History of Economic Analysis part 103 docx

[(e) The Introduction of Capital Formation and of Money.] The rest of this section may be cast into the form of an answer to the question how the fundamental schema of consumers’ and producers’ behavior is affected—or possibly upset—by the introduction of capital formation and of money. Though both subjects have been touched upon in the preceding chapter and will again have to be treated in the next, they must also receive attention here to enable the reader to appreciate Walras’ structure as a whole and to realize the extent to which he anticipated modern work in these fields in some respects and prepared the ground for it in others. In the Walrasian system, the theory of capital formation is, on the one hand, the foundation of the theory of interest and, on the other hand, itself rests on the theory of capital-goods prices. At first we consider only the prices of produced capital goods. So far, we have a theory for the prices of their services only and even this was arrived at by means of an assumption which we must now drop, namely, that the quantities of produced capital goods are given once and for all, and they never wear out or perish by accident. Accordingly, we now deduct an allowance for depreciation and also an insurance premium. 44 What remains is the ‘net revenue’ yielded by the capital goods. We have noticed before that Walras took the existence of such a surplus over depreciation and insurance as an undeniable fact which he made no effort to establish. 45 However, if we accept this for the sake of argument, then we can proceed at once to construct the theoretical market for capital goods which, according to Walras’ laudable practice, we need in order to determine their prices. 46 In this market capitalists—and not as entrepreneurs (firms)—demand new capital goods which the firms that produce them offer in response to that demand. The new capital goods that are being demanded and produced may not suffice, just suffice, or more than suffice to make up for the loss the existing capital stock currently suffers from accident or wear and tear. The last of these three cases defines saving, which, expressed in terms of the numéraire, is therefore the excess of net income, the total net value of the services sold by households, over consumption, the total value of the products bought by households. Hence, exactly as in Keynes’s General Theory, current saving is tautologically equal to current ‘investment.’ Saving is here merely a word that identifies a particular kind of demand, namely, the demand for capital goods. So far there is no meaning to the phrase ‘offer or supply of saving’ unless we wish to denote by it that part of the households’ services that is of- 44 Walras considered both as technologically determined constants. This is, of course, unsatisfactory but should be considered as another of the privileges of the pioneer. 45 Neither did Pareto, Barone, and others in the direct line of succession make such an effort. But Wicksell and Fisher filled this gap with Böhm-Bawerkian material. 46 The market we are describing now is nothing but a theorist’s construction that Walras himself later on abandoned to replace it by the stock market. To criticize this theoretical device on the score of lack of realism would spell misunderstanding. History of economic analysis 982 fered against capital goods 47 instead of being offered against bread or beer, and to say that current saving can get out of step with current investment has no more sense than to say that saving can get out of step with itself. Hence, equality of current saving and current investment is an identity and not an equilibrium condition. The equilibrium condition is that the sum total of saving in a given period should be equal to the costs to the capital-goods-producing firms of the capital goods (produced and) sold in the period, since these firms, like all others, are subject to Walras’ law of costs. Now—and this is not as in the system of Keynes’s General Theory—the only motive that capitalists can have in this set-up for demanding capital goods is in the net revenue expected from them, no matter whether this net revenue consists in the use value to them of the durable objects acquired or in the yield in numéraire to be collected from letting them to firms (or to people who wish to consume their services directly). From this follows another equilibrium condition which must be fulfilled by their prices: these prices must, under ideal conditions, be proportional to their net yields or else arbitrage operations would set in to enforce this proportionality. But this may be expressed by saying that our capital-goods market is really a market of streams of perpetual net revenues, from which standpoint all capital goods are on the same footing irrespective of their physical shapes. In order to emphasize this aspect, Walras created an ideal or imaginary commodity that represents ‘perpetual net revenue.’ This gadget—another purely theoretical construct 48 —enables us to endow each household with a marginal utility and a demand function for ‘perpetual net revenue,’ 49 and to replace all the (unknown) prices of the capital goods by a single price, which then helps to determine them, namely, the price of a unit of ‘perpetual net revenue’ per unit 47 Remember that capital goods are goods that serve more than once. It would be more correct to define them as goods which (or parts of which) survive the period of account. 48 Pareto, Barone, and others accepted this ideal or imaginary commodity and simply called it ‘saving’ (risparmio). Notice that this construct may also be harnessed into the service of theoretical schemata other than Walras’. Even in Walras’ schema, it acquired a new—and more realistic— connotation where he introduced money, as we shall see presently. For the moment, the concept does not mean anything but the total heap of all new capital goods, expressed in terms of numéraire, and only serves to isolate one aspect of them but has no separate existence: if Walras nevertheless speaks of a market of capital numéraire, this market is—unlike the market of capital monnaie, which we have not introduced as yet—not distinct from the market of the capital goods themselves. 49 The marginal utility functions are conceived as monotonically decreasing functions of the quantity of this ideal commodity alone, as in the case of all other commodities. But the demand functions for these commodities are, also as in the case of all other commodities, functions of all the prices of all products and services. Note that this implies that they are also functions of the incomes: the difference in this respect between the theories of Walras and of Keynes (General Theory) is not that Walras neglected the influence of income but that Keynes neglected the influence of the prices of the products. Equilibrium analysis 983 of time—a profound move on the analytical chessboard. This single price results from the condition of proportionality mentioned above, which may be reformulated by saying that the total demand for new capital goods (identically equal to saving) must be distributed between the industries that produce these new capital goods in such a way as to equalize their net value products (in terms of numéraire) per unit of cost (in terms of numéraire). 50 Thus the single price in question is simply the reciprocal of the rate of ‘perpetual net revenue’ (taux du revenu net perpetual), which is a factor of proportionality, common to the values of all capital goods and readily identified—so long as there is no money—with the rate of interest. With infinite care, to which justice cannot be done here, Walras developed this theory for both the cases of produced durable goods such as homes, the services of which are to be directly consumed, and of produced durable goods that are to be used in production, supplying the marginal utility (maximizing) conditions for static equilibrium 51 and arriving, as regards determinateness and stability, at results analogous to those arrived at in the cases of multi-commodity exchange and of production. If space permitted comment, it would have to be similar to the comments submitted in those cases. We must be content to state without proof that Walras’ system is not—we are still following an analysis that abstracts from genuine money—upset by the facts, as stylized by him, of capital formation and by the excursion that the theory of it involves into ‘progressive’ or else ‘retrograde,’ that is, non-stationary, states. But let us summarize what else we have got so far. First, we have a theory of the prices (values in terms of numéraire) of capital goods which we have not had before. In the first instance, this was a theory of the pricing of new capital goods. But this theory is then readily extended to the cases of existing produced capital goods and of non-produced capital goods (‘land’; Walras even extends it to labor power) by the simple device of applying to them the same ‘rate of perpetual net return’ (or of interest) 52 that emerges in the case of new capital goods. 53 Second, as a by- product of the theory of capital-goods prices we have a theory of interest which now enters 50 Remember that, with Walras, marginal and average costs are of necessity equal. The ‘correction that is necessary, if this is not so, is obvious. 51 He realized, of course, that, with positive saving, the economy under study was no longer stationary. But he also realized that its theory may still be static, if the propensities to save (dispositions à l’épargne) and the propensities to consume (dispositions à la consommation) remain unchanged during a certain time (Éléments, p. 244; this is perhaps the most convincing passage for showing that Walras fully grasped the distinction between a static theory and a stationary process (see above, sec. 3). 52 Let us note that the most important modern sponsor of this identification—which implies the belief that the existence of the ‘rate of perpetual net return’ is an undeniable fact that does not require either proof or verification—is Professor F.H. Knight. 53 From this it might be inferred, though not quite conclusively, that Walras associated the fact of interest with a ‘progressive’ society and was not unaware of the possibility that it might vanish in a retrograde, if not a stationary one. I take this opportunity to refer the reader to the brilliant papers of Professor C.Bresciani-Turroni, History of economic analysis 984 all demand and supply equations. From these, then, a comprehensive theory of its role in the economy may be read off. 54 The prices of the capital goods themselves do not enter any of the final equations of the Walrasian system other than those that describe their own conditions of supply and demand qua products. Third, since saving is merely a species of demand, there cannot be any question of equalizing its ‘demand and supply’ by varying the rate of interest or anything else. What is equalized by virtue of an equilibrium condition—not merely set tautologically equal—is the amount that people have decided to save and invest and the costs of the new capital goods. Now if this equality is not realized, this means that the values of new capital goods will be above or below their costs to the firms that produce them and therefore will have a motive to expand or restrict their production. But there is another aspect to this. Suppose that the values of new capital goods have risen above their costs. If for the sake of argument we assume that the expected net yield of the capital goods has not changed, this implies that the rate of perpetual net return has fallen, in other words, that a unit of perpetual net return will be more expensive for the capital-goods purchasing capitalist than it was before: it is this rise in the numéraire prices of new capital goods which brings home to the capitalist the implied fall in his rate of net return. In still other words, it is not the fall in the rate of interest which plays any direct causal role, but it is the rise in the values of capital goods which reduces (tautologically) the rate of interest. 55 Of course, the rate of interest thereupon also assumes an active role so far as it enters the demand and supply functions of all products and services. Yet it is important to notice that, in this analysis, it plays a passive role in the first instance because this puts a different complexion on its significance in the economic process and serves especially to put the capitalists’ reactions in a different light: they are reactions to the increase in the price of a particular type of goods the capitalist demands and not reactions to the decrease in the price of a service he renders. 56 Finally, it follows on ‘The Theory of Saving,’ Economica, February and May 1936, which shed a lot of light on the theory of saving and its history. 54 This was a stroke of genius. But its validity, of course, depends on Walras’ conception of interest. It is in order for me to observe, neglecting my principle of effacing myself in this book, that the admiration I keep on expressing for the ingenuity, nay, greatness of Walras’ analysis, should not be understood to imply agreement in every respect. 55 The individual capitalist’s loss may, of course, be compensated, in part, wholly, or more than wholly, by the gain he will then make on the stock of capital goods he owns already. This fact, however important in other respects, is not relevant here. 56 Without mentioning Walras, Cassel adopted the same view—for him also saving consists in demanding capital goods or in applying productive services to their pro duction. But he failed to understand how, on introducing genuine money, Walras shifted his standpoint radically, as we shall see in a moment. Another matter may be adverted to here. An increase or decrease in the prices of assets to be acquired is less likely to be neglected than would be a decrease or increase in the price of a service: this provides a possible argument against the view so frequently voiced at present that moderate variations in the rate of interest do not seem to have any noticeable in- Equilibrium analysis 985 from the preceding argument that, sharply renouncing allegiance to the Turgot-Smith theory of saving, Walras’ analysis agrees with Böhm-Bawerk’s in yielding the result that the prices of consumers’ goods and prices of capital goods will, within the assumptions of this analysis, in principle move in opposite directions. At last, we introduce money and monetary transactions. Deferring Walras’ other exploits in the field of monetary theory and policy to the next chapter, we must see right now how he fitted money into his schema of the economic process, how he determined absolute prices in money as well as in numéraire, and whether he was right in claiming that his monetary economy enjoys the same properties of determinateness and stability that may be attributed to his numéraire economy. For this purpose it will suffice to deal with the case of a money of given quantity that consists of a material of negligible use value 57 and to note briefly that Walras, who in the first edition (1874–7) of his Éléments had based his monetary analysis on the concept of the economy’s ‘monetary requirements,’ 58 adopted in the second edition the concept of the ‘amount of cash people desire to hold’ (encaisse désirée), 59 which was, however, not made part and parcel of his pure theory of general equilibrium—not fully amalgamated with it—before the fourth edition (1900). 60 It is there that fluence. Also, since the use of assets for capitalists consists in reaping their yields, the Walrasian theory leaves room for the possibility that an increase in the price of capital goods may cause demand for them to expand just as…[note incomplete.] 57 As we shall see in the next chapter, Walras also analyzed the cases of monometallism, bimetallism, and monometallism ‘regulated’ by the issue of token money. But his fundamental analysis is carried out for the case of a government paper money of given quantity. Observe at once that this means only that the material money is made of has no use value but not that this money itself has none: this will be explained presently. But observe also that the simplification which consists in not having to attend, when discussing fundamentals, to the problems that are raised by the value, as a commodity, of the money material is bought at the price of having to postulate an arbitrarily fixed quantity of money. In this trivial sense, our question is answered already: since this quantity is arbitrary, absolute prices cannot be determined uniquely. But the question we ask is not this one: we ask instead whether the price level and all the other monetary and non-monetary quantities in the system are uniquely determined when the quantity of money has been fixed. 58 Circulation à desservir—an old concept already familiar to Petty. Walras himself (preface, p. IX), borrowed this concept from the physiocrats. The encaisse désirée appeared first in the Théorie de la monnaie (1886). 59 We are in the habit of associating this ‘cash-balance approach’ with Marshall, who developed it independently during the 1880’s. See on the significance of this approach and cognate matters Professor Marget’s scholarly articles, ‘Léon Walras and the Cash Balance Approach to the Problem of the Value of Money,’ Journal of Political Economy, October 1931, and ‘The Monetary Aspects of the Walrasian System,’ ibid. April 1935. 60 Or, more exactly, before he presented, in the bulletin of the Société vaudoise des Sciences Naturelles, his paper on ‘Equations de la circulation’ (1899). This is much later than Marshall may be assumed to have arrived at roughly similar results (see J.M.Keynes’s Marshall biography, Essays in Biography, pp. 196–206). But not only History of economic analysis 986 the whole of the Walrasian structure of pure theory appears in all its logical beauty. The ground floor of this structure is the theory of the ‘market’ of consumers’ goods. On the second floor we find the theory of production and the ‘market’ of production services, not separated from, but integrated with, the first market. On the third floor we have the ‘market’ of capital goods similarly integrated with the two others. And on the fourth floor there is another ‘market,’ integrated with the other three, of ‘circulating capital,’ that is, of the stocks or inventories of goods—new capital goods for sale at the establishments of their producers, and consumers’ and producers’ inventories of all kinds—that are necessary to keep things going. 61 Thus, after having determined, in his theory of production, the equilibrium (numéraire) prices and quantities for both consumers’ goods and productive services—all of which, once determined, are to remain unchanged while the goods are being produced—Walras lets actual delivery of these services and of (equivalent) goods begin at once, that is, before the program of production decided on ‘in principle’ has been carried out. Of course this presupposes that households and firms are from the outset in possession of stocks of goods (inventories) which are now introduced among the data of the general-equilibrium problem. 62 As we have already seen, Walras treated them formally as he had did Marshall not publish these results until twenty years after Walras’ paper, but also he never formulated the logic of them as rigorously and completely as did Walras. Still it should be borne in mind that, in principle, all that follows applies to Marshallian as well as to Walrasian economics. 61 In order to facilitate the mathematical treatment, Walras extended the meaning of coefficients of production in a manner that is interesting because a similar device has been recently adopted by Professor Leontief in his input-output analysis. Briefly and concretely, if we have a product (A) which has, with respect to the capital-goods service (K), a coefficient of production ak, then this a k is to include not only the quantity of (K) that is necessary to produce a unit of (A) but also the quantity of (K) that, if the production of (A) is increased by a unit, is required for the concomitant increase in stocks held by producers (Walras, Éléments, p. 298; W.W.Leontief, ‘Input and Output Analysis…’ American Economic Association, Papers and Proceedings, May 1949, pp. 219–20). 62 These stocks exist of course in specific forms, such as wine in cellars or handsaws in workshops. In reality, these specific goods need not at any given moment be, even approximately, what the maximizing conditions for the subsequent period would require. Here, so it seems to us now, we have the essentially dynamic problem how the economic process adapts itself to situations that are inherited from the past and are always out of date when they have to be acted upon. But Walras eliminated this problem by the heroic assumption that stocks, like capital goods, are exactly as if they had been produced in the past with a view to conditions obtaining in the present. This is the meaning of his phrase, constructing the equilibrium system ab ovo. We may render it by saying that he created an economic world in which every element fits perfectly into its niche, even if, owing to the fact that production takes time, it had to be produced when nobody could have known exactly what the niche would be like. There is point in such a construction. But, once more, it is but the first mile stone on a long road. Equilibrium analysis 987 treated the capital goods: there are the stocks themselves and, in addition, there are the services they render currently, namely, the services d’approvisionnement. Hence stocks and their services have to be priced separately, but the price of each stock stands to the price of its service in the same relation as the price of the service of each capital good stands to the price of the capital good itself. 63 Note that the introduction of stocks and the services of stocks constitutes Walras’ method of synchronizing the economic process: on condition of paying the price of the service—that is, an interest charge on the circulating capital involved—households are now able to ‘transform’ their productive services immediately into consumers’ goods. But this is evidently no mere detail but an essential feature of the general equilibrium system to which, by way of anticipation, Walras already adverted in his theory of production (Éléments, p. 215). With the stocks enters money. It is simply a particular item in the list of inventories and also renders a service d’approvisionnement, which acquires a price, like any other service, by virtue of its marginal utility functions. 64 This 63 This conceptual arrangement, presupposing as it does the existence of a net price of each service d’approvisionnement, is open to the same objection that may be raised against the postulate of the net yield of a capital good. But as soon as we admit the existence of such a service d’approvisionnement that is capable of having a net price (i.e. a price greater than depletion of the stock plus insurance), we cannot object to the distinction of stock and service on the ground that this spells double counting. In fact, since Walras derives the prices of stocks, via the rate of interest, from the prices of their services—i.e. in a manner equivalent to a discounting process—there is here a remarkable affinity with Böhm-Bawerk’s schema although, almost tragically, those two great men completely misunderstood one another. But the affinity becomes obvious if we state the matter like this: the households receive the products they want at once (instead of receiving them at the end of the period of production), and they pay interest in order so to receive them. See next sentence in the text. 64 This price must not be confused with the price of money itself. Let p′ denote the price of money in terms of the numéraire, π′ the price of its service d’approvisionnement, and i the rate of interest, then, according to the rule for the value of capital goods that do not wear out (such as land), we have π′=p′i. If money serves as numéraire, p=1 and π=i. As regards the marginal utility curves for the services of money and stocks in general, it must be observed, however, that they are not ‘given’ in the same sense as are the marginal utility curves for beer or bread: in Frisch’s terminology, they are not as autonomous as are the latter, and they are valid only for a structure of production and for habits of payment which the economic process itself keeps on changing. Walras saw this difficulty but he comforted himself by pointing out that in practice households and firms normally know ‘very approximately’ how great a revolving fund of goods and money they need. This is true, but the theorist who avails himself of this fact must indeed point out, as did Walras, that he is excluding uncertainty by special hypothesis. Incidentally we may remark that Walras thus disposed, without intending to do so, of the later theory (J.R.Hicks) that there would be no need for holding cash in the absence of uncertainty of any kind and that, therefore, the phenomenon of money depends for its existence on uncertainty. Walras, within his schema, had no opportunity to do justice to the importance of the element of uncertainty. But he History of economic analysis 988 price emerges in a special market, which Walras called the capital market (marché du capital)—in distinction to the market of capital goods (marché des capitaux)—and which is an ‘annex’ of the market of all productive services (Éléments, p. 245). All suppliers of services are now paid, and buy products, in money. Capitalists save no longer by exchanging productive services against capital goods but they save in money and we have a quantity called monnaie d’épargne in addition to the two quantities of transaction money (monnaie de circulation) in the hands of households and of firms. The latter borrow money and buy new capital goods. The equilibrium price of the ‘commodity’ in this market, namely, of money’s service d’approvisionnement, is determined by the condition that people’s demand for this service—represented by their encaisse désirée— be equal to the total amount of money in existence. Having determined this equilibrium price we may choose money itself for numéraire and then restate the condition by saying that the rate of interest should be such as to equalize the encaisse désirée and the total amount of money in existence. 65 So far, the ‘existence’ of a unique set of solutions or of equilibrium values for the Walrasian system is not affected at all by the introduction of money: the situation in this respect remains, qualifications included, much as we found it in the case of the numéraire economy. This could be proved but should be intuitively clear from the fact that Walras fits in money by a device that amounts to setting up its service d’approvisionnement as just one more service (of no direct utility) to be traded in—which evidently no more changes the logic of the situation 66 than would the introduction of any other additional commodity or service. It should be added, however, that owing to the nature showed that meeting uncertainty is not essential for money to circulate and to be held, so that there is no warrant for the proposition that a money economy is necessarily dynamic. This does not amount to denying that all the really troublesome problems about money arise in evolutionary processes. 65 It should cause no surprise that we find ourselves suddenly in close proximity to the Keynesian theory of interest (the ‘own-rate’ theory, see General Theory, p. 223). The affinity stands out particularly well—and so does the difference—if we observe that, within Walras’ schema, there is only room for the first of Keynes’s three motives for holding cash, viz. the transaction motive, whereas there is no room for the other two, viz. the ‘precautionary’ and the ‘speculative’ motives (General Theory, p. 170). The saving schedule thus coincides with the supply schedule in the capital market. But the two other motives can be readily inserted into Walras’ picture. If we do so, then the savings schedule no longer coincides with the supply schedule of loanable funds. But this does not invalidate the Walrasian theory: it only amounts to supplementing it by additional hypotheses. See on this O.Lange, ‘The Rate of Interest and the Optimum Propensity to Consume,’ Economica, February 1938, and Franco Modigliani, ‘Liquidity Preference and the Theory of Interest and Money,’ Econometrica, January 1944. The argument of these writers is not invalidated by D.Patinkin’s criticisms in ‘Relative Prices, Say’s Law, and the Demand for Money,’ Econometrica, April 1948, although it is open to others. 66 This has been denied of late, precisely on the ground that Walras excluded money from the things or services of things that have marginal utility functions, i.e. Equilibrium analysis 989 of the service that money is supposed to render, the price of its service enters the demand and supply equations that determine the prices of all the other commodities and services in a peculiar way. This may be seen most easily by observing that variations in the price of the service of money—or, choosing money for numéraire, interest—affect directly the values of capital goods and stocks (inventories) and through these all the other prices and quantities in the system, including those of the productive services such as wages and the quantity of labor demanded and offered. This is important to keep in mind: any variation in any price affects all other prices, offers, and demands, but variations in the price of money have an additional influence of particular importance. Hence money prices are not simply translations of prices expressed in a numéraire that is not money into prices expressed in another numéraire that is not money: money prices are not proportional to numéraire prices; they are prices adjusted to a new condition, that is, the condition that governs equilibrium in Walras’ capital market. We may still formulate this monetary equilibrium condition as we did above, namely, that total encaisse désirée should be equal to the total quantity of money in existence, but we must keep in mind that the encaisse désirée depends, among other things, on the total numéraire value of transactions and that the latter also depends on the price of the service of money and cannot remain constant if this price—or the rate of interest—changes. In other words, we cannot fulfil the monetary equilibrium condition by treating as given not only the existing quantity of money but also the total encaisse désirée, and letting monetary equilibrium come about by appropriate variations in the rate of interest alone. If this fact is realized and acted upon, then we may aver indeed that the Walrasian argument determines a consistent set not only of relative but also of money prices or, if you wish, the price level. Walras himself realized this situation and must therefore be credited with having created a theory of money that is complete, consistent, and perfectly adequate, within its own assumptions, to determine absolute prices in terms of money. 67 But at the critical point he failed to go through with it. On the ground that the influence of variations in the rate of interest upon the sum total of transactions, hence upon the encaisse désirée, is only ‘indirect and feeble’ (Éléments, p. 311) he decided to neglect it altogether and then pro- from the set of things that qualify for commodities. But this view is based on nothing but a misunderstanding of Walras’ decision to consider at first a kind of money, the material of which has no value as a commodity (Éléments, p. 303) in order to defer the problems that arise if money is made of a material that has an appreciable value in consumption or production, such as gold or silver. This question has nothing to do with two other cognate ones: (a) whether the concept of a ‘service of money’ is admissible; and (b) whether Walras did or did not emphasize the parallelism between monetary and ‘real’ processes too strongly. 67 This theory has in particular nothing to fear from the man of straw some contemporary economists have baptized Say’s Law. Nor is it affected by zero homogeneity of demand and offer functions although in Walras’ theory, as in any other, it must of course remain indifferent whether people calculate in dollars or in cents. History of economic analysis 990 ceeded to base much of his reasoning about applied monetary theory on the simplifying assumption of its absence. This assumption, quite apart from the question whether it is factually justifiable or not, 68 would change the whole situation if we were to take it as part of Walras’ rigorous theory. Then, as Walras himself observed, the equation of monetary circulation would indeed be ‘external to the system of equations that determine economic equilibrium’ (ibid.), and then there would be some warrant for saying that Walras’ system is essentially a ‘real’ or numéraire system, complete as such, 011 which he threw, as a separable piece of apparel, the ‘veil of money’ (see, however, next chapter). 69 Money interest and money prices would then be no longer determined simultaneously with the relative prices and would in general be inconsistent with them. 70 In view of the spirit as well as the wording of Walras’ text, it is, however, much more natural to say that, for the purposes of applied monetary theory, Walras decided to abandon his method of general analysis and to adopt that of partial analysis. This means that he decided to adopt an approximation to which the standards of rigorous analysis do not apply. 71 But the question of stability (and of the presence of a tendency in the system to realize the equilibrium values of its elements) is now much more difficult to answer than it was before. This is not owing to any change in the logical situation that the introduction of money has brought about—which is much as it was in the numéraire economy—but to the fact that in a money economy it is more difficult to accept Walras’ general pattern of the economic process. Of this Walras was perfectly aware. Proof of it is his emphasis upon the instability of bank credit (e.g. Éléments, pp. 353–4). Apart from this it stands to reason that the insertion of a monetary capital market offers the economic engine new opportunities for stalling which are absent in a numéraire economy: we may exclude uncertainties in obedience to Walras’ directions; but in the case of a ‘commodity’ which is as volatile as money and which can be 68 It seems to me beyond question that in general it is not. It may, however, serve some particular purposes. 69 This assumption is the second reason (in addition to Walras’ careless statement on p. 303 of the Éléments, that money is to be considered as an objet sans utilité propre) that may be adduced in favor of writers who interpret Walras in that sense. There is a third one. Walras’ exposition does without money as long as possible and thereby creates the impression that the theory of money is indeed something to be plastered upon the façade of a building that had been completed beforehand. Closer analysis shows, however, that this is no more than an expository device which is of a piece with his method of abstracting from the facts of production in his presentation of his theory of exchange. The great master of ‘universal interdependence’ should be free from suspicion on this score. 70 This is obvious. If a change in the rate of interest involves, in principle at least, rearrangements of all real and monetary magnitudes in the system, then the postulate that the encaisse désirée should remain untouched is equivalent to introducing another condition that will in general make the system overdetermined and, in this sense, spell contradiction. 71 The main motive seems to have been a wish to gain possession of a simple form of ‘quantity theory.’ Equilibrium analysis 991 . History of economic analysis 986 the whole of the Walrasian structure of pure theory appears in all its logical beauty. The ground floor of this structure is the theory of the ‘market’ of. papers of Professor C.Bresciani-Turroni, History of economic analysis 984 all demand and supply equations. From these, then, a comprehensive theory of its role in the economy may be read off. 54 . theoretical device on the score of lack of realism would spell misunderstanding. History of economic analysis 982 fered against capital goods 47 instead of being offered against bread or beer,