All formal modelling must be in the nature of a “closed system” because the equations derived through the manipulation of real entities necessarily make these entities inter-dependent, that is, definable in self-referential terms that end up being tautological.
Let us specify the main features of “closed systems”. First, they reduce historical experience, human activity, to its objectification, to its products. Hence, social relations are represented as relations between things. Second, they prescribe a mathematical relation between distinct elements of these objectifications. Third, the objectified elements or variables are self-referential in the sense that they are inter-dependent. As a result, all closed systems are tautological vicious circles. The attempt of neoclassical theory to remedy this inescapable trap by seeking to adapt its axiomatic assumptions to “real variables” clearly cannot evade the fallacy because ultimately the equations must be valid in the sense that there must be as many independent equations as there are independent variables – which is the precise moment when the system of simultaneous equations becomes “closed” and all its variables become inter-dependent in that the value (in this case we are referring to market prices) of each individual variable is relative to the values (market prices) of all other variables.
Lawson’s definition of a “closed system” as one that can be reduced to the proposition “whenever x, then y” is manifestly wrong because this kind of proposition is essential to the testing of scientific hypotheses in both natural and social science; his test refers simply to experimental predictability, which applies to all scientific “laws”. Quite contrary to Lawson’s contention, then, a “closed system” becomes an analytical deductive model of the type “whenever x, then y, where x is a function of y” or f(x)=f(y): it is the classic circulus vitiosus or tautology, - nothing more nothing less: y is a function of x and x is a function of y. That is why a closed system is defined to be static, as against a dynamic system where the component variables change in ways that are not self-referential, that is, implicit in the existing variables. In this regard, Robert Clower has unleashed a vitriolic attack on “fraudulent” neo-walrasian equilibrium analysis, and proposed to replace it instead with an empiricist approach that presents economics as an inductive science – one based on observations of existing regularities in economic behaviour, including the intentions of agents. (Cf. R. Clower, Economics as Inductive Science.) The problem with this approach is quite obviously that it assumes that the existing economic system is the only proper possible object for “scientific” research!
To escape this trap, an economic theory worthy of the name must identify the interest that constitutes the motive or wealth sought in economic activity: it must address the real human purpose of economic activity – a purpose that therefore must lie outside of the quantities to which economic analysis wishes to reduce human activity and address (to invoke Adam Smith) the nature of wealth (its substance) and its causes (its pro-duction). Clearly, economic pursuits are ineluctably political because they are motivated by human inter-ests (from the Latin, inter homines esse, to live among men); they are quantitative only to the extent that quantities are substituted for social relations. Both the nature of economic activity and its causes refer to an inquiry (Smith again) that goes beyond the quantities involved in economic exchange. Whether humans co-operate or compete in the pursuit of economic interests, this pursuit remains political because it represents a “working together” (operari, work; opus, product)) or a “coveting together” (com-petere, to beg for the same object). Even where human interests are in con-flict (Latin, clashing together) there must still be a point at which they meet, an interest over which there is conflict.
A formal model or closed model in economic theory that does not account for value – the interest for which humans co-operate or compete - is merely an analytical tool which may very well have a purpose in the pursuit of an extrinsic interest, but does not explain that interest because the interest may only be implied by the tool or be concealed by it as part of a series of other tools. Thus, the distinction mirrors the one we have made between economic theory and economic analysis: the former explains the behaviour of social agents y establishing a practical motivational direct link to their interests; the latter simply provides tools to connect variables without addressing the interests behind the variables and the connections. (We shall exemplify this distinction further in connection with John Hicks’s Value and Capital.)
Given the intrinsic inapplicability of its fundamental assumptions and calculations to the historical treatment of social antagonism, neoclassical economic analysis has been entirely unable to develop a “dynamic economics” to identify the drivers of economic change despite the best efforts on the part of economic theoreticians in both the Neoclassical and the Austrian camps. All equilibrium theoreticians have shifted the subject-matter, the ground, the sub-stance, the substratum and quidditas, the “whatness” of economics from “prices and quantities”, which involve those material human interests that are and must be the indispensable foundation of all theories that even pretend to be “economic”, either to the mere “semaphoric” world of “information” and “co-ordination” or else to an imaginary institutional evolution of economic activity – with the overriding objective to account for what they assume to be the sole purpose of that activity: either the simple or the expanded (accumulated) reproduction of human society in an equilibrated co-ordination leading to the efficient maximization or optimization of social wealth taken as the aggregate of individual wealth.
Hence, in the words of Brian Loasby,
[t]he co-ordination of economic activities, of course, is what economics is overwhelmingly about, (B. Loasby, Equilibrium and Evolution, p.9).
The problem with this is that economics can never be reduced to a simple matter of “co-ordination” because it must always explain the real material object of that “co-ordination”, what makes it “economic co-ordination” and not any other kind of “co-ordination”! And the “economic” here stands for pro-duction, the actual creation of “goods and services” which ultimately involve human living labour and therefore social relations of production that relate to the interaction of human beings amongst themselves as well as with their living environment.
The quite astounding con-fusion of the “co-ordination” of economic activity with the “goal” or purpose of that activity is brilliantly exemplified by Arrow and Hahn in what is perhaps the most rigorous exposition of bourgeois neoclassical equilibrium analysis:
It is natural and proper to ask whether this enquiry into an economy, apparently so abstracted from the world, is worthwhile. We may answer in the usual way by drawing attention to the enormously complex nature of the material that economists study and the accordingly urgent need for simplification and so abstraction. This, however, leaves open the question of why the particular simplifications here used should be the appropriate ones. Our answer is somewhat different. There is by now a long and fairly imposing line of economists from Adam Smith to the present who have sought to show that a decentralized economy motivated by self-interest
and guided by price signals would be compatible with a coherent disposition of economic resources that could be regarded, in a well-defined sense, as superior to a large class of possible alternative dispositions. Moreover, the price signals would operate in a way to establish this degree of coherence. It is important to understand how surprising this claim must be to anyone not exposed to this tradition. The immediate "common sense" answer to the question "What will an economy motivated by individual greed and controlled by a very large number of different agents look like?" is probably: There will be chaos. That quite a different answer has long been claimed true and has indeed permeated the economic thinking of a large number of people who are in no way economists is itself sufficient grounds for investigating it seriously. The proposition having been put forward and very seriously entertained, it is important to know not only whether it is true, but also whether it could be true. A good deal of what follows is concerned with this last question, which seems to us to have considerable claims on the attention of economists. If confirmation of the proposition we have been discussing has been found in a particular formalization of the economy, it then becomes interesting to see how robust this result is. Will it survive a change in assumption from a perfectly competitive to an imperfectly competitive economy? Will it be overturned by external economics, by apparent irrationalities such as "judging quality by price" or by lack of sufficient "future markets" and the special role that might be taken by the medium of exchange? Some answers to these questions have been suggested in what follows. Other questions, of course, remain.
Note how here Arrow and Hahn admit the impossibility of co-ordinated economic activity on the part of atomically (decentralized) and egoistic (self-interested) market agents – because it can only lead to chaos, to the Hobbesian “war of all against all”. And yet they proceed blithely to propose as legitimate two levels of theoretical exploration for equilibrium analysis: one is that the price system is “compatible” in terms of the co-ordination (coherence) of these agents; and the other is that this system is “superior” to others – in other words, this economic system is not just formally possible (because of its co-ordination or “coherence”), but also substantively better (because of its price efficiency, and consequent “superiority” to other possible economic systems). The con-fusion consists in the fact that because equilibrium analysis can only determine relative prices, not prices based on material political values – because it does not describe the “substance” or human interest underlying prices - it is then impossible to say that the closed economic system indicated by it could ever be comparable to any other “possible systems” let alone “a large class of them”!
Furthermore, the co-ordinated “coherence” of the system is not derived from its substantive interest but by the axiomatic definition of its mathematical premises, and specifically by the postulated inclusion of a providential Walrasian “auctioneer”. It now becomes quite evident that from a political standpoint, a set of simultaneous equations such as that of Walrasian equilibrium can be co-ordinated if and only if we postulate the existence of a totalitarian omniscient and omnipotent auctioneer who (a) has complete knowledge of all the utility schedules of every atomic agent in the market, and (b) has absolute power to compel these absolutely egoistic agents to accept perfect competition (complete decentralization) and to accept the relative prices determined by the utility schedules of all other egoistic agents!
Needless to say, these equations are “simultaneous” not in any chrono-logical sense, in physical time, but in a logical sense, which most certainly excludes the notion of physical time categorically! Because formal models are “closed”, they are also time-less; they do not allow conceptually for time as the sphere of human action. In this sense, when transposed onto the societal plane, formal models appear to be eternal and immobile. A closed model describes politically a condition of inertia, of stasis or stalemate in which there is either complete paralysis or else at best a “circular flow” (Schumpeter), a simple reproduction (Marx in Volume Two of Capital). – Which is the reason why they require a beginner who originates outside the model as a disturbance or an exogenous subjective factor – a revolutionary innovator, a destructive creator who “decides on the exception”. (Antiquity, by contrast, although it had no notion of “revolution”, allowed at least corruptio [corruption] or metabole [transformation], as against autarkia [self-sufficiency] and stasis [civil war, stalemate].)
This explains the retreat of equilibrium theoreticians like Frank Hahn from the sphere of “prices and quantities” of real goods and services performed by human living labour to the semaphoric or semiotic sphere of “ideas and actions”. For Hahn,
an economy is in equilibrium when it generates messages which do not cause [its] agents to change the theories which they hold or the policies which they pursue, (quoted in Loasby, op.cit. at pp.13-4).
Similarly, Debreu has admitted that “there is no intellectual life in equilibrium” (quoted in Loasby ‘E&E’). But here the legerdemain, the subtle trick that Hahn has performed becomes absolutely evident – because Hahn has not specified a decision but rather an in-decision, a “not-changing of theories and policies”! In other words, not only does equilibrium now exclude even the most phantomatic exchange of “goods and services”, which require human living labour, but it even requires the ultimate in-action and in-decision: equilibrium finally assumes the stagnant and stationary position not just of tautology but of the most unthinkable rigor mortis – sheer death! For the modern bourgeoisie and its idiotic charlatans, economic equilibrium is the most perfect Nirvana in which absolutely Nothing happens!
Interestingly, Loasby (in “Closed Models and Open Systems”) sees “closedness” not as tautology or even as determinateness of relative prices but rather as “rest”, absence of “development” or “growth”. The central question becomes then how “to open” this “closed system” so that “co-ordination” allows for “evolution” and “growth”. This is where Adam Smith and Schumpeter differ from the other theoreticians – although, significantly, Loasby allows, contra Lawson and Langlois, that Smith was also an equilibrium thinker.
Because orthodox economic analysis cannot provide and specify an inter-est or value behind economic co-ordination or competition, or refuses to do so, then it must introduce an extrinsic agency that can ensure this co-ordination implicit in the notion of an equilibrium Schema. This will be a deus ex machina or a deus absconditus (Smith’s Invisible Hand) or a deus mortalis (Hobbes’s Sovereign) or a neutral arbiter (Walras’s auctioneer). But this expedient cannot infuse life in the formal machinery of the analysis – because there is no motive, no interest in it that can lead to historical qualitative change or trans-formation or meta-morphosis in the subject-matter of economic theory, which this analysis clearly and axiomatically leaves out! Hence, the dire need to supply other outside or external or exogenous factors to explain the change observed in real economies – the development, the transformation and growth, the trans-crescence of the real economy its cyclicality, its crises - for which there is no space in the “closed model” but are evidently present in an “open system”.
Hayek correctly captures the point that Walrasian equilibrium cannot “co-ordinate” a market in which different individuals decide; the market action of that “single mind” would still depend on the decisions of at least one other “single mind” to make an “economic decision”. For the single mind to make an economic decision and to evade tautology, it needs to be confronted with the independent plan of “another mind”, which is what general equilibrium is constitutionally incapable of doing because “its conclusions are [logico-mathematically] implicit in its assumptions” and no “time” can logico-conceptually be present!
But closedness is a totality and because economic co-ordination cannot arise from the will of market agents who are by axiom absolutely selfish, then it must be enforced coercively from an external Sovereign. This renders the co-ordination not one by agreement but one by total subjection. (This is the poignant sense given to Nazi Gleich-schaltung by K D Bracher in his masterly, The German Dictatorship.) Equilibrium analysis is totalitarian (Hayek) in its logical need for an external guarantor of the cohesion of the system – its “closure” – precisely because there is no corpus, no material common weal or pursuit, however eristic, for which its constituent individuals com-pete (Latin, “search and seek together”). Hayek, to his unending credit, was the first bourgeois theoretician able to penetrate the central difficulty with Walrasian equilibrium:
As I have suggested elsewhere in this volume,2 the tautological method which is appropriate and indispensable for the analysis of individual action seems in this instance to have been illegitimately extended to problems in which we have to deal with a social process in which the decisions of many individuals influence one another and necessarily succeed one another in time. The economic calculus (or the Pure Logic of Choice) which deals with the first kind of problem consists of an apparatus of classification of possible human attitudes and provides us with a technique for describing the interrelations of the different parts of a single plan. Its conclusions are implicit in its assumptions: the desires and the knowledge of the facts, which are assumed to be simultaneously present to a single mind, determine a unique solution. The relations discussed in this type of analysis are logical relations, concerned solely with the conclusions which follow for the mind of the planning individual from the given premises. (Individualism and Economic Order, p.93.)
Even so, Hayek’s analysis of general equilibrium is still incorrect because for “a single mind” Walrasian equilibrium is merely “classificatory” but not “tautological”. Even for “a single mind” no decisions can be made in equilibrium analysis because simultaneous equations involve a “semaphoric”, logical “classification” of information that is independent of “time” as a concept. Walrasian equilibrium is tautological only if it pretends to explain, as it does, how “many minds” can co-ordinate their economic decisions. Where a single mind is concerned, however, equilibrium theory does not involve a “single plan” or any “plan” at all (!) because that would imply the possibility of decision! But the point to a “classificatory” or “semaphoric” (or functional or illustrative or anatomical) schema is that no decision is involved because there is and there can be no “time” in such an ana-lytical “sketch” or “blueprint” or “map”. A map is “timeless”: it is not a “plan” in the sense of “a sequence of decisions”!
To be sure, Hayek – who did not possess the sharpest philosophical mind – still believed that equilibrium analysis, though solipsistic, that is to say, entirely akin to the thought-process of a single mind, left room for time:
Since equilibrium is a relationship between actions, and since the actions of one person must necessarily take place successively in time, it is obvious that the passage of time is essential to give the concept of equilibrium any meaning. This deserves mention, since many economists appear to have been unable to find a place for time in equilibrium analysis and consequently have suggested that equilibrium must be conceived as timeless” (Hayek 1937).