II. Equilibrium Analysis and the Capital Problem

CHAPTER II EQUILIBRIUM ANALYSIS AND THE CAPITAL PROBLEM IT was suggested in the first chapter that most of the shortcomings of the theory of capital in its present form are due to the fact that it has in effect only been studied The construction o( under the assumptions of a stationary state, a stationary state Is where most of the interesting and important unsullable (or discussion o( capital capital problems are absent. This is so problems largely because the characteristic problems of capital theory are problems of the interdependence of different industries and consequently only arise in con nection with a theory of general equilibrium, and because most of the current systems of economic theory (par ticularly the most influential, that of Marshall) do not really consider any state of general equilibrium which is not at the same time stationary. The so-called short-term equilibria, if this concept is to have any meaning, must necessarily be conceived as partial equilibria. 1 And the long-period equilibrium, which alone is a general equi librium, is (as Marshall himself has pointed out) identical with" the supposition of a stationary state of industry". 2 1 The reason for this will beCOlne clear as we proceed. Here it need only be pointed out that the method of short-term equilibrium essentially consists in disregarding all these consequences of a given change whose significance, for the problem immediately under consideration, is of the second order of smalls. This means that we deliberately neglect conse quences because they do not affect the parts of the system with which we are mainly concerned - a procedure which is clearly inadmissible when we are interested in the equilibrium of the system as a whole_ • Cf. A_ Marshall, Principles of Economics, 7th ed., p_ 379 note: .. But in fact a theoretically. long period must give time enough to enable not only the factors of production of the commodity to be ' adjusted to demand, but also the factors of production of those factors of production to be adjusted, and so on; and this, when carried to its logical consequences, will be found to involve the supposition of a 14 CR. II Equilibrium Analysis and Capital Problem 15 An effective discussion of the problems of capital theory must, however, move precisely in that neglected field which deals with general equilibria that are not at the same time stationary states. It must p'roceed Gonoral equilibria by way of a theory of general equilibrium which are not b 't d I 'th th . tit' h' stallonary ecause 1 ea S WI e In eITe a IOns IpS between groups of industries, and in particular with those effects of changes in one industry on another which are deliberately neglected when we study the particular short-period equilibrium of a special industry or group of industries. And it must not be confined to the stationary state, because here ex definitione most of the problems with which the theory of capital must be concerned have disappeared. 1 The main problems are to explain what types of instruments will be produced under given con ditions, and what will be the consequences of producing particular instruments. And these problems will of course be non-existent if we assume from the beginning that the same stock of instruments will be constantly reproduced. The impossibility of treating the problems of capital adequately within the framework of a station ary equilibrium becomes, of course, even more obvious as soon as we include, as we must, the problems relating to wha,t are usually described as "saving" and (new) " investment", since these are activities which imply by stationary state of industry in which the requirements of a future age can be anticipated an indefinite time beforehand. . . . Relatively short and long periods go generally on similar lines. In both use is made of that paramount device, the partial or total isolation for special study of some set of relations." See also ibid. p. 367, where the stationary state is described as a state in which " the same amount of things per

head of the population will have been produced in the same ways by the same classes of people for many generations together; and there fore this supply of the appliances for production will have had full time to be adjusted to the steady demand." 1 Cf. W. E. Armstrong, 1936, p. 1: "All that is significant and vital in the concept of Waiting (as the equivalent of Capital) belongs to the economics of the developing community, and cannot without violent wrenching of ideas outside their proper context be transferred to the study of Stationary States ".

16 Introductory PT. I definition that the persons undertaking them want to alter their future position, and consequently will do in the future something different from what they are doing in the present. Perhaps the irrelevance of the stationary equilibrium construction for the treatment of capital problems comes out most clearly when we remember that this fictitious Stationary equIlIbrium without reference to what happens 10 the process of reaching It state could not conceivably be brought about at any given moment in society as it exists, but could be reached only after the lapse of a very long time. 1 The equip ment which is given at any moment is always the in heritance from a past in which future developments have been foreseen only very imperfectly. And, as we shall see, it is precisely the existence of this equipment and its effect in determining what we can and what we cannot do for a very long time ahead, which constitutes the datum that creates the peculiar problem of capital. A theory which starts out by assuming that adjustments have pro ceeded to the point where no further changes are required 1 Stationary equilibrium presupposes the existence of equilibrium relations between the existing things, that is, it assumes that the exist ing goods are of exactly the same kind as those which under existing conditions it will be profitable. to reproduce. It is not an equilibrium determined by the types of goods which happen to exist, but an equilibrium which has found expression in the past production of particular types and quantities of goods. For this reason it is without significance for the explanation of what happens prior to the time when all goods that are not permanent have been replaced by such goods as it will be advantageous to reproduce indefinitely in identical forms and quantities. It is supposed to be determined solely by the permanent resources and the vague concept of a given supply of free capital, and to be independent of the particular forms in which capital actually exists. The equilibrium in which we are interested here is not an equilibrium that is already embodied in the things, but an equilibrium between the different activities of creating new goods, as determined by the goods which happen to exist at the outset. This concept is in fact no less realistic than that of a stationary equilibrium: since in order to arrive at a stationary equilibrium it would be necessary to pass through a phase in which the changes required to bring about a stationary state were still going on but their results were correctly foreseen.

CU. II Equilibrium Analysis and Capital Problem 17 is without relevance to our problems. What we need is a theory which helps us to explain the interrelations between the actions of different members o.f the com munity during the period (which is the only period of practical importance) before the material structure of productive equipment has been brought to a state which will make an unchanging, self-repeating process possible. This extension of the technique of equilibrium analysis which we propose to use here is still somewhat unfamiliar. It may therefore be useful, before we proceed to develop it further, to throw some added light on to bl f The am gully 0 Ihe the difference between the two concepts of concepl of "dynaequilibrium involved, by a short discussion mles" of a closely related ambiguity in the use of the concept of dynamics in economics. This concept has indeed two altogether different meanings according as it is used in contrast to the concept of a stationary state or in contrast to the wider concept of equilibrium. When it is used in contrast to equilibrium analysis in general, it refers to an explanation of the economic process as it proceeds in - time, an explanation in terms of causation which must necessarily be treated as a chain of historical sequences.

What we find here is not mutual interdependence between all phenomena but a unilateral dependence of the succeed ing event on the preceding one. This kind of causal explanation of the process in time is of course the ultimate goal of all economic analysis, and equilibrium analysis is significant only in so far as it is preparatory to this main task. But between the concept of a stationary state and the problems of dynamics in this sense, there is an inter mediate field through which we have to pass in order to go from one to the other. The term dynamics is some times also applied to this intermediate field, but here it refers to phenomena which still come within the scope of equilibrium analysis in the wider sense. All that the use of the term dynamics means here is that 18 Introductory !'T. I we do not postulate the existence of a stationary state; but it says nothing about the method which we use.!

Now as I have tried to show elsewhere,2 the general idea of equilibrium, of which the stationary state is merely a particular instance, refers to a certain type Non-stationary equl-of relationship between the plans of IIbria denned different members of a society. It refers, that is, to the case where these plans are fully adjusted to one another, so that it is possible for all of them to be carried out because the plans of anyone member are based on the expectation of such actions on the part of the other members as are contained in the plans which those others are making at the same time. This is clearly the case where people know exactly what is going to happen for the reason that the same operations have been repeated time after time over a very long period. But the con cept as such can also be applied to situations which are not stationary and where the same correspondence be tween plans prevails, not because people just continue to do what they have been doing in the past, but because they correctly foresee what changes will occur in the actions of others. This sort of fictitious state of equi librium which (irrespective of whether there is any reason to believe that it will actually come about) can be con ceived to comprise /tny sort of planned change, is indis1 It is at least questionable whether the introduction of the terms statics and dynamics into economics (by J. S. Mill following A. Comte's similar division of sociology) which is responsible for this confusion was beneficial. It seems to me that the only relevant distinction is between two methods, that of logical analysis of the different plans existing at one moment (" equilibrium analysis ") and that of causal analysis of a process in time. For this distinction the terms statics and dynamics seem altogether inappropriate, and it would probably be better if they were to disappear entirely from economics.

2 In an article on " Economics and Knowledge", Economica, N.S" vol. iv, no. 13 (February 1937), and, in a rather unsatisfactory form, much earlier, in an article on "Das intertemporale Gleichgewichts. system der Preise und die Bewegungen des Geldwertes"; Weltwirt· 8chaftliche8 Archiv, vol. 28 (1928).

CR. uEquilibrium Analysis and Capital Problem 19 pensable if we want to apply the technique of equilibrium analysis at all to phenomena ~hich are ex definitione absent in It stationary state. It is in this sphere alone that we can usefully discuss equilibrium relations ex tending over time, and in which consequently the pure theory of capital mainly falls, and the latter might almost be said to be identical with the whole of this intermediate field between the theory of the stationary state and economic dynamics proper. Yet this field has never been systematically explored. It must be admitted, however, that there is partial justification for this in the fact that there is no reason to believe that any general equilibrium could ever be fully realised except after all changes in data Why the concept 01 had ceased (that is as a stationary state a temporary partial equlllbrium Is load. was reached), and that in consequence there quate lor our puris no obvious need for the explanation of the pose economic process as it proceeds in time to make use of such a hypothetical construction. It may be thought that this is more than we require or can expect from the equi librium method: and that all we need do is to explain how temporary equilibria are formed on particular markets.

This would involve explaining how, once the more mobile elements have been adjusted, a temporary state of rest is arrived at which will last until the slower changes in the more permanent part of the productive equipment are effected. We could then describe the conditions that will prevail when all these changes have been completed (that is the hypothetical state which would ultimately be reached where all the data would remain unchanged). After all, decisions about what and how to produce are being made and revised periodically at fairly short intervals, and it may seem that period analysis which makes use of the concept of partial short-term equilibrium at each stage takes account of this essential fact and will come as near a realistic explanation of events as we can reasonably hope for from this type of approach.

20 Introductory PT. 1 There arises serious doubt, however, whether the concept of short-perioq. equilibrium, if applied to an economic system as a whole,! has any definite meaning. The question is whether there is any such interval of comparative rest between the moment when the more mobile factors have been adjusted and the time when the more rigid elements of the structure can be effectively adjusted. 2 This presupposes that with respect to the time it takes to adapt them to new circumstances, the existing means of production can be divided into two distinct groups. It assumes that the times it takes to alter different items of the stock of existing resources by using them up and producing new ones (which will depend on the durability of the individual resources and the time it takes to produce them) are not dispersed over a fairly continuous range but are definitely clustered about two most frequent points with a more or less empty interval between them. It seems highly doubtful whether this assumption is in any way justified by the facts, and for this investigation at any rate I prefer to adopt what seems to me the more plausible assumption that these periods are spread fairly continuously and without any 1 I.e. as distinct from a particular industry in which special con· ditions make it possible to mark off a particular periofl as being short compa.red with another.

2 Without some such assumption the use of the term equilibrium has no justification whatsoever. It becomes a completely empty con· cept, saying no more than that at any moment some factors have had time to adjust themselves and others have not had time, and this would be true of any position. The distinction between short. and long. period equilibrium does of course make sense where, as in all the examples used by Marshall, it is applied to a particular industry, because in many cases the changes inside that industry will take place in two stages separated by an interval of time. But to make the later of these changes (i.e. the changes in the durable equipment) possible, changes must be going on during the interval in some other industry. And while we may be justified in disregarding these changes elsewhere so long as we are only concerned with the situation in the first industry, this becomes clearly illegitimate when we speak about the system as a whole. The use of the concept of a general short· term equilibrium in recent monetary analysis seems to me highly questionable.

UH. II Equilibrium Analysis and Capital Problem 21 marked break (though not necessarily evenly) over the whole range of periods in question. l Yet, quite apart from this particular point, it is apparent that this use of the equilibrium concept fails to take advantage of some of the most valuable aids that are to be derived from this powerful intel lectual tool. So long as the pretence is kept up that the idea of equilibrium must refer to something which we can observe in the real world, or which at least can be shown To make full use of the equilibrium con cept we must abandon the pretence that It refers to something real to arise spontaneously under certain conditions, there is probably no other way of dealing with these problems. But I am inclined to helieve that these attempts to give the equilibrium concept a realistic interpretation (the legitimacy of which remains in any case somewhat doubt ful) have deprived us of an at least equally important use, which the concept will serve if we frankly recognise its purely fictitious character. It has often been empha sised that the concept of a state of equilibrium is inde pendent of any possibility of showing how such a state will ever come about. The reason why this assertion has had so little effect on the use which is actually made of the· equilibrium concept is probably that those who made it did not properly show how such a fictitious construction could help to explain real events. In fact when it came to any concrete use of the concept, either it was defined as timeless, 2 1 The distinction between the "short" and the ." long " period equilibrium is the most general cas~ of a distinction which arises in several interconnected fields. The distinctions between" prime" and " supplementary " cost, between " circulating" and "fixed " capital, and between "current" production and (gross) "investment ", all belong to the same category and raise the same difficulties. They ought all to be treated, and win be so treated here, as limiting cases of a continuous range of variations, and not as representative of a particularly characteristic or most frequent type. No attempt will be made here to draw any arbitrary line of division in place of a frank recognition that these forms of the phenomena in question shade im perceptibly into each other.

2 In which case, as I have tried to show in the article already referred to, it is meaningless.

22 Introductory PT. I or else resort was had to the stationary state. In the sphere of capital theory, as we have seen, the construction of a stationary state is particularly useless because the main problem, that of investment, arises I t t I I just because people intend to do in the n er empora equ Iibrlum and capital future something different from what they analysis d' . th t Th' t t are oIng In e presen . e Inves men itself they may intend continuously to repeat as the instruments created need replacement. But the results of investment, whether they be direct services for con sumption or (as in the majority of cases) an aid to further production, will necessarily alter the things that need to be done and can be done in the future. To postulate a self-repeating stationary state is to -abstract from the very phenomena that we want to study. Nevertheless there is a very significant sense in which the concept of equilibrium can be of great use if it is made to include plans for action varying at successive moments of time.

The essential problem remains that of. whether the plans of different individuals will tally and will accordingly all stand a chance of being successful, or whether the present situation carries the seed of inevitable disappointment to some, which will make it necessary for them to change their plans. We must not lose sight of the reason why we are interested in the analysis of a particular economic system at a given moment of time: our purpose is to be able to proceed from a diagnosis of the existing state of affairs to a prognosis of what is likely to happen in the future. Now, if we want to predict at all, it must be on the basis of the plans which entrepreneurs are likely to make in the light of their present knowledge, and of an_ analysis of the factors which in the course of time will determine whether they will be abl~ to carry out these plans or whether they will have to alter them. It seems natural to begin by constructing, as an intellectual tool, a fictitious state under which these plans are in complete correspondence without, however, asking whether this eH. II Equilibrium Analysis and Oapital Problem 23 state will ever, or can ever, come about. For it is only by contrast with this imaginary state, which serves as a kind of foil, that we are able to predict what will happen if entrepreneurs attempt to carry out any given set of plans. The description of the equilibrium position in this sense is at the same time a description of the mutual interdependence of the decisions of different entre preneurs.

The direction in which an entrepreneur will have to revise his plans will depend on the direction in which events prove to differ from his expectations. The state ment of the conditions under which individual plans will be compatible is therefore implicitly a statement of what will happen if they are not ,compatible. 1 It will be seen that this extension of the equilibrium concept provides the bridge from equilibrium analysis to the explanation in terms of causal sequences, since it is designed to elucidate the factors which will Relation to causal compel entrepreneurs to change their plans analysis and to the ex ante and ex and to help us to understand the way in post view of a given which their plans will have to be changed. situation In fact this use of the .equilibriumconcept is not funda mentally different from the comparison between the prospective and retrospective (or ex ante and ex post) views ·of a particular situation, as used by the younger Swedish economists, 2 since the ex post situation can be derived from the ex ante only by reference to the degree of correspondence or non -correspondence between indi vidual intentions. The state of equilibrium as here under stood is a state of complete compatibility of ex ante plans, where in consequence (unless changes occur in the external data about which economic theory cannot say anything 1 This is strictly true only if we are thinking of a single deviation of a particular element in a situation which is otherwise in equilibrium, that· is on the assumption that all other expeetations are confirmed.

If more than one element turns out to be different from what was expected, the relation is no longer so simple. 2 Cf. G. MyrdaJ, Monetary Equilibrium (London, 19:1H). p. 4H.

24 Introductory 1'"1". I in any case) the ex post situation is identical with the ex ante. It serves as a kind of standard case by reference to which we are able to judge what to expect in any concrete situation. The significance of these abstra'ct considerations will be clearer if we illustrate them by reference to the prob lems of investment. The problems of capital or of Application to prob-investment, as here defined, are problems lems of Investment connected with the activity of making provision in the present for the more or less distant future. The relevant future with which we are con cerned is, however, somewhat more extensive than the periods for which the individual consciously invests at a particular date. His plans at any moment will be based on the expectations of a certain future state of the market which will allow him to dispose of his products at a certain price; and beyond this his interest will not extend. But the objective "state of the market" on which he counts is largely the result of the present decisions of other people. In order that he may succeed in disposing of his products as he expected, it will be necessary for others to have made preparations which will enable them to use just those products at the prices at which he expected to sell them. In other words, the state of the market at the time for which he plans will largely depend on what others have decided at the same time as he made his plans. This is so not only, or even mainly, because the incomes which these other people will have to spend will depend on what they have pro duced, but also because what instruments and materials they will need will depend on what plans for production they have embarked upon. This means that although every individual will be guided only by (more or less well founded) expectations of particular prices, he will actually be performing part of a larger process of the rest of which he knows little; and his success or failure will depend on whether what he does fits in with the other CH. II Equilibrium Analysis and Capital Problem 25 parts of that larger process which are undertaken or contemplated at the same time by other people. What he performs will in the majority of cases be no more than a single step in a long chain of successive operations.

His action may be removed from ultimate consump tion by many stages, and its success will be dependent at each stage, not so much on the final demand as on the presence or absence of complementary ipstru ments in proportionate quantities, and on there being people willing to use them in subsequent stages of pro duction. All these successive operations have to be viewed as parts of one integral process,each of them having chances of success only by reason of its position in the whole. In any system with extensive division of labour (par ticularly where it is of the "vertical" type and many successive operations by different entrepreneurs are dependent chainwise upon one another) every decision to produce one thing rather than another will be dependent for its success on other things being produced in appro priate quantities. Thus we have definite quantitative relationships between the required output of different kinds of goods, which (owing to the technological character of the process) will usually be of a more rigid character in the case of producers' goods than in the case of consumers' goods. Almost any quantitative combination of different kinds of consumers' goods. will be capable of use in some way or other. But the limits within which the proportions between the quantities of the different kinds of producers' goods may vary are much narrower. There are definite proportionalities, quantitative relations, between the different parts of the structure of production, which must be pre served if some of these parts are not to become completely useless.

It is clearly possible to study the quantitative relations between the different parts of the real structure of pro26 Introductory PT. 1 duction that will result from current plans, independently of the question of the forces which will secure, or fail to secure, the actual bringing about of such a corre spondence. In any given situation there will be one (and The correspondence inmost instances only one) way in which between production the plans of the various entrepreneurs can plans analysed by treating them as parts be made to harmonise with one another of a single plan and with the preferences of the consumers. The use of the equilibrium method ·here then means con structing an. imaginary state in which the plans of the different people (entrepreneurs and consumers generally) are so adjusted to one another that each individual will be able to sell or buy exactly those quantities of com modities which he has been planning to sell or buy. \ What will exist will of course still be only the separate plans of different individuals which are connected only by the fact that the quantities of goods which are expected to pass at different dates out of and into the possession of the various individuals exactly match. Any particular person need know neither who will take his products nor who will provide him with what he expects to get - he will only have expectations about what the anonymous 1 group called the market will provide and take; nor need he know much about the way in which the goods which pass into his hands have been produced, or about the way in which the goods he has produced will be used.

Nevertheless coincident expectations about the quantities and qualities of goods which will pass from one person's possession into another's will in effect co-ordinate all . these different plans into one single plan, although this " plan" will not exist in anyone mind. It can only be constructed, and it is in fact often convenient to adopt the practice, which has been followed by many economists, of proceeding for a time on the assumption that the actions of the different individuals are directed by somebody in 1 cr. F. Machlup, "Why Bother with Methodology 1 " Economica, N.S., vol. iii, no. 9 (February 1936), pp. 43 et seq.

CR. II Equilibrium Analysis and Capital Problem 27 accordance with a single plan. 1 In the nature of the case this fictitious assumption can be only provisional, and must later be abandoned in favour of the assumption of separate but perfectly matched plans of the different individuals-that is: of competitive equilibrium in the sense outlined above. It is inevitable that opinion will be divided about the usefulness of such an admittedly fictitious construc tion as the concept of equilibrium here employed. And there is no way of demonstrating its use-R f b" elaUon 0 I .. slale fulness other than by applying it to a of equilibrium 10 t· I bl It' h . realliy par ICU ar pro em. IS, owever, Important that no misunderstanding should arise about the justification that is claimed for it. Its justification is not that it allows us to explain why real conditions should ever in any degree approximate towards a state of equilibrium, but that observation shows that they do to some extent 2 1 This device was used most systematically by F. Wieser, first in his Natural Value and later in his Social Economic8, where he prefixed his theory of the social economy with an elaborate theory of what he called a " simple economy", i.e. a centrally directed economy. More recently Professor Pigou (in his Economics of Stationary State8, 1935) has once again made use of Robinson Crusoe for the same purpose.

It is interesting to note that Marshall, when he comes to discuss invest. ment, finds it also convenient first to discuss it " by watching the action of a person who neither buys what he wants nor sells what he makes, but works on his own behalf" (Principks, 7th ed. Book V, chap. iv/I). 2 It should be remembered that nearly the whole of economic science is based on the empirical observation that prices" tend" to correspond to costs of production, and that it was this observation which led to the construction of a hypothetical state in which this "tendency" was fully realised. A good deal of confusion has been caused in this con· nection by the vagueness of the term tendency. A given phenomenon may tend to (approximate towards) a certain magnitude if in a great number of cases it may be expected to be fairly near that magnitude, even if there is no reason to expect that it will ever actually reach it, however long the time allowed for the adjustment. In this sense " tendency" does not mean, as it is usually understood to mean, a move· ment towards a certain magnitude but merely the probability that the variable under consideration will be near this magnitude. The ideal state in which all the variables would be at the magnitude to which they tend to approximate in this sense is a state which one could not expect ever to be reached.

28 Introductory PT. I so approximate, and that the functioning of the existing economic system will depend on the degree to which it approaches such a condition. The explanation of why things ever should, and under what conditions and to what extent they ever can, be expected to approxi mate to it, requires a different technique, that of the causal explanation of events proceeding in time. But the fact that it is probably impossible to formulate any conditions under which such a state would ever be fully realised does not destroy its value as an intellectual tool. On the contrary it seems to be a weakness of the tradi tional use of the concept of equilibrium that it has been confined to cases where some specious "reality" could be claimed for it. In order to derive full advantage from this technique we must abandon every pretence that it possesses reality, in the sense that we can state the con ditions under which a particular state of equilibrium would come about. Its function is simply to serve as a guide to the analysis of concrete situations, showing what their relations would be under "ideal" conditions, and so helping us to discover causes of impending changes not yet contemplated by any of the individuals concerned.