special sense in which it is true to say, that in this set-up absolute prices (or the ‘price level’) are indeterminate. 19 Now we ask: do these conditions suffice to determine values of these variables? This, to repeat, is the question of the ‘existence,’ in the mathematical sense, of a set of values that will satisfy the conditions. This question is synonymous with the question whether the equations embodying the conditions are capable of being simultaneously solved. But it is neither the question whether there is any tendency in our market to establish these solutions, if they do exist, nor the question whether these solutions or equilibrium values are stable or not. Of all the unjust or even meaningless objections that have been leveled at Walras, perhaps the most unjust is that he believed that this existence question is answered as soon as we have counted ‘equations’ and ‘unknowns’ and have found that they are equal in number. We have already seen that he made sure of one additional prerequisite— independence of equations. But as we analyze his argument we discover further that, though his mathematical equipment was no doubt deficient, his genius saw or sensed all or almost all the other relevant problems and practically always arrived at correct results. If he failed to answer all questions satisfactorily, there was immortal merit in his having posited them. If his work is not the culmination of this type of analysis, it certainly is its foundation. He saw the possibility that our system of equations may not admit ofany solution at all. He also saw, and even proved, that the solution, if it exist, may not be unique. All he claimed was that solutions exist normally and that, if the commodities in the market are numerous, there will in general be a unique solution (Éléments, p. 163). Since in his schema quantities demanded and offered are single-valued functions of the prices and since his marginal utility functions are monotonically decreasing, so much may be readily granted, although Walras did not emphasize, perhaps was not fully aware, that the unique solution, where it ‘exists,’ need not be economically meaningful in the sense that an actual system might work with it. 20 19 This merely means that, although it seems natural to put the ‘price’ of the numéraire, p n , identically equal to unity, p n −1≡0, we could of course just as well put it equal to any other arbitrary figure without altering anything else in this set-up. Walras discussed the theory of the numéraire very carefully, giving, among other things, the rule for translating the prices expressed in one numéraire commodity into prices expressed in another (Éléments p. 150). It should be clear that this rule does not apply to money or does so only under quite unrealistic assumptions. 20 The occurrence of such a case, e.g. of the inability of some participants in the market to secure a ‘maximum of satisfaction’ above starvation point, might be treated as a special form of economic, if not of mathematical, breakdown of the system. In itself, however, it is perfectly natural that a system that only represents the logic of certain relations cannot, in the absence of additional information, tell us anything about the size of the resulting shares in terms of goods. Also it cannot be repeated too often that since so far as Walras treated only a problem in the pure logic of simultaneous determination of variables, and therefore neglected, e.g., all lags of any History of economic analysis 972 We may as well ask the further question: can we not do better than that? This question divides up into two parts. We ask first, can we state more rigorously the conditions on which the existence of solutions, and especially of a unique solution, depends within the Walrasian assumptions themselves? The answer is affirmative. Such a more rigorous statement has in fact been provided by Professor Wald. 21 Without going into several delicate questions that Wald’s brilliant work raises (and without subscribing to every sentence of it), we simply note that Walras’ analysis emerges substantially unimpaired. 22 But, second, we have to ask whether the existence theorem still stands if, as we must, we make total and marginal utility a function of all the commodities that enter a household’s budget. This is of course the real difficulty. But the answer, under restrictions that seem tolerable, is affirmative even in this case. It has been given by Professor Amoroso. 23 For a treatment of the whole subject from the standpoint of the theory of demand the reader is referred to the standard work by Professor Wold. 24 We turn to the question of stability, with which we shall include the question of the presence of a tendency toward such unique (theoretical) solutions as may exist. 25 It is one of the greatest merits of Walras to have distinguished kind, the explanatory value of this part of his argument does not go beyond clearing up one of the many aspects that even pure theory must attend to. 21 See Abraham Wald (1902–50) in the periodical Ergebnisse eines mathematischen Kolloquiums (vols. 6 and 7, 1935 and 1936), and Wald’s non-technical report on his investigation in ‘Über einige Gleichungssysteme der mathematischen Ökonomie,’ Zeitschrift für Nationalökonomie, December 1936. [This article has been translated as a memorial to Wald, ‘On Some Systems of Equations of Mathematical Economics,’ Econometrica, October 1951.] 22 Wald’s (justified) attack upon the manner in which Walras tried to establish stability is another matter and will be touched upon presently. I do not think it correct, as Wald does, to mix this up with the question of the ‘existence’ of solutions in the sense explained. I also think that Walras’ reason, given on p. 163 of the Éléments, for expecting that the solution will in general be unique, if there are very many commodities in the market, compares favorably with Wald’s more rigorous statement that uniqueness will exist if the marginal utility functions are such that the utility value (marginal utility times quantity, the concept is due to von Wieser and Fisher) is an increasing function of the quantity. See also Walras, Éléments p. 125. 23 That is, Amoroso proved in a manner with which I cannot find any (serious) fault that, given the prices, the set of the quantities of commodities with which an individual will leave the market is uniquely determined, not indeed always but under acceptable hypotheses. This is only part of the thema probandum but, in the case where marginal utilities are partial differentials, a very important one. See ‘Discussione del sistema di equazioni che definiscono l’equilibrio del consumatore,’ Annali di Economia, 1928. 24 Herman Wold, ‘A Synthesis of Pure Demand Analysis,’ three (English) papers in the Skandinavisk Aktuarietidskrift, 1943–4. 25 I wish to re-emphasize that in general it seems to me an error to identify the problem of the ‘tendency’ with the problem of ‘stability’: a golf ball that rests on a green has no tendency to get into the appropriate hole unless there is a player to Equilibrium analysis 973 between the ‘existence’ and the ‘stability’ problems and to have paralleled the argument about the former by an elaborate argument about the latter. However, he treated the problem of stability in a peculiar way, because it posed itself to him in connection with what in strict logic is an entirely different problem, namely, the problem of the relation between the mathematical solution of his equations and the processes of any actual market: first and foremost he was anxious to show that the people in the market, though evidently not solving any equations, do by a different method the same thing that the theorist does by solving equations; or, to put it differently, that the ‘empirical’ method used in perfectly competitive markets and the ‘theoretical’ or ‘scientific’ method of the observer tend to produce the same equilibrium configuration. Posing this problem then naturally puts the question of stability into the foreground, that is, the question how the mechanism of competitive markets drives the system toward equilibrium and keeps it there. Since it is clear from the outset that the markets of real life never do attain equilibrium, this question can only be posed for markets that are still nothing but highly abstract creations of the observer’s mind. The people, who appear with initial stocks of commodities and definite marginal utility schedules, are confronted with prices criés au hasard by someone. They decide to give away certain quantities of some commodities and to acquire certain quantities of others at these prices. But as we know they do not actually do so but only note on bons what they would ‘buy’ or ‘sell’ at those prices should they persist or, if they enter into contracts, they reserve the right of recontract. It is easy to see that if no recontract proves necessary and if the bons are redeemed, then the conditions embodied in the equations must indeed be fulfilled in practice. Whenever they are not, there will be recontracting at different prices, which are higher or lower than the original ones, according to whether there is positive or negative excess demand in the respective commodities, until demand and offer are equated in all cases (Éléments, p. 133). Whatever we might have to say about this on the score of realism, 26 it seems at first sight to be intuitively clear that, so long as no other mechanism of reaction is admitted than the one exclusively considered by Walras, equilibrium will be attained under these assumptions; that, in general, this equilibrium will be unique and stable; and that the prices and quantities in this configuration will be those we get from our theoretical solution. 27 Nevertheless, Walras himself hit it and sometimes not even then. But if somebody puts it into the hole it will stay there in stable equilibrium. This should show the rationale of distinguishing between the two problems. In our case, however, the factors that make for stability of the equilibrium situation are at the same time ‘forces’ that may account for a tendency of our variables to get into the equilibrium configuration. And so we waive our objection, which is important only for evolutionary processes. 26 See again Nicholas Kaldor, ‘A Classificatory Note on the Determinateness of Equilibrium,’ Review of Economic Studies, February 1934. 27 This prima facie impression may account for the fact that even today theorists are not greatly exercised about the problem as thus posed. We may combine the individ ual demands and offers in the m commodities into m equations of the form D i (p 1 … History of economic analysis 974 displayed hesitation on a very important point that has been strongly re-emphasized by Professor Wald (Zeitschrift, op. cit. p. 653). It is this. Equilibrium values in the perfect market are established by a game of trial and error (tâtonnement)—prices being adjusted and quantities being readjusted in response. For clearness, suppose that all prices except one do equate the respective demands and offers. We have a rule by which to adapt the one price that does not equate demand and offer. But if we do adapt it we thereby upset the equilibria in all the other sections of the market, whose prices are no longer equilibrium prices since they equate supply and demand in these other markets only with reference to the one price that failed to do so. Therefore we have in turn to adjust the others, and the only reason Walras gives for expecting that the new configuration is nearer to equilibrium all round than was the original one is that this is ‘probable,’ because the effects of the adjustment of the price that was originally out of line upon the excess demand of the corresponding commodity are direct, strong, and all in the same direction, whereas the effects of the necessary readjustments of the other prices are most of them indirect, weaker, and not all in the same direction: in part they compensate one another. As it stands, this attempt at proving both tendency toward, and stability of, the equilibrium of the market evidently lacks rigor. This has been increasingly recognized of late but no entirely satisfactory solution of the problem has been offered as yet. 28 [This subsection is unfinished.] [(d) Walras’ Theory of Production.] We turn to the second branch of Walras’ pure theory of the economic process, namely, the theory of production, which, as we know, is nothing but a theory of the manner in which the p m )=O i (p 1 …p m ). Of these equations we lose one owing to the fact that it follows from the others. Of the m prices we lose one owing to zero homogeneity. Stability is secured by imposing the condition that any price higher than the equilibrium price induces negative, and any price lower than the equilibrium price induces positive, excess demand, a condition carefully safeguarded by Walras. All the doubts that really worry theorists, so far as they do not proceed from their qualms about the assumptions that identify Walras’ set-up, enter only on the introduction of genuine money. 28 Readers who are sufficiently interested in these delicate questions may welcome the following signposts on this road. First we note that Pareto did not improve the Walrasian argument in this respect except for recognizing more explicitly that oscillations in the neighborhood of values may lead away from them as well as toward them. Second, from Pareto to Hicks, very little advance was made in this respect, however much headway was made in others. It was Professor Hicks who formulated stability conditions that were then improved by other writers, especially Samuelson and Metzler. Samuelson was, I believe, the first to point out that the problem of stability cannot be posed at all without the use of an explicit dynamic schema, i.e. without specification of the manner in which the system reacts to deviations from equilibrium. Third, our report shows that Walras did present such a dynamic schema: he specified a sequence of steps by which the system is supposed to work its way toward stable equilibrium for which he did not receive the credit he deserves. This schema covers not more than a special case but for this special case a more rigorous proof is possible in spite of the fact that he himself failed to give it. Equilibrium analysis 975 mechanism of pure competition allocates the ‘services’ of all the different kinds and qualities of natural agents, labor power, and produced means of production. 29 This theory of allocation in turn is the same thing as the theory of the pricing of these services, because it is the price mechanism which brings these services into the place they actually hold in the great jig-saw puzzle and keeps them there. Finally, we do not say more than this when we say that the theory of production tells us which quantities of which products each firm will decide to produce, and which quantities of which productive services it is going to buy in view of the given tastes of prospective consumers of its products and the given propensities of these same consumers considered as ‘owners’ of productive services. Now, the total quantities of these services, that is, the quantities of them that are potentially available during a given period of time, are given because their sources are. But they need not be completely absorbed by production, nor do they necessarily go to waste if they are not. For an essential feature of the Walrasian schema is that they are all of them capable of being consumed by their owners directly. 30 Thus, their total quantities and the propensities of their owners to consume them—possibly even to acquire further quantities of them for the purpose of consumption—or to part with them, constitute the second group of data, and Walras’ problem was to show how these data interlock with those of the first set, the consumers’ tastes, so as to produce a consistent set of quantities and values. 31 We perceive immediately that Walras strove for a solution of this problem that was to be entirely symmetrical with the solution lie had previously worked 29 Remember that these produced means of production, on the level on which we are moving now, are being let in kind, and are indefinitely durable, postulates that we are going to remove presently. 30 With Walras, the services that are used in production therefore have also a use value for their ‘owners.’ This creates difficulties that are particularly obvious in the case of specific instruments of production, such as machines. To assume that, potentially at least, a machine can, at the will of its owner, be instantaneously turned into an easy chair is indeed heroic theorizing with a vengeance. Only in part is this assumption then relaxed in the theory of the ‘new capitals’ (capitaux neufs). But it has its virtue when it is the logic of the structure of the capital-goods stock which is to be explained ab ovo. We may make it more tolerable by saying that a capitalist’s former decision as regards the use of the capital good he actually owns has determined what species of capital good he actually does own. It stands to reason that this attempt at saving the situation wrecks completely the static framework of the theory. No such assumption was made by either Marshall or the Austrians but this was only because they were less rigorous than was Walras. Let me use this opportunity to emphasize again that, on an infinitely higher level of rigor, Walras really reformulated the theories of production of A.Smith, J.B.Say, and J.S.Mill. The latter’s theory of production, of course, must not be looked for exclusively in his Book I. 31 In his Manuel, Pareto refined this set-up into his general theory of tastes and obstacles which, in fact, leads on to a higher level of abstraction and serves especially to bring out more clearly the logical problems that are lurking in this set-up. The practical value of the Paretian generalization shows in the ease with which it embraces the case of the socialized economy. But it does not help us much on the level on which we now find ourselves. History of economic analysis 976 out in his general theory of barter in a multi-commodity consumers’ goods market. In fact, his theory of production may be described as an attempt to resolve, in the spirit of J.B.Say, the case of production into the more general case of exchange between services and goods and, in the last analysis, simply between services. He was aware of the costs of this attempt and was willing to pay them. First, though he did introduce into his mechanism an entrepreneur who was not merely a capitalist, he reduced him, as we saw, to the purely formal role of buyer of productive services 32 and seller of consumers’ goods without any initiative—or income—of his own. 33 In order to emphasize this, we shall replace the term ‘entrepreneur’ by the impersonal term ‘firm’: it is clear that in Walras’ thought the households were really the agents that, both as buyers of products and as sellers of services, determine the economic process. Second, though he was, of course, aware of the fact that production and adaptation of production involves delays, he at first purement et simplement neglected these delays (Éléments, p. 215), deferring partial recognition of their role to the far-off section on circulation and money. We do the same thing and even accept, for the moment, the apparently impossible assumptions of constant coefficients of production, 34 absence of any overhead, and all firms in every industry producing exactly equal amounts of product. 35 And we ask, first of all, as we did before in the case of multi-commodity barter, whether with all these ‘simplifications’— some of which were in the end discovered to be complications—there exists a unique set of solutions for a system of equations that covers both consumers’ and producers’ behavior, or represents, as it were, the chassis of economic life. 32 We have seen that Walras was fully aware of the importance of the stocks and flows of raw materials and semifinished products that entrepreneurs buy from other entrepreneurs. But where he posed the fundamental problem of production (leçons 20 and 21), he dealt with them cavalierly, confining himself to showing—which is indeed easy if we neglect all sequences or lags—that these purchases by entrepreneurs from other entrepreneurs are intermediate steps in a process, the understanding of which does not suffer by leaving them out. 33 Let me emphasize once more that in the equilibrium of a purely competitive process, where nobody is able to exert any influence upon the prices of either services or products, every entrepreneur would in fact be an entrepreneur ne faisant ni bénéfice ni perte: this is neither a paradox nor a tautology (i.e. it is not the result of a definition) but, under Walras’ assumptions, an equilibrium condition (or, if you prefer, a provable theorem). [This point is further discussed in the next section (8).] 34 This involves really two distinct assumptions: (1) that these coefficients, namely, the quantities of all services that enter the unit of the product, are technologically given or that there is, for each product, only one technologically possible way of producing it; and (2) that these coefficients do not vary in function of the quantity produced or that there are no economies or diseconomies of scale. This set-up was altered, later on, by Walras himself. But these questions will be taken up in the next section. 35 Walras does not seem to have observed what was often urged later on, namely, that this makes the number of firms indeterminate though it does not prevent determinateness of the output of each industry. Since this is not important in our present argument, we defer consideration of this point also to the next section. Equilibrium analysis 977 Intuitively we realize that, with the same qualifications that we had to make in the general case of multi-commodity exchange and with the further qualifications that are imposed upon us by the additional assumptions made by Walras in order to reduce the problem of production to manageability, the answer will be affirmative. We may balk at the assumptions. We may question the value of a theory that holds only under conditions, the mere statement of which seems to amount to refuting it. 36 But if we do accept these qualifications and assumptions, there is little fault to be found with Walras’ solution. It comes to this: the households that furnish the services have in Walras’ set-up definite and single-valued schedules of willingness to part with these services. These schedules are determined, on the one hand, by their appreciation of the satisfaction to be derived from consuming these services directly 37 and, on the other hand, by their knowledge of the satisfaction they might derive from the incomes in terms of numéraire that they are able to earn at any set of consumers’ goods and service ‘prices.’ For the ‘prices’ of consumers’ goods are determined simultaneously with the ‘prices’ of the services and with reference to one another: every workman, for instance, decides how many hours of work per day or week he is going to offer in response to a wage in terms of numéraire that is associated with definite prices, in terms of numéraire, of all the consumers’ goods that would be produced with the total amount of work being offered at that wage rate. Mathematically, we express this by making everybody’s offer of every service he ‘owns’ a function of all prices (both of consumers’ goods and the services) and, for the same reason, everybody’s demand for every commodity another function of all prices (both of the services and the consumers’ goods). Everybody’s demand for the numéraire commodity follows simply from everybody’s 36 Those who, like myself, do not go so far, must rate the pioneer performance as such very highly and see a merit precisely in the fact that Walras chalked out the work that had (in part still has) to be done in the future. 37 Cassel’s popularization of Walras’ system lacks this feature. In consequence, Cassel had to put the (potentially) existing quantity of services equal to the quantity to be employed in production in equilibrium. It has been pointed out by Wicksell and later on by von Stackelberg (‘Zwei kritische Bemerkungen zur Preistheorie Gustav Cassels,’ Zeitschrift für Nationalökonomie, June 1933) that it will in general be impossible to fulfil this equilibrium condition with constant coefficients of production. This is not serious because the difficulty vanishes when we introduce variable coefficients, i.e. substitutability (see sec. 8). But if we accept the constant coefficients and at the same time refuse to accept Walras’ theory that part of the services are directly consumed by their ‘owners,’ then there will be in general unemployment of some services for which the necessary complements do not exist. These unemployable surplus services will then, by seeking employment, depress the wages of the employed services of the same kind, but this lowering of wages may do but little (namely, by cheapening the products which absorb relatively much of the services in which there is a surplus) to reduce the unemployment and thus may unstabilize the whole system, owing to incompatibility of equilibrium conditions. The case is of no importance. But some Keynesians may have it in mind when arguing for the possibility of unemployment equilibria. History of economic analysis 978 balance equation, which (since we are as yet abstracting from both genuine money and saving) is exactly analogous to the balance equation in the case of multi-commodity barter, except that in the present case the offers are offers of services and only the demands refer to commodities. 38 From these individual demands and offers we get the aggregate (net) offers of services and the aggregate demands for products in the market, all in function of all service and product prices. But the rest of the set-up is crippled— evidently in order to focus attention upon the great social relation between the ultimate factors that simultaneously shape consumption and production—by the assumption of technologically fixed and constant coefficients of production, which readily yield the remaining restrictions that we need for the determination of prices. To determine prices we need the equations, equal in number to the number of services, which express that the quantities of the services employed in all industries must add up to the total offer of these services, and the equations, equal in number to the number of products, which express that the coefficients of production of the services used in each industry, each multiplied by the price of these services, must equal the unit price of the industry’s product or that in all industries average cost, in Walras’ case the same as marginal cost, must equal price. The number of variables to be determined can easily be shown to be equal to the number of equations. As to the mathematical question whether these can be solved for the variables—whether an equilibrium solution ‘exists’—we have to say much the same as before: Walras did not present an answer that will satisfy the standards of the modern mathematician, though it could be shown 39 that he saw and either took or avoided all the hurdles that stand in the way to an affirmative answer. Of course, we have to repeat that, in the same sense as before, existence of a set of solutions or even of non-negative solutions does not necessarily mean the existence of economically meaningful—that is, practically possible, ‘tolerable,’ and so on—solutions. But within his assumptions and with qualifications already mentioned, the affirmative answer 38 Walras has often been berated on the score of the clumsiness or heaviness of his mathematics. It is submitted, however, that the argument in leçon 20, where he solves the ‘theoretical’ problem, is not inelegant, particularly as regards the manner in which the offers of services emerge from marginal equilibrium conditions (op. cit. p. 210). It seems to me that some critics, including some mathematical critics, stand to learn from it. Present practice, born of pedagogical convenience, is to make the individual demands for products functions of their prices only and of ‘income.’ While this practice has its advantages, especially now when it helps the student to grasp the relation of Keynesian to Walrasian economics, it really obscures Walras’ fundamental conception and makes things more difficult in the end. 39 Space to do this is lacking. We must confine ourselves to repeating that his assumption that services have use value for their ‘owners,’ in fact, avoids the only serious difficulty which in the case now under discussion is added to the difficulties glanced at in the case of simple multi- commodity barter, namely, the difficulty that lurks behind the constant coefficients of production. Of course, the statement in the text must be understood to hold without qualification only where marginal utilities are exclusively functions of the quantity of the corresponding commodity. Equilibrium analysis 979 stands and objections against it are much more due to the critics’ failure to understand Walras than to any mistakes or oversights of his. 40 Also it may be averred that, so far as this part of the Walrasian analysis is concerned, our result is, or comes near to being, the common opinion of theorists. 41 As regards questions of stability and of the presence in the economic process of a tendency to establish that equilibrium set of prices and quantities, the situation is still more seriously affected than we have already found it to be in the case of multi- commodity barter by the difficulty of accepting Walras’ assumptions. 42 We have again to rely on the method of bons. But in this case, if the prices that are being experimentally fixed (criés) at first do not prove to be (miraculously) the equilibrium prices, the rearrangements that are to lead toward equilibrium involve instantaneous rearrangements of all the tentative decisions to produce that are embodied in the bons, which is a matter of much more difficulty than would be mere rearrangement of tentative decisions to acquire or to give away existing commodities. And even if all firms and all owners of productive services did succeed at this task, they would still have to carry out this production program which takes time, during which nothing must be allowed to change. Walras himself posed the problem exactly as he posed it for the case of multi-commodity barter, namely, in the guise of the question whether his theoretical problem was the one that is actually solved in the markets of the services; and he arrived, by the same reasoning, at the same conclusion, namely, that a process of trial and error car- 40 One of these objections, which was of course never raised by mathematical economists, deserves mention in passing. By suitable eliminations we may represent all product prices and quantities as functions of the prices of the services. It should be clear that this formal truth does not constitute the latter as ‘causes’ of the former, since the service prices themselves are determined in an argument that at every step takes account of the corresponding product prices. Some economists, however, Austrians especially, inferred from this universal and simultaneous interdependence of all prices that the Walrasian system fails to explain any prices at all: this was sometimes expressed by calling it ‘functional’ to distinguish it from the Austrian ‘causal’ system. I indulge in the hope that it is unnecessary, at this hour of the day, to go into this. 41 For a rigorous proof, the reader is referred to A.Wald (Zeitschrift, op. cit.). The reader may indeed derive a slightly less favorable impression from this paper, but he should observe that Professor Wald deals with Cassel’s system rather than with that of Walras. The modification suggested by Zeuthen and K.Schlesinger, which Wald mentions on p. 640, has merits of its own but is not necessary in order to make Walras’ system tractable. 42 However, if we do accept them, stability may be proved, if anything, more convincingly than it can in the barter case. This has been done for a pattern that admits substitution by Professor Hicks (Théorie mathématique de la valeur, 1937) and others, particularly by L.M.Court (‘Invariable Classical Stability of Entrepreneurial Demand and Supply Functions,’ Quarterly Journal of Economics, November 1941). Both reintroduce the entrepreneur whom we have eliminated and therefore put their proofs into the form indicated by the title of the latter paper. Historically, it is important to note that, however superior in technique, these and other contributions do no more than spell out the suggestions that are already present, although some of them only implicitly, in Walras’ analysis. History of economic analysis 980 ried out under conditions of pure competition and with only the one mechanism of reaction allowed—prices being increased where there is positive and reduced where there is negative excess demand—will ‘probably’ insure that each step in adjustment actually does lead toward, and not away from, equilibrium. I have thought it necessary to put this matter fully before the reader. Lest he should thereupon turn away from Walras’ construction on the ground of its hopeless discrepancy from any process of real life, I wish to ask him whether he ever saw elastic strings that do not increase in length when pulled, or frictionless movements, or any other of the constructs commonly used in theoretical physics; and whether, on the strength of this, he believes theoretical physics to be useless. In the footnote below, I add one or two other comments that may reduce the reader’s discomfort. It remains true, however, that both Walras himself and his followers greatly underestimated what had and has still to be done before Walras’ theory can be confronted with the facts of common business experience. 43 43 First of all, the reader should observe that his discomfort stems mainly from his familiarity with an economic process that is incessantly disturbed by technological revolutions. In any process that, without being strictly stationary, is at least not too far removed from stationarity, households and firms would have a reliable stock of routine experience that would help them greatly to perform the tasks that look so impossible at first sight: the tentative prices, to which they are to react by formulating tentative programs of production and consumption, are not really criés au hasard, as Walras has it, but are rather informed guesses to be corrected, as a rule, by relatively small adjustments. It is only in order to bring out the logic or rationale of the derivation of demand and supply functions that Walras refuses to avail himself of this fact. We can learn from Marshall how to put flesh and skin on Walras’ skeleton, although it does remain true that a more realistic theory raises a world of new problems that are beyond Walras’ (and also Marshall’s) range. Second, the elements of reality that do enter Walras’ schema are indeed overgrown by other elements which we must try to conquer in due course. But the former are nevertheless observable or verifiable even where they take such unfamiliar forms as tâtonnement by means of bons. Third, it should not be said that in Walras’ system all the burden of adaptation is put upon prices alone: quantities are adapted to prices as prices are to quantities, and it is only an abbreviated manner of speaking which accounts for the impression alluded to. Fourth, there is realism in some of the items of Walras’ set- up in which we should least expect it. Thus, a little reflection will show that workmen’s demand for the ‘services’ of their own labor power (i.e. for leisure) is actually a very important factor in the shaping of the process of production. Though it would be absurd to deny this for the present age, there never was a time in which this demand was completely ineffective, and the surface fact that a laborer accepts a fixed working day which he is powerless to alter (‘he must accept it or die’ says a contemporary economist) contradicts Walras’ analytic arrangement very much less than it seems to. Finally, fifth, classroom experience induces me to add that propositions such as Walras’ law of cost or full employment in perfect competition are indeed properties of his system when in perfect equilibrium. But they are unobjectionable when properly understood (on the full-employment proposition see the remark at the end of this section) and, above all, they are theorems that follow from the postulates that define the system and not postulates that are imposed upon it (so that they could cause overdeterminateness). Equilibrium analysis 981 . although some of them only implicitly, in Walras’ analysis. History of economic analysis 980 ried out under conditions of pure competition and with only the one mechanism of reaction allowed—prices. incompatibility of equilibrium conditions. The case is of no importance. But some Keynesians may have it in mind when arguing for the possibility of unemployment equilibria. History of economic analysis. occurrence of such a case, e.g. of the inability of some participants in the market to secure a ‘maximum of satisfaction’ above starvation point, might be treated as a special form of economic,