appended to this chapter. Meanwhile I am content to point out that measures of the kind envisaged by Marshall come within the range of any reasonable definition of planning. No doubt he only scratched the surface. But any proposition that avers that a piece of planning can ‘improve’ upon the working of ideally perfect competition means a breach in an old wall and is therefore of great historical importance. No mere criticism of capitalism on ethical or cultural lines—however important in other respects—could have accomplished precisely this. Others, Edgeworth and Pareto among them, were not slow to widen the breach. 3 Of far greater importance was another achievement. Three leaders, von Wieser, Pareto, and Barone, who were completely out of sympathy with socialism, created what is to all intents and purposes the pure theory of the socialist economy, and thus rendered a service to socialist doctrine that socialists themselves had never been able to render. As we know, Marx himself had not attempted to describe the modus operandi of the centralist socialism which he envisaged for the future. His theory is an analysis of the capitalist economy that is no doubt geared to the idea that this economy, by means of the inevitable ‘breakdown’ and of the ‘dictatorship of the proletariat’ resulting from this breakdown, will give birth to the socialist economy; but there is a full stop after this and no theory of the socialist economy that deserves the name follows. 4 Most of his disciples, as we also know, evaded the problem instead of meeting it, though some, Kautsky in particular, did display awareness of its existence by pointing out that the socialist regime, after the revolution, would be able to use the pre-existing capitalist price system as a provisional guide—an idea that points in the right direction. Now the Austrians were in the habit of using the model of a Crusoe economy for the purpose of explaining certain fundamental properties of economic standpoint of those who abhor the use of the consumers’ surplus concept) but I believe that the statement in the text above renders what he really meant and that the usual criticism is hardly fair to him. The main point of this criticism was first made, not against him but against Pigou’s formulation of his doctrine, in a review, ‘Pigou’s Wealth and Welfare,’ by A.A.Young (Quarterly Journal of Economics, August 1913). It turns on Marshall’s suggestion that subsidies to industries that realize (relatively to others) large economies in expanding might be advantageously raised by taxes on the product of industries that ‘obey the law of diminishing returns.’ Though valid within static theory, the objection can be met by considerations that lie outside its precincts. 3 Wicksell also attacked the doctrine of maximum satisfaction. But he held (Lectures I, pp. 141 et seq.) ‘that free competition is normally a sufficient condition to ensure maximization of production’ (my italics). This is not correct either, although the extent of the error depends on what we mean by ‘normally.’ But his position was nevertheless far ahead of that of Walras. 4 It is indeed possible to assemble from Marx’s writings a number of hints that go beyond the phrases of his day, e.g. the hint at the necessity, in the socialist commonwealth, of an elaborate bookkeeping system. But substantially he confined himself to such phrases as that, of course, workmen will be anxious to produce most efficiently so that, we are led to infer, there really will be no scarcity problem (no problem of ‘economizing’ factors) at all. History of economic analysis 952 behavior. Therefore, it was particularly easy for them to realize that there was nothing specifically capitalist about their basic concept of value and its derivates such as cost and imputed returns: these concepts are really elements of a completely general economic logic, of a theory of economic behavior that may be made to stand out more clearly in a model of a centrally directed socialist economy than it can in the capitalist garb in which it presents itself to the observer whose historical or contemporaneous experience is with a capitalist world. For instance, when we are trying to describe how Crusoe allocates his scarce resources in order to maximize the satisfaction of his wants or, in other words, to formulate the rules he follows in transforming these resources into objects that will satisfy his wants, we discover immediately that his economy may be characterized by certain ‘coefficients of transformation’ which fill the same function that prices fill in competitive capitalism. If we consider a socialist economy, it is still more obvious that, for instance, maximization of satisfaction requires that the ratio of marginal utilities for each pair of consumers’ goods must be identical for all comrades; that in every line production must be so organized as to make the technologically optimum use of all means of production; and that the marginal value productivity of all scarce means must be the same in all their uses or, at all events, must in every use be at least as great as it would be in any other. But all this amounts to saying that any attempt to develop a general logic of economic behavior will automatically yield a theory of the socialist economy as a by-product. The first to realize this explicitly was von Wieser (Natural Value, 1st German ed., 1889). Pareto, in the second volume of his Cours (1897), 5 excelled Wieser in clearness and skill of presentation, if not in insight, and has more claim than any other individual to being considered as the originator of the modern pure theory of the socialist economy. 6 Actually, however, his contribution has been overshadowed by that of Barone, who presented the whole of the subject in a famous piece of work that, so far as essentials are concerned, has remained unsurpassed to this day. 7 Many economists of our own day have added details and some further developments. I mention O.Lange and A.P.Lerner and for the rest refer the reader to A.Bergson’s paper mentioned in footnote 6. Barone’s performance consists in a nutshell in this: after having presented on Walrasian lines 8 the system of equations that describes economic equilibrium under conditions of pure competition in a private-property economy, he wrote down the analogous system of equations for a socialist economy of a certain type. Whereas in the private-property economy incomes, simultane- 5 See, e.g., p. 94 of the second volume. He carried his argument considerably further in ch. 6, 52–61, of his Manuel (1909). 6 The development of this theory has been described by Abram Bergson in his contribution ‘Socialist Economics’ (in the Survey of Contemporary Economics, ed. H.S. Ellis, 1948) in a manner that leaves nothing to be desired. 7 Enrico Barone, ‘Il Ministro della produzione nello stato collettivista,’ published in the Giornale degli Economisti, 1908, trans. in F.A.von Hayek, ed., Collectivist Economic Planning (1935) as ‘The Ministry of Production in the Collectivist State.’ 8 There are, however, several original points, two of which will be mentioned below. Equilibrium analysis 953 ously with all the other variables of the system, are determined by the economic process itself—so that, as we have said before, production and distribution are but different aspects of one and the same process—there is of course a separate problem of distribution in the socialist commonwealth. That is to say, society must first of all decide by a separate act, for instance by a clause in its constitution, what the ‘incomes’ or relative shares in the social product of the individual comrades are to be. Then a central social agency or ministry of production could be created for the management of the economic process, and a unit of account could be introduced. A definite amount of such units could be allocated to every comrade, which he is free to spend according to his tastes on the consumers’ goods that the commonwealth produces or to ‘save,’ that is to say, to hand back to the ministry of production in consideration of a premium that the latter is prepared to pay for deferment of consumption. We thus derive demand functions for consumers’ goods and supply functions of labor and saving, and the reader will have no great difficulty in seeing how, guided by these functions and by its own technological knowledge, the ministry will cause appropriate quantities of consumers’ and investment goods to be produced. This arrangement is, of course, not the only possible one and can be varied in many ways. For instance, we may exempt provision for investment from the range within which comrades are permitted free choice, and subject it to the decision of the ministry or of a parliament, just like expenditure for national defense. Also, we may either offer the comrades equal ‘incomes,’ and then postulate that they must accept the ministry’s directions as to the kind and amount of work which they are to do, or else we may devise a system of differential income rates so as to call forth the free offer of the kinds and amounts of work that are to be done in every line, thereby introducing ‘wages’ and labor markets. Barone blocked out a theory of a socialist commonwealth that assumes freedom of choice all around as to consumption, as to saving (investment), and as to employment. But whether we follow him in this or not, the formal similarity between a socialist order of things and the order of things that would obtain in a perfectly competitive capitalist society stands out strongly. It is not even lost in the case of dictatorial socialism: the perfect dictator would in fact behave according to a pattern of which the prototype is the Crusoe economy. But also the nondictatorial socialist commonwealth can be run on principles other than the principle of consumers’ sovereignty. It is quite thinkable, for instance, that comrades should not get what they actually wish to have but what some experts or bureaucrats think that they should have. However, theoretical difficulties do not arise in any of these cases but only in the case of federalist socialism, where there is no central agency and each industry is controlled autonomously by the workmen attached to it: in this case the problem becomes oligopolistically indeterminate. The essential result of Barone’s or any similar investigation is that there exists for any centrally controlled socialism a system of equations that possess a uniquely determined set of solutions, in the same sense and with the same qualifications as does perfectly competitive capitalism, 9 and that this set enjoys similar maximum properties. 10 Less technically, this means that so far as its pure logic is concerned the socialist plan makes sense and cannot be disposed of on the ground that it would necessarily spell chaos, waste, or irrationality. This is no small thing and we are within our rights when we emphasize again the importance of the fact that this service to socialist doctrine has been rendered by writers who, since they were not socialists themselves, thereby victoriously History of economic analysis 954 vindicated the independence of economic analysis from political preference or prejudice. But, at the same time, this is all. We must not forget that, just like the pure theory of the competitive economy, the pure theory of socialism moves on a very high level of abstraction and proves much less for the ‘workability’ of the system than laymen (and sometimes theorists also) think. In particular, the proposition about the maximum properties of the solution that characterizes the equilibrium of a socialist economy is of course relative to its institutional data, and avers nothing concerning the question whether this purely formal maximum is higher or lower than the corresponding maximum of the competitive economy—especially if we refuse to go into the further questions, whether the one or the other institutional set-up is less exposed to deviations from its own ideal or more favorable to ‘progress.’ These questions are so much more important in practice than is the question of determinateness or ‘rationality’ per se, that it is sometimes not easy to tell whether the later critics of the socialist plan, especially von Mises, 11 really meant to deny the validity of the Pareto-Barone result. For it is quite possible to accept it and yet to hold that the socialist plan, owing to the administrative difficulties involved or for any other of a long list of reasons, is ‘practically unworkable’ 12 in the sense that it cannot be expected to work with an efficiency comparable to the efficiency of capitalist society as revealed by the index of total output. But although pure theory contributes little to the solution of 9 See below sec. 7. In fact, it can be shown that the case for unique determinateness (which, of course, implies consistency) is somewhat easier to establish for centralist socialism than for a private-property economy, even if perfectly competitive. 10 Of course, so far as the competitive regime fails to achieve a true maximum, the socialist plan would also have to deviate from the competitive pattern. 11 L.von Mises, ‘Die Wirtschaftsrechnung im sozialistischen Gemeinwesen,’ Archiv für Sozialwissenschaft und Sozialpolitik, 1920; trans. in F.A.von Hayek, ed., Collectivist Economic Planning (1935) as ‘Economic Calculation in the Socialist Commonwealth.’ 12 See A.Bergson, op. cit. While we cannot go into this set of problems, it is necessary to point out that there is also a purely theoretical anti-socialist argument (sponsored by Professors von Mises, von Hayek, and Robbins), which is definitely wrong, namely the argument that, although there exists a determined set of solutions of the equations that describe the statics of a socialist commonwealth, there is, without private property in means of production, no mechanism by which to realize them. They can be realized by the method of ‘trial and error’ described below. Equilibrium analysis 955 these problems, 13 it helps us to posit them correctly and to narrow the range of justifiable difference of opinion. We thus arrive at the same conclusion as in the case of non- socialist planning; ever since Marshall, the theoretical possibility of improving the purely competitive mechanism by public policy should no longer be a matter of controversy; but it is of course still possible—as Marshall well understood—to criticize either particular measures or even the whole idea of planning on such grounds as lack of confidence in the political or administrative organs that are available for the task. (It seems as if Marshall had been alone in understanding this situation.) 6. PARTIAL ANALYSIS The unwieldy system of the innumerable quantities that make up the budgets of all the individual households and firms—microanalysis, to use Frisch’s phrase again—invites simplification, for instance, by combining them into a few comprehensive social aggregates—macroanalysis. But there is also another method that, for some purposes, achieves simplification just as effectively. When we are interested in those economic phenomena that can be observed in small sectors of the economy, for example in individual ‘industries’ of moderate size and, in the limiting case, in individual households or firms, we may assume that nothing that happens in these small sectors exerts any appreciable influence on the rest of the economy. This assumption does not necessarily imply that the latter remains unchanged, although this is what we mean when using the ceteris-paribus clause; but it does imply that, if some external influence be exerted upon the small sector under consideration, then this sector adjusts itself without exerting, in turn, more than a negligible effect on the rest of the economy or any element of it (Principle of the Negligibility of Indirect Effects): a change in wage rates, for instance, that occurs in a small sector, whether brought about by the conditions of this sector or imposed from outside on it alone, may be treated as if it did not affect national income or market demand schedules at all. This postulate defines the method of Partial Analysis. Though it has been used since the beginning of time, it acquired a novel definiteness and an apparatus of its own at the hands of Cournot, von Mangoldt, and, in the period under survey, Marshall, who, as we have already noticed, became and remained for many economists primarily the master of partial analysis. 1 The method appeals to our common 13 It does contribute something, however. First, it removes an objection by virtue of which the critic might excuse himself from entering at all into a discussion of the practical details of the socialist plan. Second, it shows up certain relevant properties of the latter, e.g. that it would be free from the class of wastes that are inherent in imperfectly competitive situations such as the economic warfare between oligopolists. 1 In addition to developing the appropriate conceptual apparatus, Marshall also developed the general philosophy of the method which turns upon the principle of the negligibility of indirect effects. See especially Industry and Trade, 3rd ed., Appendix A, p. 677. There he did not hesitate to invoke the authorities of Newton and Leibniz, with the Nautical Almanack thrown in. With due respect both for Marshall History of economic analysis 956 sense, which tells us that, so long as we are content with an approximation, we need not take account of at least the great majority of effects and counter-effects that, on principle, the slightest alteration in the conditions of, say, the production of pins exerts upon national income and through national income upon the demand for gasoline. But the same common sense should also tell us that the postulate, which is so powerful a simplifier, severely restricts the method’s range of application and in fact removes from it all the relations that cannot be observed in small sectors but only in the economy as a whole. 2 Therefore, while it is understandable that partial analysis has been and is being widely used, it is equally understandable that it has been condemned from the first by theorists of the sterner type. especially by Walras and Pareto. 3 [(a) The Marshallian Demand Curve.] The standard tool of partial analysis is Cournot’s or Marshall’s market demand curve. It represents the quantity of a commodity that buyers are willing to purchase at a given price as a function of this price alone: 4 all the other factors that affect their willingness to purchase, especially their incomes, are taken care of by the shape of the demand curve. Moreover, the marginal significance to them of the income unit (‘marginal utility of money’) is not supposed to vary as they move along the demand curve so that the purchases they have made at any price P 0 have no influence upon their willingness to buy additional quantities at any price and for his admirable attempt to display, in this case, the intimate relation that no doubt exists between scientific methods in all their fields of application, we cannot deny that the argument for the principle mentioned does not carry the same weight in economics that it carries in astronomy. 2 The wage-rate problem illustrates how neglect of these restrictions may produce error and futile controversy. The results of partial analysis concerning the effects of variations of wage rates in small sectors are completely inapplicable in the case of variations of wage rates in large sectors or the whole of the economy: propositions that are true for small sectors may be nonsense for the economy as a whole. 3 Walras attacked the partial analysis of Cournot, von Mangoldt, and Auspitz and Lieben (Untersuchungen über die Theorie des Preises, 1889, of which the first chapter had been printed and distributed in 1887 and which contains industrial total cost and expenditure curves plotted together with the curves of their derivatives) in an article reprinted as Appendice II to the 4th ed. of the Éléments. He showed there that neither a demand nor a supply curve that represents quantity demanded or supplied as a function of the price of that commodity alone can ever be accepted as exact because to change the price of a commodity amounts to disturbing the whole of the existing equilibrium situation, every element of which must be correspondingly readjusted; and that, if we wish to uphold the method as one of approximation, we meet with the difficulty that the assumptions which it is necessary to make for this purpose are, in strict logic, contradictory. Pareto repeated these arguments with added emphasis. And they have been re-emphasized time and again. 4 Usually we put the independent variable, in this case the price, on the X-axis of a rectangular system of co-ordinates and the dependent variable, in this case the quantity, on the Y-axis. This is in fact usually done in the French literature. But Marshall chose the X-axis for quantity co-ordinate and the Y-axis for price co-ordinate, and this is usually done in the Anglo-American literature. Equilibrium analysis 957 P i <P 0 . If the significance people attach to a unit of their incomes should vary for reasons other than that they spend more or less upon the commodity in question, then the individual and market demands are displaced and/or altered in shape (they ‘shift’). In his Principles (pp. 171 et seq.) Marshall developed the theory of these demand curves carefully, laying in fact the whole foundation for the demand studies of the future. But he hardly emphasized enough the severity of the restrictions to which their validity, even as approximations, is subject. Actually they can be used only for commodities that are relatively unimportant—absorb but a small part of buyers’ total expenditure—or for relatively very small variations in the prices of important ones. 5 It is in such cases only that demand curves of individual households may be treated as ‘translations’ of the law of diminishing utility into terms of price (op. cit. p. 169) without having to be redrawn for every price and that Marshall’s development of Dupuit’s invention, consumers’ rent, acquires its true meaning. [(b) Elasticity Concepts.] The concept of consumers’ rent will be discussed below in the Appendix to this chapter. I take this opportunity to introduce Marshall’s price elasticity of demand (embryos of which are, as we have seen, contained in Cournot’s and Mill’s treatises). The behavior at any point of any continuous and differentiable ‘curve’ is rendered by its slope or differential coefficient at that point: if the ordinate (the price in our case) be denoted by Y and the abscissa (the quantity in our case) by X and if x 0 identify the point in question, the expression is Fuller information is conveyed by higher derivatives but this does not concern us here. Our expression has, however, the disadvantage that it is not a pure number and that its value is not invariant with respect to the units in which the price y and the quantity x are measured. A simple device for remedying this is to divide the increments dy and dx by the respective price and quantity to which they refer. Thus we get: dy/y÷dx/x or: xdy/ydx, which is called the flexibility of price. If, however, we wish to express the sensitivity of quantity demanded to small variations in price, we had better choose the reciprocal of this, that 5 Marshall himself was of course aware of the fact that the ‘marginal utility of money’ is not in general constant with respect to variations of expenditure upon any particular commodity: this awareness is obvious from his mathematical notes II and VI in the Appendix to the Principles and from the text of the Principles itself (see especially p. 207). But in chs. 3 and 4 of Book III he argued nevertheless on the assumption of constancy (where in these chapters he allows ‘marginal utility of money’ to vary, it is because people’s money incomes change). And this involved no great error because he was careful to make tea the standard example on which to reason and by which to illustrate—a commodity of sufficiently small importance to pass muster as an instance in which partial analysis, even in its strictest acceptance, is a tolerable approximation and actually neglects nothing but quantities of the second order of smallness. Both adherents and critics have overlooked this. Incidentally, they also overlooked that the requisite small importance can practically always be enforced by sufficiently narrow definitions of commodities: if meat is not unimportant enough, we may consider the demand for lamb chops. History of economic analysis 958 is, dx/x÷dy/y=ydx/xdy, the ‘elasticity.’ And since this expression is essentially negative because quantity demanded falls when price increases and vice versa, at least with the Marshallian demand curve, we might prefix a minus sign so as to have a positive number: −ydx/xdy is, then, what Marshall called elasticity of demand and what is now called, more precisely, price elasticity of demand. The cases must be rare in which so modest a contribution has met with such applause (see, for example, Lord Keynes’s eulogy in Essays in Biography, p. 228). We may as well continue this report of the history of ‘elasticity’ concepts—the word is infelicitous for it raises in the beginner’s mind quite unjustified associations—to avoid the necessity of having to return to it in Part V. First, Marshallian clasticity of demand refers to a point on the demand curve—it is ‘point elasticity’—and is therefore applicable, with increasing inaccuracy, only to infinitesimal changes in price and quantity. Hence, the wish to have a measure that will apply to finite stretches of the demand curve. This problem of ‘are elasticity,’ first posed by Mr. H.Dalton, has been the subject of a discussion to which Professor A.P.Lerner made the leading contribution, ‘The Diagrammatical Representation of Elasticity of Demand,’ Review of Economic Studies, October 1933 (see also Professor R.G.D.Allen’s analytic treatment and Lerner’s reply, ‘The Concept of Arc Elasticity of Demand,’ I and II, Review of Economic Studies, June 1934). But it must not be forgotten that point elasticity serves tolerably for variations of a few per cent of price whereas are elasticity, intended to serve for larger variations, is much more likely to violate the restriction to which partial analysis is subject. Second, reasoning in terms of elasticities presents the same advantages that it possesses in the case of the Marshallian demand curve in many other cases. Accordingly a rich crop of elasticity concepts has matured—we speak of elasticities of the total, average, and marginal cost functions; of income elasticity of quantity demanded; of elasticity of substitution (Hicks, J.Robinson); and so on. Income elasticity presents a new problem: no difficulty arises when we express the elasticity of an individual’s demand for a commodity with respect to his income; but if we express the elasticity of aggregate demand for a commodity with respect to national income, we run up against the fact that given changes in the latter have different effects upon quantity demanded, according to the manner in which the increase or decrease of national income is distributed among buyers or potential buyers. This problem has been treated by Professor Marschak and by Mr. P.de Wolff (see, e.g., the latter’s ‘Income Elasticity of Demand,’ Economic Journal, April 1941). Finally we may notice R.Frisch’s ‘elasticity calculus’ (see R.G.D.Allen, Mathematical Analysis for Economists, 1938, pp. 252–3). Third, in introducing the concept of income elasticity we have already stepped out of the domain of the Marshallian demand curve but without leaving the domain of partial analysis. We do the same thing or, at all events, we practice partial analysis while recognizing that the sector studied is actually an element of a more comprehensive system, when we use the concept of ‘partial elasticity,’ for example, of partial price elasticity. In itself, the conces-sion we make in this case consists only in replacing the ordinary differential coefficient that enters into the elasticity expression by a partial differential coefficient in order to indicate that we are not simply ‘freezing’ the rest of the economy but that we are holding its elements constant at a certain level. But once we have gone as far as this we may equally well express the elasticity of demand for a commodity with respect to variations in the price of any other commodity (‘cross Equilibrium analysis 959 elasticity’) or, successively, with respect to variations in the prices of all commodities, factors as well as products. This has been done systematically by H.L.Moore (see his Synthetic Economics, 1929) and, for the elasticity of substitution, by Hicks and Allen (see the latter’s exposition, op. cit. pp. 503 et seq.). In those cases elasticity concepts become tools of general analysis, that is, tools that may be used for the purpose of exploring relations in which we are primarily interested because they also assert themselves in the economy as a whole. [(c) Concepts Useful for General Analysis.] It follows that partial analysis is not separated from general analysis by any sharp dividing line but rather shades off into general analysis as we extend the scope of the concepts that have been in the first instance conceived for its purposes. The best illustration of this is Marshall’s Book V. Primarily, it is the classic of partial analysis, the theory of the individual industry that is small relative to the economy as a whole. 6 Industrial demand curves are there matched with industrial supply curves from which they are supposed to be independent. 7 The theory of these supply curves is a development of Cournot’s theory of costs and is subject to restrictions that are still more severe than those that partial analysis places upon demand curves. 8 But Marshall clothed his schema with such a mass of luxuriant detail as to give it an importance not really its own and to make it the backbone of a study of all non-aggregative industrial processes, 6 This implies of course the existence of perfect markets—markets in which there is but one price for all buyers—and hence the existence of well-defined and perfectly homogeneous ‘commodities,’ the production of each of which defines an ‘industry’ that faces a definite market demand curve. Marshall and all the economists of his age were not fully alive to the difficulties inherent in these concepts that have induced Professor Chamberlin and others to abandon the idea of ‘industrial demand curves’ altogether. But, neither were they blind to them. 7 The principle of the negligibility of indirect effects requires that the variations in the quantity produced by any industry must not affect the incomes earned in the same industry so strongly as to shift the demand curve for its product, let alone the aggregate demand for all products. 8 This is why Barone, who has done more than anyone else to clear up this situation, did not use supply curves of products as freely as did Marshall. Instead he confined himself to speaking of supply curves of individual factors, in order to avoid the assumption that the prices of the latter are given and do not change relatively to one another as we move along supply curves of products, an assumption that is admissible in special cases but not in general. See ‘Sul trattamento di quistioni dinamiche,’ Giornale degli Economisti, November 1894. Pigou also, from his own standpoint, realized this restriction more explicitly than did Marshall himself. See in particular his ‘Analysis of Supply,’ published in the Economic Journal as late as June 1928. History of economic analysis 960 a role which it has been made to play right into our own time. 9 And in doing so he developed concepts that are also valuable in general analysis or, as we have put it before, serve the purpose of exploring relations in the economy as a whole. An example is the concept of quasi-rent: the fact that ‘appliances made by man’ may behave exactly like natural agents for longer or shorter periods of time, though displayed by Marshall in connection with his partial analysis, is of course just as important in a general analysis of the Walras type. 10 But the most important example is the ‘principle of substitution’ which creeps in quite modestly (op. cit. p. 420) à propos of producers’ substituting less expensive for more expensive combinations of factors and eventually rises to the proud position of ‘Thünen’s great law of substitution,’ which pervades and controls the whole economic process and opens one of several possible roads toward the recognition of the universal interdependence of economic quantities. 11 From the standpoint, and within the precincts, of partial analysis, 9 In developing this schema Marshall no doubt put a greater burden upon it than it is actually able to bear. The most important instance of this practice may well be mentioned here. This schema works best when a monotonically falling market demand curve for the product of a small industry is made to intersect with an industrial supply curve that is monotonically rising in the operative interval. But Marshall was evidently reluctant to confine himself to this construction, which seems to leave out of account the fact that in practice firms and industries operate on falling supply curves most of the time. He therefore admitted such falling supply curves and introduced for their explanation his famous concepts of internal and external economies. But it should be clear that supply curves which do depict these phenomena deal with an irreversible process and are therefore not at all like the ordinary supply curves on which a firm can travel back and forth. They depict historical processes in a generalized form. This led to a well-known difficulty about the equilibrium of an industry under conditions of pure competition: whenever a falling supply curve intersects with a demand curve from below, that is, in such a way that, to the left of the point of intersection, marginal costs are lower and, to the right of the point of intersection, marginal costs are higher than are the demand prices for the respective quantities, Marshall would say that the point of intersection is a point of stable equilibrium, whereas it is quite clear that there is no reason for any individual firm to call a halt at that point unless we admit some element of monopoly. But the difficulty is quite gratuitous. In the case of both internal economies and external economies the industrial supply curve is displaced (shifting downward) and there is no point whatever in calling the curve that depicts this displacement a supply curve. 10 Marshall’s handling of this concept, just as his handling of the rent concept, was somewhat impaired by inconsistencies. But it was, as we have seen, one of the most important tools he produced in his attempts to grapple with the difficulties inherent in the ‘element of time.’ Similarly, his theory of long and short periods grew out of considerations about small industries, or even individual firms, but is also of general applicability (see Principles, p. 519); and still more obviously is this the case with Marshall’s theory of expectations (see, e.g., pp. 422 and 446) and risk. 11 This becomes obvious if we add to the technical or factor substitution introduced on p. 420 of the Principles, the still more fundamental product substitution practiced by consumers. Though Marshall also recognized the latter he never fully co-ordinated the two in the manner that was developed before him by Carl Menger. In consequence, Marshall’s principle of substitution never appeared in his work and the Equilibrium analysis 961 . than did Marshall himself. See in particular his Analysis of Supply,’ published in the Economic Journal as late as June 1928. History of economic analysis 960 a role which it has. they were not socialists themselves, thereby victoriously History of economic analysis 954 vindicated the independence of economic analysis from political preference or prejudice. But, at the. Representation of Elasticity of Demand,’ Review of Economic Studies, October 1933 (see also Professor R.G.D.Allen’s analytic treatment and Lerner’s reply, ‘The Concept of Arc Elasticity of Demand,’