with are not quantities of objective physical inputs applied; we are concerned with the subjective notion of sacrifice undertaken by each individual in his past decisions. There is no way of comparing the subjective sacrifices undertaken by different individuals. Even if each individual had somehow succeeded in expressing his “quantity of sacrifice” in terms of money, the addition together of these sums of money representing the sacrifices of different individuals cannot succeed in representing a meaningful adding together of the different subjective sacrifices expressed by these sums.

But let us disregard this difficulty, let us imagine that somehow the sacrifices of different individuals can be added together into a single aggregate quantity. Can the resulting quantity serve as a measure of aggregate capital? In what sense does the size of this aggregate sacrifice attest to the size of the capital stock? For an individual, the size of the sacrifice that he undertook in the past, measures the quantity of capital produced through this sacrifice as anticipated at the time the sacrifice was undertaken. Even if the anticipations have been proved incorrect, there may still be interest in measuring the size of the present capital stock as it was anticipated at the time its construction was undertaken. But when we aggregate the sacrifices made by a large number of individuals, whose past anticipations are likely, at least to some degree, to have been mutually contradictory, we obtain a quantity which hardly seems to have any meaning at all. If A anticipated warm weather and produced an air-conditioner at great sacrifice, while B anticipated cold weather and produced an oil burner with similar sacrifice, then it is clear that in no sense did the “society as a whole” made up of A and B, anticipate conditions in which both capital goods are as valuable as indicated by the respective costs of production incurred.

Nor is the situation greatly different when we consider the possibilities of aggregating forward-looking measures of capital. We have seen that the rationale of such measurements is that the “quantity of a resource” is nothing but another way of describing the additional quantity of input flow which the availability of the resource can make possible. Measuring capital in a forward-looking manner expresses the anticipated usefulness of the capital stock to its owner. We have seen that this presumes a definite plan on the part of the prospective capitalistic producer. This plan in turn depends on the anticipations which he holds concerning the plans of others, in particular as these will express themselves as prices of products and of complementary inputs. If we add together the measures of the capital stocks possessed by different individuals, as measured in a forward-looking way, we are likely to be combining, in effect, mutually inconsistent plans. The point of this whole discussion is that a measure of capital differs from a measure of output in that the former, unlike the latter, depends crucially on some definite plan of production in which the capital is to play a role. Whether backward-looking or forward-looking, a measure of capital necessarily involves the consideration of some plan (either past or prospective) in which the capital appears (as end or as means). A measure of output can, at least in principle, be considered apart from the plans to which the output is to be ascribed (although this does not necessarily provide the most theoretically satisfying measure). Because output can be considered apart from individual plans, the attempt to measure aggregate output (whatever other theoretical difficulties it encounters) does not necessarily have to grapple with the problem of mutually inconsistent plans.

Simon Kuznets seems to have something of this in mind when he criticizes the aggregate measure of capital formation as viewed only as “mechanical sums of bookkeeping entries by business firms and individuals.” “Even if the purpose were to study capital purchases and consumption as items that influence the decisions of businessmen. . . . This purpose would call for ‘motivational’ entries which, by and large, are neither additive nor capable of manipulation mathematically, except within a framework of distinct motivational structures.”[12]

All this may seem quite discouraging insofar as concerns the attainment of a meaningful aggregate measure of a nation’s stock of capital. Certainly the definite collections of physical things that are possessed by individuals permit of being conceptually added together to be considered as a single such collection, (but without any analytical purpose being served by representing this collection as a uni-dimensional quantity). But insofar as each individual is able to measure the capital of which his stock of machines consists, in terms of their prospective usefulness to him in production (either as viewed when their construction was originally undertaken, or as viewed currently), it appears clear that the resulting measures are unique to each individual, do not in general permit comparisons between individuals, and yield no meaningful aggregate when added together. To become aware of this is surely a step forward in one’s understanding of the nature of capital within the framework of the decisions that make up the productive process.

And yet it cannot be denied that one is left not entirely satisfied with this conclusion. Is it really without meaning to say that the capital per head in country A is greater than in country B? Is it meaningless to attempt to explain the higher productivity of labor in country A by reference to the larger quantity of capital combined with each man-hour of labor? It is indeed difficult to deny that we, in fact, use aggregate concepts of capital in this manner; what is the meaning to be attached to such concepts, and how do they relate to the “individualistic” concept of capital that has been adopted for the purpose of this essay?

Careful reflection on the matter will, it is believed, reveal that the aggregate concept of capital, the “quantity of capital available to an economy as a whole,” is, for a market economy, a wholly artificial construct useful for making certain judgments concerning the progress and performance of the economy. When using this construct one is in fact viewing the economy in its entirely as if it were not a market economy but instead a completely centralized economy over which the observer himself has absolute control and responsibility. When, for example, one is concerned with the size of the stock available to society in a forward-looking sense, what one is really thinking is as follows. Supposing one were to be able to draw up a complete social listing of output priorities and supposing one were in command of all the information necessary to formulate centralized production plans for the future, what is the additional flow of this “social output” during future years, that is to be ascribed to the presence of the nation’s stock of capital. One is thus not merging the plans of all the individual capital owners who participate in the market economy, one is conceptually replacing these plans by a single master plan that one imagines to be relevant to the economy as a whole, and against which one gauges the performance of the economy as a whole.[13]

Now, in order to use such a holistic capital concept with consistency, and in a manner parallel to that which we adopt with respect to the individual capital notion, certain assumptions have to be made. If one wishes to talk of the “cost of the economy’s stock of capital,” in the sacrifice notion of the backward-looking capital measure, it is necessary to imagine that the existing stock of capital has come into being as the result of past integrated centralized decisions over the years. Only then, with the additional assumption of a holistically conceived scale of social values, can one think in terms of the “social sacrifice” involved in the past production of the present stock of capital. Now, so long as this aggregate concept of capital is used with continual awareness of the special assumptions needed to give it meaning, no very great harm can result. But when, as is so frequently done, the aggregate quantity of capital is used in conjunction with discussions of the market process, things become very blurred indeed. The truth is that the aggregate concept of capital has meaning only on assumptions according to which all parts of the capital stock are completely integrated with one another. Each piece of capital equipment in the stock is assumed to have been constructed as part of the same central plan which led to the rest of the stock. Each capital good has its part to play; no two capital goods has a function which precludes the full utilization as planned, of the other. But these conditions can exist in a market economy (in which planning is decentralized) only in the state of equilibrium. The essential function of the market is, after all, to bring individual plans which do not mesh, into greater mutual coordination. So that it turns out that the aggregate concept of capital presupposes conditions that are not only violated in the real world, but which assume away some of the major problems which it is the task of a market theory of capital to elucidate. It is the realization of all this that seems to have inspired much of the work of Professor Lachmann in the theory of capital, with his wholesome stress on the problems raised by the need for complementarity among the different items that compose the aggregate capital stock.[14] And, at the close of his notable review article of Mrs. Robinson’s Accumulation of Capital (in the course of which he subjects her discussion of the problems of capital measurement to devastating criticism) it is thus that he sums up the future tasks of the capital theorist: “How bold, then, would the next step be, viz. the realization that the notion of a stock of capital which invariably has the ‘appropriate’ composition required by circumstances, is an obstacle rather than a help to our understanding of the nature of economic progress?”[15]

THE CAPITAL MEASUREMENT PROBLEM IN THE LITERATURE

In the second half of this chapter we turn now to examine critically some of the ways in which the capital measurement problem has been treated in the literature, with special attention to the more recent contributions. Our examination and criticisms will rely heavily on the discussion of these matters that has been presented in the first half of the chapter. Much has been written concerning capital measurement, with the perspective being variously that of economic theorist, statistician, or econometrician. We will discover that many of the points raised in our discussion earlier, have been raised somewhere in the literature, we will however also find, unfortunately, that much of the confusion that has surrounded the treatments of these points is to be ascribed to the prevalent failure to place the theory of capital in the context of the relevant individual plans. Our criticism of the various treatments of the capital measurement problem will thus repeatedly draw attention to the ways in which awareness of the individual planning context of capital stocks might either have cleared up points that have raised unnecessary difficulty, or might have revealed points of real difficulty that have in fact apparently escaped attention.

Physical Goods or Abstract Fund—What Are We Trying to Measure?

A considerable amount of disagreement has concerned the question of what precisely is being sought in a measure of capital, a measure of physical things or a measure of an abstract capital fund which these physical things supposedly represent. This disagreement has much to do with the familiar controversies concerning the way in which the economist ought to look on capital in general. J. B. Clark, who argued in favor of the notion of capital as a homogeneous fund of productive capacity, distinguished sharply between the value of the capital stock which measures the size of this fund, and the physical description of the heterogeneous capital goods in which the capital fund is embodied at any particular time. Böhm-Bawerk, who rejected the fund concept of capital, saw no reason why the possibility of measuring a stock of capital as a value, implies that what is being measured is an abstract quantity apart from the concrete capital goods. To show that capital has a value, is by no means sufficient, he argued, to establish that capital is a value.[16] The same points were made again in the course of the Hayek-Knight debate during the thirties. Knight contrasted what he considered the discredited notion of capital as “things,” with what he considered the appropriate view of it as a “fund”, this fund being “thought of as either a value or a ‘capacity’ to produce a perpetual flow of income.”[17] Hayek’s objections to this view, cited in earlier chapters, did not deny that the various capital goods possess a “common attribute of being a condition of making investment possible;”[18] but in his view this does not at all justify treating “capital” as if it were a quantity of something apart from the particular goods that make up the capital stock. Böhm-Bawerk himself, Hayek charges, was partly responsible for the spurious notion of homogeneity that has given rise to the fund-concept, because he stressed the capacity of capital goods to act as a subsistence fund.[19]

It is not to be thought, of course, that the mere search for a single measure of capital, one that should overcome the problems of heterogeneity, necessarily involves the fund-notion of capital. While it is true that Samuelson, for example, contrasts the position which refuses to aggregate heterogeneous capital goods into a single capital quantity with what he calls the “Clark-like concept of aggregate capital,”[20] we have already noticed that Böhm-Bawerk was willing to measure capital as a value without conceding anything to Clark. More recent writers, too, have discussed the possibility of two measures, one measuring the physical things in the capital stock, the other measuring the value of the ‘fund’ considered to be represented by these things. Hicks especially has stressed the need for both capital concepts,[21] both being measurable in principle.

From the point of view adopted in this essay the issues seem quite clear. The only common attribute that different constituent parts of the capital stock possess, is that they are intermediate products. This provides no basis whatsoever for their conception as a homogeneous fund of any kind. Nonetheless, we have seen in the first part of this chapter, there may be, in principle, the possibility of measuring a stock of heterogeneous capital goods in terms of past sacrifice, or of future potential productive contribution associated with them. Clearly what would be sought thus to be measured would be the physical goods themselves, but only by reference to the economic history, past or future, associated analytically with these goods. The stock of physical things that make up capital is not homogeneous. There is no underlying “fluid” (mystic or otherwise) that is represented by these physical things; so that a collection of these things in no sense represents a fund. Nonetheless, since these things are intermediate products—that is, they are (a) the results of earlier production processes and are (b) planned to be used in future production processes—we may wish to measure them by the past sacrifices to which they are to be ascribed, or by the future yield to which they are planned to give rise. But this does not mean that these physical things themselves are to be viewed as a “stock” of past sacrifices, nor as a “fund” of future productive capacity. They are not to be viewed as a stock of past sacrifices, because bygones are bygones; past sacrifices in no sense effect the current economic status of these capital goods. On the other hand they are not to be viewed as a fund of future productive capacity because their ability to contribute to future output calls for a whole series of new decisions to be made; capital goods in themselves are, indeed, potential inputs, but that is all.

The Heterogeneity of Capital as an Obstacle to its Measurement

One brief review of the ambivalence with which the literature has treated the capital concept, now as a collection of physical things, now as a homogeneous fund of some kind, leads us naturally to a more general examination of how the physical heterogeneity of capital goods has been handled in the capital measurement literature. Some writers seem to have understood the problem of capital measurement as arising almost entirely out of the heterogeneity of the constituents of the capital stock.[22] An attempt to measure a stock of capital must add together entirely different items. At the same time many writers have pointed out that the heterogeneity problem is by no means peculiar to capital.[23] Any attempt to measure the aggregate flow of labor, for example, will very soon run into the same difficulties of adding together fundamentally different entities. Other writers, again, have denied that the heterogeneity of capital is responsible for the characteristic difficulties that surround the measurement of capital. Even if all capital goods were identical, these writers argue, the real problems that plague the measurement of capital would remain.[24]

We have already, in the first half of this chapter, expressed the opinion that no useful analytical purpose is served by a measure that has no other goal than that of deliberately suppressing the heterogeneity that does, in fact, characterize a stock of capital goods. If a measure of capital seeks to discover some factor common to the various different goods, for example, their capacity to yield a product, or their having been produced at a sacrifice, that is one thing. But if the seeker after a capital measure is not concerned with these possible aspects of homogeneity in the stock,[25] if he confines his attention strictly to the present physical aspects of the capital goods, then, we argued, an attempt to construct an index of capital quantity draws away attention from significant aspects of capital, because decision-makers must, in fact, never lose sight of the unique quality of each capital good. And, just as the decision maker dare not lose sight of capital heterogeneity, so is it unnecessary for the theorist to ignore it. “With our armchair omniscience,” Hahn and Matthews remark, “we can take account of each machine separately.” Insofar as the capital measurement problem arises from capital heterogeneity it is “no problem at all because we never have to face it if we do not choose to.”[26] A number of writers have insisted that the aggregation of capital in the sense of physical things, into a single quantity, is analytically unnecessary.[27] And it has also been pointed out that if an index of physical things is constructed, this necessarily injects some kind of value element into the measure, so that the measure is not strictly a physical one anymore.[28]

Heterogeneity has been seen as a problem associated with that of capital measurement in yet an additional sense. Even if all the physical things that make up the capital stock were identical, Lerner has argued, the “measurement of the marginal product of capital still would involve measuring the capital and consumption goods in the same units so as to obtain a pure number for the marginal product of capital that could be compared with the rate of interest.” So long as capital goods are physically different from consumer goods, it is argued, homogeneity of the goods making up capital stock would appear not to have solved anything at all.[29] Hicks has somewhat similarly endorsed the measurement of a capital stock as equivalent to a homogeneous fund of consumption goods, partly on the grounds that this makes possible the measurement of a capital increment in the same units as the saving that corresponds to it.[30] For the same kind of reason a number of theorists have chosen to discuss models in which there exists only one physical commodity (such as the perennial in Knight’s Crusonia economy discussed in the previous chapters) that can be either consumed or used as capital in the production of more of itself.[31] Dewey has written of the advantage which this model possesses of avoiding the spurious problem of capital measurement.[32] (Compare also Böhm-Bawerk’s conception of capital as inchoate consumer goods “so that the whole economy can be thought of as a single consumption-goods sector.”)[33]

On the other hand, however, it has been objected in the literature that the one-product model necessarily slides over interesting aspects of capital theory.[34] From the point of view adopted in this essay one of the principal objections to this one-product simplification is that it obscures the real economic difference between the constituents of a stock of capital on the one hand, and both the original inputs and the final output on the other hand. Measurement of capital in terms of an allegedly equivalent quantity of consumer goods is one thing (to be discussed briefly later in this chapter); but a model which measures capital as a quantity of consumer goods because the capital consists physically of consumer goods is necessarily viewing the capital stock in entire abstraction from its economic role. It measures the capital stock purely as a collection of bald physical items, misleadingly implying that these items are economically identical with similar physical items that are planned as outputs.

These objections to the artificial homogenization of the capital stock (and especially the achievement of such homogenization by its reduction to consumer goods) are magnified when the capital measure sought is an aggregate one for the entire economy. As already noted earlier in this chapter one of the most fruitful insights into the market process in a capitalistic economy consists in noticing how this process brings about continual adjustments in the decisions of capital goods producers in the direction of more complete complementarity between the heterogeneous items that make up the aggregate stock of capital.[35] Models which deliberately treat capital as if it were homogeneous, and measures of capital that not only slur over inconsistent plans on the part of the various owners of capital goods, but treat capital as something with respect to which inconsistent plans are in principle an impossibility, do a disservice to the extent that they facilitate (and have in fact facilitated) the tendency to ignore entirely this aspect of capital theory in the context of the market.

Heterogeneity, Quality Changes, and Forward-Looking Measures of Capital

A special case of heterogeneity exists where a particular capital good, highly specific to a given branch of production, is being produced today in a quality superior to that of the corresponding good produced last year. Both goods are “typewriters,” or “locomotives,” but the later model is “better” than the older one. If an old model locomotive was considered one unit of capital (when it was new), should a new model locomotive be considered as more than one unit of capital, and, if so, how much more?—or should we say that one locomotive is still one unit of capital, but that capital has now become more productive? The problem of quality change is one with which statisticians and econometricians have to grapple in a number of contexts, the problem in the present instance is to devise a theoretically valid way of dealing with quality changes in capital goods that should take into account the special nature of capital goods (as against, for example, that of consumer goods). This constitutes a special case of the heterogeneity problem, in that while the two locomotives are different, they are yet both locomotives, so that one’s natural reaction is to compare their respective output. This had led to an examination of forward-looking capital measures for possible use in this special case, far more readily than in the general case.

It should be observed that quality change is not the same thing as technological progress. Different qualities of locomotives may, for example, be produced in different years as a result of changing cost conditions. Nonetheless the treatment of quality change has much in common with the treatment of technological progress (and the two seem to have sometimes become confused in the literature). Especially where technological progress is wholly “embodied” in the capital goods being most recently produced—i.e. where the marginal productivities of capital goods produced earlier is not affected by the change[36]—both kinds of change raise virtually identical problems. Should a measure of capital reflect these changes as increasing the quantity of capital (per “locomotive”) or as increasing the productivity of capital (per unit of capital)? Clearly this relates to the question of whether to use a forward-looking measure of capital or not. Those who have deliberately avoided forward-looking measures of capital, have had to face the same kind of heterogeneity problem that complicates capital measurement in general, (except that they have had to repress with some sternness the natural tendency to consider a better locomotive as being “more locomotive,” an urge which does not present itself in connection with goods that have no function in common).[37] Among those who have in this context sought alternatives to forward-looking measures of capital have been especially those wishing to be able to talk of increases in the productivity of capital, arguing that forward-looking measures render this impossible by definition (that which produces more simply representing a greater quantity of capital).[38]

On the other hand, those who have considered the use of forward-looking capital measures as a means of homogenizing capital goods of different quality, have encountered some of the characteristic problems which such measures necessarily face. Perhaps foremost among these has been the question of defining the output to be imputed to the capital good involved, in the light of the variable proportions in which capital goods may be combined with complementary inputs. One quantity of machines may, with a given quantity of labor, produce the same output that another number of machines (of different quality) is able to produce with the same labor. But it may be that when combined in turn with some other quantity of labor, each of the two sets of machines yields an output different from that of the other. Under these conditions it is not a simple matter to use the forward-looking approach in order to measure the relative quantities of capital in the two sets. This has been a widely recognized difficulty with the forward-looking approach to capital measurement;[39] in the context of the attempt to handle quality changes it has given rise to a good deal of ambiguity and disagreement. Thus Hicks apparently considered a forward-looking measure of capital such that one new machine shall be said to consist of twice the capital represented by an old machine when the new machine produces, together with a given quantity of labor, twice the output produced by the old machine with the same quantity of labor.[40] Green, on the other hand, wishes us to say that the new machine consists of twice the capital represented by the old machine only when the former produces, with a given quantity of labor, as much output as two old machines can produce when combined with the same total quantity of labor.[41] One of the forward-looking measures considered (and rejected) by Denison involves yet a third criterion.[42]

Green, in fact, uses his version of the forward-looking measure to deny altogether that such a measure rules out by definition the possibility of increase in the marginal productivity of capital. Disembodied technological progress, he argues, is entirely able to increase the marginal productivity of a unit of capital (as he wishes us to define it).[43] A machine which last year produced, with a given quantity of labor, output in a certain quantity, may this year produce a greater quantity of output with the same labor. Green’s own measure enables him to read this as an increase in productivity, while Hicks’ measure would interpret it as an increase in capital. All this illustrates the treacherous territory that the would-be measurer of capital must traverse in connection with quality change. It must be confessed that Green’s argument in this respect, while perfectly consistent as a matter of mere definition, seems nonetheless to be undeservedly seeking the best of both worlds. If one wishes to use a forward-looking measure of capital, one that focuses attention not on past cost, nor on physical specifications, but on output capacity, then it seems strange that a sudden disembodied technological advance which enables each machine to generate double the output it generated previously in each of its possible uses, is to be viewed as leaving the capital stock no larger than it was before.

Moreover, from the point of view of the discussion in the first half of this chapter it should be clear that no great advantage has been won by being able to use a forward-looking capital measure without having to surrender the notion of changes in the productivity of capital. With the focus of our interest centered on the decision maker, it is clear that the marginal productivities with which he is concerned, are never those of inputs in general, or of capital in general, but are always those of individual bits of input (whenever the different bits of input are in fact significantly different from one another). We have seen that the decision maker’s use of the production function concept never homogenizes capital goods of different qualities so that where the productivity of capital goods is concerned, the notion of homogeneous capital quantity is irrelevant. On the other hand, where an individual wishes to assess his potential future flow of output, and associates the likelihood of this flow concretely with the capital goods at his present command, he is no longer directly concerned with the marginal productivities at all. So that where a legitimate interest in a homogeneous forward-looking capital measure may exist, the specification of the production function (and the possibility of its changing under the impact of technological progress) no longer holds our attention.

And again, pursuing further the views developed in the discussion in the first half of this chapter, the whole search for an “objective” forward-looking measure of capital, involving, as we have seen, all the ambiguities and confusion arising from the treatment of complementary inputs, seems to imply an unfortunate approach to the problem. What is being sought by the writers whom we have cited in the present section, is a forward-looking measure of capital that in no way depends on the decisions to be taken with respect to the employment of the capital goods in question. It may almost be described, perhaps, as a technological, rather than an economic measure of the output capacity of the capital. What is being sought, in this literature, is a measure of capital that should express its productive potential in the same way as an engineer might express the thermal capacity of a particular fuel. Naturally this capital measure encounters the problems and ambiguities created by the alternative ways in which the capital goods can be combined with the other inputs—the very alternatives which impose the necessity to make decisions. The truth is that when one considers a forward-looking measure of capital one ought to renounce interest in all other aspects of the capital stock in question and inquire only into the output flow which possession of the existing stock promises to generate. From this point of view the forward-looking capital measure measures future prospects; it is of the essence of the theory of capitalistic production that future prospects cannot be simply read off from the list of capital goods now possessed. Future prospects represent the output flow expected from a particular plan being contemplated with respect to the capital stock now possessed. Only in the context of such a contemplated plan, can the owner of a stock of capital measure it in a forward-looking manner.

Market Value as a Measure of Capital

We turn now to review briefly the manner in which the capital measurement literature has dealt with the possibility of using the market prices of capital goods as a measure of the quantity of capital they represent. As Lerner has observed, this procedure is most tempting; a market value is expressed in terms of homogeneous money, it is a value measure that can be related to income, it corresponds to the way in which the businessman measures his capital, it facilitates calculations involving the rate of interest.[44] Nonetheless many economists have expressed uneasiness on the matter, both from the point of view of the practical feasibility of the procedure, and from that of its theoretical validity.

As far as concerns the practical feasibility of measuring the quantity of capital represented by a collection of capital goods by reference to their market value, the problem is a simple one. It has been pointed out that the characteristic immobility and specificity of capital goods leads to a high level of transaction costs, with a consequently weak second-hand market. Market prices for most goods in the capital stock are thus difficult to obtain.[45] This difficulty, of course, is of more concern to the statistician than to the theorist.[46]

From the theoretical standpoint the market value measure of capital has been criticized on a variety of grounds. It has been pointed out that market prices reflect individual valuation only as made at the margin, so that the use of market prices to measure the total value of capital is inappropriate. (This criticism is, of course, relevant to the measurement also of other economic quantities, such as that of consumer goods, in terms of market value.)[47] This objection seems a very powerful one with respect to attempts to measure the quantity of capital in the economy as a whole.

It has also been pointed out that for purposes of comparison over time, not many of the characteristic problems of capital measurement can generally be avoided by the use of market values. As soon as one wishes to make corrections in order to adjust for price changes over time, one is faced with the problem of constructing an index of capital goods prices. But in order to construct such an index one must be able to measure the quantity of capital in units other than money. We are “back to the point where we started.”[48] It ought to be observed that this objection has relevance primarily to the use of market values in order to measure capital goods viewed as mere physical goods. When market values are considered (as they were, with limited results, in the first half of this chapter) in order to facilitate a backward or forward-looking capital measure, the problem of adjusting for price changes is in principle no more difficult than it is in connection with other kinds of economic measurements.[49]

Several writers have objected to the market value measurement of capital quantity “because we do not identify quantity with money value for any other class of commodities, so how can we justify it for this one?”[50] Lerner, for example, shows how the measurement of labor by its market value might lead to a reduction in the quantity of labor (so measured) when the number of man-hours worked is in fact increasing. The confusing consequences for the specification of the marginal product of labor are not difficult to imagine.[51] This objection, too, seems to have relevance only to the measurement of capital in the sense of physical goods; only then can one demand parallelism with the measurement procedures used with the other factors of production. Nonetheless it is important to notice the asymmetry between the treatment of other factors of production on the one hand, and of capital (in the forward-looking sense, say) on the other hand. This asymmetry has been noticed by several writers.[52]

A number of writers are dissatisfied with a market value measure of capital because they are interested in a measurement of the quantity of capital partly in order to explain the rate of interest. Since the market values of capital goods necessarily reflect already the rate of interest (at which future yields are discounted), the resulting aggregate quantity can hardly be used as an independent factor in explaining the determination of the market rate of interest.[53] One’s appraisal of the seriousness of this objection will depend on the importance one attaches to an explanation of market interest rate determination that rests on the aggregate quantity of capital in the economy. (And it must not be forgotten that, no matter what the market rate of interest, the participants in the capital goods market never lose sight of their own individual subjective scales of time preference, in their calculations of the present subjective value to them of anticipated output flows of various time shapes).

Ultimately, then, the usefulness of market values for capital measurement depends on what precisely it is than one is seeking to measure. If it is physical things that one seeks to measure, without regard to their “capital”-character, then clearly market values will not do. Market values reflect the valuations of the market participants. If it is in the past (“cost”) history of the capital goods that one is interested, market values can again be of little use; market prices do not in general directly reflect bygone conditions.[54] Only if one is interested in a forward-looking measure of capital do market values hold any promise of being at all useful. The limitations to their usefulness in this regard, (especially insofar as concerns the aggregate quantity of capital in an economy) have been discussed in the first half of this chapter.

Cost Measurements of Capital

Among the various proposals towards the measurement of capital that have been put forward in the literature are a group which concern themselves with the cost of capital goods. We will now briefly examine these proposals, and discuss their relationship to the “backward-looking” capital measure that was considered (and rejected) in the first half of this chapter.

The attempt to measure the quantity of capital represented by the cost of capital goods has been made in a number of variants. We find (a) real cost measures; (b) cost measures in terms of foregone consumption goods; and (c) a cost measure, that differs from either of these two measures, that has been proposed by Denison.

(a) Real cost measures seek to measure capital by finding out what inputs the capital goods “embody.” If capital good A was produced by 10,000 man-hours of labor, then it is to be described as consisting of twice the capital represented by capital good B, produced by 5,000 man-hours. Good A embodies twice the input embodied by good B. In principle a real cost measure of capital could be devised such that all inputs (including if so considered, “abstinence” or “waiting”)[55] should be reflected in the measure.[56] Mrs. Robinson, however, has proposed a pure labor-cost measure of capital.[57] The obvious weaknesses of this rather surprising proposal have been thoroughly criticized by a number of writers, among whom we may perhaps include Mrs. Robinson herself.[58] One general objection (over and above these criticisms) thrusts itself forward, from the point of view adopted in this essay, against all real cost measures. This is that, as explained in the first half of this chapter, they cannot reflect the past sacrifices, subjectively understood, that were undertaken for the sake of today’s capital goods. All that real cost descriptions of capital goods can furnish is the technical, not the economic history of these goods. (Even the inclusion of “waiting” in the real cost concept that Dorfman has presented does not exempt it from this stricture, because, as discussed in the preceding chapter, the waiting concept used is itself not appropriate to the explication of the economic choices made.)

(b) A second cost measure of capital is that which measures a stock of capital goods by the sacrifice in terms of consumption goods that the capital goods represent. While no thoroughgoing attempt to develop such a measure seems to have been undertaken, a number of writers have discussed the possibility of such a measure, and seem to have assumed its theoretical validity.[59] The basic idea is to reduce the capital stock to “its equivalent” in consumption goods, on the basis of the universal necessity to forgo the latter if capital is to be possessed. If this can be accomplished, if capital can be expressed as its equivalent in consumption goods, we would have a measure that can be compared with income and can be used in conjunction with interest rate comparisons. Such a measure would be a cost measure since it represents the opportunity cost, in terms of immediate consumption, of the capital stock.[60]

While there is a certain initial attractiveness in a proposal to measure capital—representing the basis of our anticipations for greater “future” consumption—in terms of the associated sacrifice of “present” consumption, the proposal cannot be pronounced theoretically satisfying. A comparison of the notion of sacrifice involved in such a proposal, with that which provided the rationale for the (unsuccessful) search for a backward-looking capital measure in the first half of this chapter, at once reveals the inadequacies of the proposal here being discussed. This proposal finds the quantity of consumption goods that has a market value equal to that of the capital stock, and then immediately states the former quantity to be what is foregone in order to maintain possession of the latter. Now insofar as the individual capital owner is concerned, it is quite true that the market value of his capital goods expresses the immediate consumption that he rejects in order to ensure for himself the future output flow to be derived from his capital stock. This expresses his subjective assessment of the present value of the future output stream as being greater than the current market price of the capital goods (in terms of its current purchasing power over consumption goods).[61] This, after all, was the reasoning behind the use of the market value of capital as a forward-looking measure. But it is difficult to see how this provides the basis for an aggregate measure of capital (as the writers cited above apparently intend it to be used). It is difficult to read meaning into such a concept as the aggregate present consumption foregone for the sake of the aggregate capital stock. How could a choice be made now by the economy as a whole between its entire stock of capital on the one hand, and its “equivalent” in consumption goods on the other. If the sacrifice in consumption goods pertains to that which has been foregone in the past during the history of the accumulation of the present capital stock, then, as discussed at length in the first half of this chapter, it is necessary to specify the decisions responsible for these sacrifices, and it is further necessary to gauge these sacrifices in terms of the choices made at the dates of these decisions, and in terms of the value rankings relevant to these dates. Nothing in the brief statements of the proposal here under discussion makes any mention of all this, or of the theoretical difficulties we have already seen all this to entail.

(c) We refer finally to the rather special cost measure proposed by Denison in his pioneering paper on capital measurement.[62] Denison specifically rejects forward-looking measures of capital, and asks for a measure based on cost. Two machines which, in a given year, would cost equal amounts to produce, are to be described as consisting of equal quantities of capital, in spite of the possibly superior productivity of one of the machines. Denison emphasizes[63] that his is not a real cost measure: two identical machines produced, in different years, with different quantities of labor, still represent equal quantities of capital, because in any given year they would be produced at equal cost (since they are identical). In fact, it is clear, Denison’s measure is not all a “cost” measure in the sense of measuring the economic sacrifice historically involved. Rather Denison is attempting to measure machines in physical terms and reasons that physically equal things can be produced by physically identical inputs in a given year. This provides the rationale for using production cost as an index of physical quantity. One’s appraisal of this measure must largely rest on what one conceives it to be that one wishes to measure. Denison’s own interest, as developed at length in his paper, is quite a practical one. For those seeking a notion of capital measurement that should help to sharpen one’s theoretical concept of the nature of capital and its place in the production process, Denison’s measure can be of little assistance.

The Durability of Capital as an Obstacle to Measurement

Our review of the capital measurement literature has revealed a number of aspects of the matter that have given rise to difficulty. In closing this survey we draw attention briefly to one further aspect which, in the opinion of several writers, is responsible for much of the practical difficulty of measuring capital. These writers refer to the durability of capital goods as a source of difficulty.[64] The matter is of some interest in that it reveals what these writers seek to be measured by a capital measure, and also illustrates their view on the economic role of capital in production.

Where two otherwise identical machines are of different durabilities, these writers contend, the market will value the longer lasting machines more highly and will thus distort the measurement of the quantity of capital. What we have here are two identical machines, but the market does not consider them identical. In order to obtain a correct capital measure, it is thus necessary to adjust by reducing the value placed on the more durable machine.

Clearly what is being sought to be measured is “the number of machines,” rather than the quantity of capital represented by these machines, in any of the senses usually attached to the term. The focus of attention for these writers is not a period of time long enough for the different durabilities of the machines to make a difference, but rather one so short that each of the “identical” machines be for all practical purposes equal to the other. The search for such a measure of physical things necessarily diverts attention from the future economic history of these things, and also (insofar as different costs may have been incurred for the sake of different durabilities) diverts attention from the past economic history of these things. We are left with the search for a measure of physical things in respect of which varying durability is a distinct nuisance.

More fundamentally, it seems, at least part of the problem raised for these writers by varying durability, is to be ascribed to the particular view of the nature of capital that has been discussed in Chapter Two in connection with the work of Haavelmo and of Smith. It will be recalled that these writers saw the function of capital in production to consist of making its productive contribution by simply being there. In this view the essence of the role of capital is to increase the productivity of the flow inputs while itself not being used up. It follows that insofar as different machines are capital, their productive contribution is completely independent of their durabilities. Where the market bids the price of the prospectively longer-lived machine higher, this in no way reflects any greater quantity of the currently-stocked input. With the time aspect of production plans pushed into the background in this way, the first requisite for a measure of capital is to adjust matters so that the varying lives of different machines can be ignored.[65]

---

[1] The terms “forward-looking,” and “backward-looking” measures of capital were introduced by Hicks (1961). It will be seen that they are used here in a sense somewhat different from that used by Hicks.

[2] As we will discover in the second half of this chapter, an examination of the literature turns up many attempts to measure capital goods in purely physical terms. A widely employed justification for such attempts has been the wish to be able to measure changes in the “productivity of capital,” or to examine the production functions in which capital goods appear as inputs (and are thus measured in physical terms). Insofar as interest in these aspects of capital pertains to decisions made by potential producers, the discussion in the text denies validity to such attempts at physical (as distinct from economic) homogenization. On the relevance of “productivity” measurement to the decision-making approach to economic analysis see G. Stigler (1961).

[3] The distinction is ascribed by Hayek (1941) p. 66, to R. Frisch. See also Lutz and Lutz (1951) p. 5.

[4] Even in point input-point output cases the difficulty will still exist with respect to the different capital goods produced at different dates.

[5] See Little (1950) pp. 84–85; Rothenberg (1961) Appendix to Chapter 2, and Weckstein (1962).

[6] See Mises (1953) p. 48.

[7] “Any measure based on market prices was bound to be forward-looking. . . .” Malinvaud (1961b) p. 306.

[8] Cf. Lindahl (1939) pp. 313f.

[9] Cf. the discussion above pp. 21f; 62f.

[10] On this point see Smith (1962) p. 487.

[11] Even if one were concerned with a centrally planned economy the objections raised above (pp. 105f) in connection with the individual, would apply with equal force to the state.

[12] Kuznets (1957) pp. 271–272.

[13] Cf. above p. 34. See also Hayek’s (1941) (Part II) treatment of capital in which this approach is explicitly adopted (pp. 27, 99) with references to the antecedent literature. The concept of “intact maintenance of capital” for an economy as a whole must be understood in the same way. (See above p. 68 for the arbitrary judgments required to give meaning to this concept even for the individual).

[14] See Lachmann (1956).

[15] Lachmann (1958) p. 100.

[16] Böhm-Bawerk (1921) pp. 60–61.

[17] Knight (1935) p. 57.

[18] Hayek (1941) p. 93.

[19]Op. cit. ibid. See also Hayek (1936) pp. 372–376. On this point see also Kendrick (1961) p. 105.

[20] Samuelson (1962) p. 193.

[21] Hicks (1963) pp. 342f. Cf. also Griliches (1961) p. 118.

[22] See e.g. Dorfman (1959b) pp. 351f; Boulding (1950) pp. 177–182; Hahn and Matthews (1964) p. 888. See also Green (1964) Part IV.

[23] Smith (1962) p. 486; Kendrick (1961) p. 107; Domar (1961) pp. 404–5; Andersen (1965) p. 69; Haavelmo (1960) p. 45.

[24] Haavelmo (1960) p. 45; Lerner (1953) p. 540; Metzler (1950) p. 292.

[25] In the discussion in the first half of this chapter queries were raised as to whether either past sacrifices or future yields do, in fact, present homogeneous aspects of capital. While these questions do not seem to have been raised in the literature on sacrifice, several writers have noticed the problem of heterogeneity in yield. See Kendrick (1961) pp. 108f; Sen (1960) p. 17; Robinson (1956) p. 119; Lachmann (1958) p. 93.

[26] Hahn and Matthews (1964) p. 888.

[27] Solow (1956) pp. 101–102; Samuelson (1962) p. 193.

[28] Sen (1960) p. 17.

[29] See Lerner (1953) p. 540. Note that Lerner’s own position is that the marginal product of capital is not the magnitude that should be compared with the rate of interest, so that this problem disappears.

[30] Hicks (1963) pp. 344–345.

[31] Ramsay (1928); Hahn and Matthews (1964) p. 783; see Lerner (1953) p. 541.

[32] Dewey (1963) p. 134n.

[33] Dorfman (1959b) p. 355.

[34] Smith (1962) p. 484.

[35] On all this see Lachmann (1956).

[36] The distinction between “embodied” and “disembodied” technical change has been elaborated on especially by Solow see e.g. (1962) and (1963).

[37] See at length Denison (1957).

[38] See Hicks (1961) p. 30. More recently (1963) p. 349, Hicks has for this reason endorsed the partial use of the “Physical Things” concept of capital. Cf. also Ruggles (1961) p. 389.

[39] Ruggles (1961) pp. 388–389; Hicks (1963) p. 345; Solow (1956) p. 102; Green (1964) p. 11; Barzel (1964) p. 142; H. A. Simon cited in Hammer (1964) p. 16, n.29.

[40] Hicks (1961) p. 30.

[41] Green (1964) p. 94.

[42] See his “method (2)”, Denison (1957) pp. 219, 227–229. Denison’s method (3) is more closely akin to Green’s criterion, but is not identical with it.

[43] Green (1964) p. 94.

[44] Lerner (1953) p. 539.

[45] Hicks (1961) p. 19, Barna (1961) p. 79, Domar (1961) p. 404, Smith (1962) p. 487.

[46] However Mrs. Robinson (1954) p. 120, points out that the narrowness of the market affects the theoretical value of the prices actually prevailing on it.

[47] Kennedy (1955) p. 38. See also Knight (1956) p. 47n; Hicks (1963) p. 343.

[48] Barzel (1964) p. 142; see also Ruggles (1961) p. 391; Hicks (1963) p. 344.

[49] Cf. Hicks ibid.

[50] Dorfman (1959b) p. 352.

[51] Lerner (1953) p. 539.

[52] See e.g. Hicks (1961) p. 30n. Cf. also Denison (1957) pp. 228f.

[53] Robinson (1954) p. 115; Sen (1960) p. 18; Dorfman (1959b) p. 352.

[54] On this see the exchange between Denison and Kuznets (1957) pp. 275, 283.

[55] On the notion of measuring the congealed quantity of waiting “embodied” in capital goods, see Dorfman (1959b) and our discussion above Ch. 3, pp. 89–91.

[56] See e.g. Denison (1957) p. 227, n.13. Cf. also Hicks (1961) for a “backward-looking” measure of capital, the philosophy of which differs considerably, however, from the real cost measures here discussed.

[57] Robinson (1954) p. 115, (1956) p. 20.

[58] Kendrick (1961) pp. 106–108; Samuelson (1962) pp. 203–4; Lachmann (1958) pp. 94–95; see also Sen (1960) p. 18; Robinson (1954) pp. 115–116.

[59] Denison (1957) p. 227, n.13; Kuznets (1957) p. 276; Robinson (1956) pp. 119–21; Hicks (1963) p. 343.

[60] Mrs. Robinson (1954) p. 116, in arguing for a labor cost measure of capital, rejects the consumption sacrifice cost of capital notion, “for the addition to the stock of productive equipment made by adding an increment of capital depends upon how much work is done in constructing it, not upon the cost, in terms of final product, of an hour’s labour.”

[61] Green (1964) p. 88, in fact, has used this insight to justify measuring capital in terms of its equivalent in current consumption goods, not as a cost measure, but as a measure of prospective yield.

[62] Denison (1957) pp. 218, 222–227.

[63]Op. cit. pp. 227, 282.

[64] Haavelmo (1960) p. 82; Griliches (1963) p. 118; Domar (1961) p. 404; Andersen (1965) p. 69.

[65] Cf. also Smith (1962) p. 486, n.3.