tion, as the second of the two descriptive functions that I have called the two pillars of the classic theory of that time. 25 The old ‘laws of returns,’ properly generalized and polished, lay at hand to supply the properties which the production function was to enjoy, either generally or ‘normally,’ and which we shall now restate again. If we wish to define marginal productivity of a service as the partial derivative of the production function with respect to the quantity of that service, we must, as has been pointed out already, assume first of all that these partial derivatives exist. We may postulate in addition that they are positive, that is, that a small increase in the quantity of any services will increase the quantity of the product. 26 Following Turgot we may postulate further that this rate of increase itself increases at first , then passes through a single maximum and, after having reached this point, keeps on declining In this case two corollaries follow: (1) there exists a point beyond which the average productivity of every service (x/ν i ) decreases also (law of decreasing returns in the secondary sense); (2) cross derivatives are positive, which means that if I increase the quantity of a productive service v i by a small amount, this will not only decrease (after the point indicated) its own marginal productivity but also increase the marginal productivities of all the other productive services A methodological remark may be usefully inserted here. Among the properties to be assigned to the production function, there are some that follow from others and therefore may be ‘proved deductively’ or ‘stated as theorems.’ Thus decrease of average productivity (after a certain point) may be deduced from, or proved by, the decrease of marginal productivity and there is then no need for any separate observational or experimental proof. Thus Wicksell (see his article in the Thünen Archiv, 1909) was right in holding, and F. Waterstradt (ibid.) was wrong in denying, that the ‘law’ of decreasing average productivity follows from other properties of the production function which we usually assume. But, though we have in general some latitude in deciding which properties we wish to postulate and which we wish to formulate as 25 See first sentence of this section. By using this simile, I do not mean to deny that from some standpoints, especially the Austrian one, there is reason to object to looking upon the utility and production functions as completely equal in analytic status, and something to be said for regarding utility as the one and only pillar of the building. 26 Beyond an ‘operative interval’ this need not be so of course: so many workmen may be already employed in a plant that additional workers would reduce output—everybody treading on the toes of somebody else. It does not make any real difference whether this possibility is expressed by saying that after a certain point marginal productivity becomes negative or by saying that, since no employer, if a free agent and acting upon the rules of economic logic, will take on any service increments that will decrease output, marginal productivity cannot fall below zero. For certain purposes the first alternative is preferable. History of economic analysis 1002 theorems, this is not always so. Thus, there is no economic axiom that would imply the proposition that physical marginal productivity (after a point) decreases monotonically. And in any case we always have to postulate some propositions for which, within a deductive sector of our (or any) science, it is not possible to provide logical proof. This raises the question of their status or nature. Formally they enter as hypotheses (or as definitions in B.Russell’s sense), which on principle we can frame at will. But when, with a view to application, we ask whether they are ‘true’ or ‘valid,’ that is, whether results arrived at by means of them may be expected to be verifiable (in general or with respect to certain phenomena or aspects of phenomena), then there are only two possibilities: they may be deductively provable in some wider system that transcends economics or its deductive sector, or they must be established by observation or experiment This is the case of the proposition that asserts decrease (after a point) of the marginal productivities of productive services in function of the quantities of these services. This means that when we assert this proposition we are asserting a fact and this imposes upon us the duty of factual verification. Of course evidence for such a proposition may be so overwhelming that we may refuse the challenge as vexatious. But since there is no logically binding rule for deciding what is and what is not vexatious, we must on principle be always prepared to meet the challenge: we have no logical right to reply that the challenged proposition is ‘obvious’; and we are committing a definite error, if we call it ‘evident.’ For us, these truths are important because they have been and are frequently sinned against in the matter of ‘laws of returns’: we shall presently see an interesting instance of this is the discussion on first-order homogeneity. Let us note in passing that here we are brushing against an interesting problem of general epistemology. I take this opportunity to mention Edgeworth’s analysis of the ‘laws of return’ (pub lished originally in the Economic Journal, 1911; republished in Papers Relating to Political Economy, vol. I, pp. 61 et seq. and 151 et seq.), which has been rightly called one of his most important contributions to economic theory by Professor Stigler (op. cit. pp. 112 et seq. to which the reader is referred). It is as interesting to note that Edgeworth had still to struggle for the recognition of quite elementary matters such as that the ‘law’ of diminishing returns does not apply to land only, as it is to note that Edgeworth, whose chief merit it was to teach the distinction between decreasing marginal and decreasing average returns, had repeatedly confused the two himself and that his presentation in the paper in question is not correct in every detail. The matter was taken up again by Karl Menger (the mathematician, son of the economist) in his ‘Bemerkungen zu den Ertragsgesetzen’ (two articles in Zeitschrift für Nationalökonomie, March and August, 1936; see also a comment by K.Schlesinger, ibid.). We must be grateful to the eminent mathematician for the lesson on slovenly thinking which he administered to us and which may serve as a shining example of the general tend ency toward increased rigor that is an important characteristic of the economics of our own period. But in effect, the logical crimes revealed—except the confusion between decreasing marginal and average returns—have hardly been productive of serious er rors in results. Even as regards that confusion it should be mentioned that, though no less a thinker than Böhm-Bawerk committed it, it remained quite harmless in his case, for he reasoned correctly about decreasing marginal returns to his roundabout process. Equilibrium analysis 1003 The reader will have no difficulty in understanding why it was that the properties of the production function—that is, the use of a production function that constitutes the only relation between the productive services employed, all of which are assumed to be ‘substitutional’—recommended themselves to theorists, particularly for classroom and textbook purposes. Such a production function is easy to handle and yields simple results. Moreover it picks up, from the mass of relevant technological facts, just those that are subject to economic choice and thus serves well to display the economic logic of production. It cannot be repeated too often that this production function is valid only on a high level of abstraction, for planned and not for existing plants, and for a limited region of the production surface at that. But on that level, and for that range, it is an advantage and not a blemish that it discards all the cases in which the economic logic if thwarted by additional restrictions of a purely technological nature. These additional restrictions exist however, even in the stage of planning an enterprise; many more impose limits upon long-run and still more upon short-run adaptations of existing concerns; and as we approach the patterns of real business life we lose that pure logic more and more from sight, especially because the restrictions prevent even immediately adaptable services— such as labor that can be hired by the week or day or hour—and their prices from behaving according to the marginal productivity rules, even apart from the facts that perfect equilibrium and pure competition are never fully realized. And the reader will also understand that some economists will express this situation by saying: ‘the marginal productivity theory is of universal application on a high level of abstraction,’ whereas other economists will prefer to say: ‘the marginal productivity theory is erroneous.’ Barring the regrettably frequent cases of failure to grasp the meaning of the theory, this is all there is to the controversy on the production side of ‘marginalism’ that has been carried on to this day. 27 In particular, all that Pareto 27 Telling illustrations of this statement may be gleaned, e.g., from the controversy between Professor R.A.Lester, ‘Shortcomings of Marginal Analysis for Wage-Employment Problems’ (American Economic Review, March 1946) and Professors F.Machlup, ‘Marginal Analysis and Empirical Research’ (ibid. September 1946) and G.J.Stigler, ‘Professor Lester and the Marginalists’ (ibid. March 1947, where the reader also finds Lester’s reply to Machlup and the latter’s rejoinder). In this connection a warning to the reader suggests itself: in appraising an author’s view on marginal productivity theory it is always necessary to make sure what an author means by this term: Pareto and Stigler, e.g., seem in places to mean only theories that assume all ‘factors’ to be connected by one relation only, this relation expressing universal substitutability Statements may be true of this marginal productivity that are not true of marginal productivity theories that admit also other relations between the factors. The latter is the meaning adopted here. For instance, Walras’ original theory, which worked with constant coefficients of production and admitted no substitution except the substitution of production of a product for production of another product and Wieser’s theory which did the same are still marginal productivity theories for us. This is important to remember: the circumstance that a theory includes boundary conditions, which will History of economic analysis 1004 can have meant by renouncing the marginal productivity theory is that we cannot be content to deal with the case of substitutable services—the case of the single substitutional relation—any more than we can be content to deal with the case of constant coefficients, but that we must take both into account and, in addition, cases in which coefficients of production vary with the quantity produced 28 —which simply amounts to saying that the fundamental analytic schema that uses nothing but the substitutional relation needs to be supplemented if we wish to approach reality more closely, 29 but remains valid within its proper sphere. [(c) The Hypothesis of First-Order Homogeneity.] If, following Wicksteed, we further endow the production function with first-order homogeneity, that is, if we assume that there are no economies or diseconomies of scale, we secure further simplifications which explain why many authors cling to it, 30 even though it is generally recognized by now that we do not need it for proving that distribution according to marginal productivity rules will just exhaust the product. Again I have to report a long, inconclusive, and unnecessarily prevent some factors from earning at the rate of marginal physical productivity multiplied by either the prices of the product or the marginal revenue, does not prevent us from calling this theory a marginal productivity theory. 28 This led him to define the coefficients of production in a new way, which is useful only if we wish to retain these coefficients while getting rid of the assumption of their constancy. He expressed the quantities of productive services employed as functions of the quantities of products. His coefficients of production are then the partial derivatives of these functions with respect to the various services (Manuel, p. 607). A similar idea was used by W.E.Johnson (‘The Pure Theory of Utility Curves,’ Economic Journal, December 1913) and in some respects generalized by A.W.Zotoff (‘Notes on the Mathematical Theory of Production,’ ibid. March 1923, a brilliant contribution, the neglect of which might provide subject matter for another homily about the manner in which economists work). Neither author acknowledged indebtedness to Pareto. 29 In trying to do so we discover of course that the range within which ‘factors’ can be substituted for one another rapidly decreases as we make factors more and more specific. With the time- honored triad of the services of land, labor, and capital, substitutability holds almost unrestricted sway. When it comes to Douglas fir lumber, dentists, and cutting tools, it almost vanishes in the short run. This merely means that we must state, in each instance, what type of factors, of periods, and of problems we have in mind, and there should be no reason for quarreling either about marginal productivity or about ‘method’ in general. It sounds almost incredible and yet it is the fact, nevertheless, that this has remained a source of controversy to this day—of controversy that was, in part at least, kept alive and embittered because both parties erroneously believed that there was a political interest at stake. 30 In order to satisfy himself of this the reader need only observe the frequency with which first- order homogeneity turns up (sometimes unnecessarily) in Professor Allen’s treatment of problems of production and distribution (see his Mathematical Analysis for Economists, passim). A still more telling instance is Professor Hicks’s ‘Distribution and Economic Progress,’ Review of Economic Studies, October 1936. One of the most important of these simplifications refers to the coefficient of elasticity of substitution. Equilibrium analysis 1005 acrimonious discussion 31 which hardly deserves more than the following comments. First of all, he who asserts first-order homogeneity of the production function asserts a fact, at least hypothetically. Since this fact is not implied in any of the other properties that, in general, normally, or for particular purposes we have previously agreed to attribute to the production function, 32 it can be established or denied only by factual evidence if at all. Edgeworth’s early criticism of Wicksteed’s use of first-order homogeneity is indeed disfigured by misplaced irony. But it had at least the merit of realizing correctly that it is facts and not speculations which are needed to refute the hypothesis: this is why he hunted for contradicting instances. The vast majority of participants in the discussion, however, have tried to this day to ‘prove’ or to ‘refute’ it by logical argument or by appeal to its obviousness or lack of obviousness, 33 which inevitably leads into deadlock. Second, we must not forget that asserting (denying) the practical possibility of multiplying all ‘factors’ by a constant λ is one thing; and asserting (denying) that output would also be multiplied by λ, if it were practically possible to multiply all ‘factors’ by λ, is quite another thing. 34 Nobody denies that the 31 It is not possible—and neither would it be profitable—to follow this discussion in detail. Therefore I shall mention here, besides Wicksteed and his earliest and most severe critic, Edgeworth, only a few modern contributions, namely: F.H.Knight, Risk, Uncertainty and Profit (1921); N.Kaldor, ‘The Equilibrium of the Firm,’ Economic Journal, March 1934; A.P.Lerner, Economics of Control (1944), pp. 143, 165–7; G.J.Stigler, Theory of Price (1946), p. 202n.—all of whom stand for first-order homogeneity. Strongly on the other side of the fence: P.A.Samuelson, Foundations, p. 84; and E.H.Chamberlin, ‘Proportionality, Divisibility, and Economies of Scale,’ Quarterly Journal of Economics, February 1948. See ibid. February 1949 for two criticisms and Chamberlin’s rebuttal. 32 Such a particular-purpose property is that all ‘factors’ be substitutional. Some writers seem to have believed, though more often implicitly than explicitly, that first-order homogeneity follows from this property. H.Schultz even tried to prove it (‘Marginal Productivity and the General Pricing Process,’ Journal of Political Economy, October 1929, Appendix 1). This is an error. 33 Appeal to obviousness can of course be met by simple denial, but it should not be met by saying, as has been said by Professor Samuelson (Foundations of Economic Analysis, p. 84) that the hypothesis is ‘meaningless’ since anyone who declares it to be obviously valid will, if challenged, defend it by labeling any contradicting facts as ‘indivisibilities’ (see footnote 35, below), thus making the hypothesis true by definition. This is not so, though I do not deny that uncritical reference to indivisibility of some factor ‘which must of course exist if the production function does not display first-order homogeneity’ does give some color to the indictment: indivisibilities, too, are facts that call for, and admit of, empirical verification. Nor is it relevant (see Samuelson, ibid. p. 8411.) to point out that any function may be made homogeneous in a variety or hyperspace of higher dimension: the relevant question is whether it is homogeneous in the n factors (or a subset of these) which it is always possible to enumerate completely. 34 Pareto for instance denied validity of the first-order homogeneity assumptions on both grounds (Cours II, 714). History of economic analysis 1006 practical possibility is more often absent than present. Controversy should therefore be confined to theorems for which the assumption is both necessary and sufficient. Since neither assumption is necessary for the ordinary marginal productivity theorems, it is readily seen that the room for disagreement could have been greatly reduced if this distinction had been kept in mind. It is a striking illustration of the lack of rigor prevailing in economic discussion that this was not done. Third, one obstacle to first-order homogeneity that is universally recognized by its sponsors is indivisibility or ‘lumpiness’ in some factor or factors—such as management, railroad tracks, rolling mills. Such factors cannot be varied by small quantities even in the blueprints of a plant that is still in the planning stage—where size of plant is a variable— and much less so within the framework of a going concern, 35 where it is only or mainly variation of output from 35 To deny the existence or importance of such indivisibilities and their relation to often very large intervals of increasing physical returns would be absurd. The claim that they account satisfactorily for observed deviations from first-order homogeneity can therefore certainly be made good to some extent, and the theorist, especially the teacher of elementary theory, who assumes homogeneity of the production function (with proper qualification as regards a direct relation between output and the quantity of some ‘factor’ or ‘factors’), disturbed by indivisibilities, may feel sure that he is covering perhaps all the ground he cares to cover. Also, indivisibilities may be reduced by taking account of the cases in which ‘lumpy’ factors, such as managers, may be varied by hiring the part- time services of consultants or again the cases in which the ‘lumpy’ units in which a ‘factor’ is available (units of costly machinery for instance) may be explained by the structure of the demand for it and not by technological necessity. I am not denying anything of that. All I wish to show is, on the one hand, how all this explains the duration and inconclusiveness of the debate and, on the other hand, how easy it is to slip, from the tenable assertion of these facts, into a habitual and thoughtless appeal to indivisibility in general. Indivisibility of course also interferes with the assumptions of continuity and differentiability of production functions. On this see P.A.Samuelson, op. cit. especially pp. 80–81. Finally, reference should be made to cases where absence of first-order homogeneity (presence of economies of scale) is made to spell indivisibility (and vice versa) by definition (Stigler, Kaldor). There is no point in quarreling about definitions. In this case Professor Samuelson is right in holding that indivisibility is void of empirical content (and in this sense ‘meaningless’) but this is no reason for refusing to work out theories that rest on the homogeneity hypothesis, which does retain empirical content however we label the cases to which it does not apply. On the other hand the choice of the word indivisibility seems to suggest that Professors Stigler and Kaldor mean more than a definition. They may mean to agree with Professor Knight, who declared absence of economies of scale to be ‘evident’ if all services in a combination and the product are ‘continuously divisible.’ This is an assertion about supposedly unchallengeable facts and not meaningless in Samuelson’s sense: we may challenge either the facts or, even if we do not challenge the facts of any particular case, we may deny that the proposition in question is universally ‘evident.’ If a product requires n kinds of services and if one of them is a lubricant—all of them being substitutional and as divisible as you please—it is not evident to me that the quantity of lubricant applied must be proportionately increased in order to increase the product in the same proportion, even if all the other services must. Equilibrium analysis 1007 a plant of given ‘size’ which is under discussion. We conclude by glancing at a circumstance of a different type. Fourth, then, we note that a given hypothesis may be verified not only by observations that bear upon its validity directly but also by observations that do so indirectly by verifying consequences that follow from it: many physical hypotheses are verified in this way alone. Now, if there were any sense in speaking of a national production function at all, first-order homogeneity of this function would supply a very simple explanation of a remarkable fact, namely, the relative constancy of the main relative shares of ‘factors’ in the national dividend. For two factors, v 1 and v 2 , such a ‘social’ production function of the form, x=v 1 α v 2 1−α , (α<1), was first suggested by Wicksell (Lectures, I, p. 128) and has been extensively used by Douglas and Cobb. 36 So far we have, throughout this section, defined marginal degree of productivity by means of a partial derivative, that is, our marginal product has been the increment of product which we get when adding an infinitesimally small amount to the quantity of a service employed while keeping the quantities of all other services strictly constant. 37 We have indeed seen that the latter is not always technologically possible and that when it is not, marginal productivity breaks down. But now we have to add that even where the addition of an infinitesimal amount to some service employed, all other conditions remaining the same, yields a determined increment of product, this procedure need not be the most economical method for securing this increment: it may be more economical to adjust the quantities of the other services employed as well. It is true that these adjustments may be of the second order of smallness, especially if we are very strict about the smallness of the increment we contemplate adding in the first place. But this need not be so. Furthermore it is true that there are purposes for which it is proper and useful to keep all other services constant in order to isolate the effects upon product of the one singled out for study; 38 but there are other purposes, among them 36 C.W.Cobb and P.H.Douglas, ‘A Theory of Production,’ American Economic Review, Supplement, March 1928. This was the original paper that was to be followed by an impressive series of econometric studies, Professor Douglas’ treatise on The Theory of Wages (1934), and further studies summed up in his Presidential address, ‘Are there Laws of Production?’ American Economic Review, March 1948. Also see V.Edelberg, ‘An Econometric Model of Production and Distribution,’ Econometrica, July 1936. Professors Cobb and Douglas inserted a second constant into the formula above so as to make it read: x=cν 1 α ν 2 1−α , but this does not make much difference. 37 See Marshall’s Principles, p. 465. 38 We then get the marginal productivity curves turned out, e.g., by agricultural experiment stations. Thus, a steer may be kept in strictly invariant conditions except for the number of pounds of hay he is being fed: this will isolate the effects upon his weight of successive increments of hay. Or, the wheat yield of a given plot of land may be studied in this manner as a function of the quantity of nitrogen contained in a fertilizer applied. It will be observed that this method will produce a theoretically infinite number of marginal productivity curves for each ‘factor,’ one for each of the theoretically infinite number of combinations of other circumstances. History of economic analysis 1008 the analysis of business behavior and of the behavior of distributive shares, for which it may be quite misleading to do so. This difficulty worried Marshall greatly and induced him to emphasize the dangerous concept of Net Marginal Product, 39 that is to say of the marginal product that results from an increment in the quantity of a factor, after corresponding rearrangement of the others. Marginal productivity in this sense is no longer properly expressed by a partial differential coefficient. 40 Output being evidently measurable, the production function is not exposed to the criticism that induced economists, 01 most of them, to drop the utility function: you can see and count loaves of bread; you cannot see and measure satisfaction, at least not in the same sense. Technically it is however just as possible to do without the production function as it is to do without the utility function: the fundamental theorem that the marginal productivity (utility) of a dollar’s worth of each ‘factor’ (consumers’ good) must be (at least) equal to the marginal productivity (utility) to the firm (household) of the marginal productivity (utility) of a dollar’s worth of any other ‘factor’ (consumers’ good) follows in both cases, though in a different garb, whether we use production (utility) functions or simply marginal rates of substitution or transformation. This can be visualized, if we agree to admit two factors only, V 1 and V 2 , and mark off their quantities, v 1 and ν 2 , on the two axes of a rectangular system of co-ordinates in space, reserving the third axis for output: the latter then swells up from the factor plane in a loaflike fashion, forming the production surface. 41 Sections parallel to the factor plane will cut out contour 39 See Principles, pp. 585–6. The net marginal product is a value concept and the difficulty in question arises in the precincts of the cost problem rather than in the immediate neighborhood of the production function. We may, however, bring it in here by defining the marginal degree of productivity by means of an ordinary instead of a partial differential coefficient. Suppose again that there are two ‘factors’ only, v 1 and v 2 , so that the production function reads: x=f(v 1 , v 2 ). Write the total differential Then, dividing through, e.g. by dv 1 , we can define marginal degree of productivity as For use to be made presently, note that if dx=0, we have 40 Marshall also observed that, if we take rearrangements into account, marginal productivity will vary according to the time that is allowed for adaptation. See on this E.Schneider (op. cit. p. 28) and his concepts of total and partial adaptation. 41 Readers not familiar with this construction which is by now classic had better look up Allen, op. cit. no. 11.8, pp. 284–9, and, for the derivation of (stable) demand functions for ‘factors,’ pp. 370– 71 and 502–3. Equilibrium analysis 1009 lines that are loci of constant output. Projected on the factor plane they will cover the positive quadrant of the latter with equal-product curves or isoquants, 42 each of which depicts all the combinations of the two factors that result in a given quantity of output, 43 and isolates nicely the relation of substitutability from the other relation that enters when we proceed from any equal-product curve to a higher one, that is, increase output. 44 All this has been worked out and made fruitful—and brought into general use—only in our own time, mainly by the efforts of Professors Allen and Hicks and their followers. I mention it here to emphasize the historically important fact that it stems from Edgeworth and Pareto and that, by 1914, all the elements of the modern theory were present at least embryonically. Similarly, it should be intuitively clear that the theory of production functions and of the families of equal-product curves must have done much to improve the theory of cost. The great contribution of the period to 1914 was indeed the theory of opportunity cost—and its application to the problems of income formation—which has already been dealt with in Chapter 6 and owes little to the rigorous elaborations in the field of cost phenomena with which we are concerned here. 45 But in itself this contribution touched but peripherically upon the problems of what we now understand by the theory of cost. So far as exact aspects are concerned Pareto’s was the chief performance. 46 However, instead 42 The term ‘isoquant’ was introduced by R.Frisch but originally for a different concept, for which it should have been reserved. 43 That is, along each equal product curve, dx=0. The marginal rate of substitution (dv 2 /dv 1 ) is subject to the usual restrictions (to which homogeneity of the production function may or may not be added). The ‘law of decreasing returns’ to any (substitutional) service is expressed by the condition that equal-product curves be convex to the origin in the operative interval. 44 I hesitate to call this other relation complementarity because this term has by now acquired a different meaning (see Allen op. cit. p. 509). But the two-factor diagram (Allen, p. 371) is perhaps the best means of showing, on an elementary level, how services that co-operate in production may within limits compete with one another and vice versa and how the two relations stand to one another in the case of two substitutional factors. 45 It is perhaps not superfluous to mention that a rigorous formulation of the theory of cost from the standpoint of the maximum problem of the individual firm—with the production function introduced as a restriction—is one of the best means of settling the question of the pricing of factors that have no, or no eligible, alternative opportunities of employment. From this standpoint, the opportunity-cost principle reveals itself as a special case of a more comprehensive principle. But this procedure is not the only possible one. The Austrian theory of imputation also took care of this case (the vineyards that, unless used as vineyards, could not be used at all or used only for grazing goats), and Böhm-Bawerk, in particular, said all about this that there is to be said. 46 For a good presentation of Pareto’s theory of cost, see H.Schultz, op. cit. sec. v. Along with Pareto we should again mention W.E.Johnson. For modern presentations see Allen, passim; J.R.Hicks, Value and Capital (1939), Part II; P.A.Samuelson, Foundations, ch. 4. Also see von Stackelberg, Grundlagen einer reinen Kostentheorie (1932) and L.M.Court, ‘Invariable Classical Stability of Entrepreneurial Demand and Supply Functions,’ Quarterly Journal of Economics, November 1941. History of economic analysis 1010 of entering into these developments, I shall conclude by noticing another development that stems directly from Marshall. In doing so we re-enter the field of partial analysis but in a region that borders upon general analysis. (d) Increasing Returns and Equilibrium. Marshall himself undoubtedly did more than any other leader to pack a maximum load of business facts upon his theoretical schema. The width of his grasp shows nowhere more impressively than in his theory of production. But we may duly admire this performance and yet feel that his marvelous comprehension both of purely analytic and of ‘realistic’ aspects resulted in an exposition that seemed to leave many loose ends about and certainly left plenty of problems for his successors. Thus, his emphasis upon the element of time in relation to the phenomena of decreasing marginal and average cost 47 constitutes a major contribution. 48 His familiar concepts of prime and supplementary costs, of quasi-rent, of the representative firm, 49 of normal profit, and, above all, of internal and external economies, together with his attention to particular patterns of the data that individualize almost every firm’s environment, 50 go far toward presenting all the clues that are needed for a satisfactory treatment of decreasing costs in all its various meanings and aspects. Nevertheless we get clues only and Keynes was right in asserting that in this field Marshallian analysis was least complete and left 47 Throughout the discussion that we are about to survey, decreasing cost and increasing returns, increasing cost and decreasing returns, were as a rule treated as synonyms, which of course they are not. As late as 1944, Professor Lerner found it necessary to advert to this (Economics of Control, p. 164). But I am not aware of any error that could be attributed to this bad habit. However, it may have confused many a beginner. 48 Modern factual investigators who keep on discovering the existence and importance of the intervals of falling average and marginal cost in the cost curves of individual firms—intervals, as we have already seen, that may cover the whole of the observable range of these cost curves—and believe that these findings shake the foundations of ‘neo-classic’ cost analysis, are really rediscovering Marshall: a striking illustration of the fact that the majority of economists do not read. 49 The analytic intention that gave birth to the methodological fiction called Representative Firm stands out on p. 514 of the Principles; and so does its relation to decreasing cost. In the subsequent discussion, Professor Pigou introduced the concept of the Equilibrium Firm, which differs from Marshall’s representative firm only in that the latter does, and the former does not, represent the modal conditions of the industry (see Economics of Welfare, 3rd ed. p. 788). This conception of a modal firm is important for more than one possible purpose of realistic theory but has never been exploited fully. (See however the study by S.J.Chapman and T.S.Ashton on ‘The Sizes of Businesses, Mainly in the Textile Industries,’ Journal of the Royal Statistical Society, April 1914.) 50 See, e.g., Principles, p. 506. But chs. 10 and 11 of Book V are full of suggestive remarks—and warnings—of this kind. It should be emphasized again that Marshall made it more difficult for himself to express his meaning, and for his readers to understand him, by the false or at least misleading parallelism that he had before (pp. 397–8) set up between the ‘laws’ of decreasing and increasing returns which he himself disavowed repeatedly, e.g. by the statement that increasing return shows seldom in the short run (pp. 511–13). Equilibrium analysis 1011 . for each of the theoretically infinite number of combinations of other circumstances. History of economic analysis 1008 the analysis of business behavior and of the behavior of distributive. Entrepreneurial Demand and Supply Functions,’ Quarterly Journal of Economics, November 1941. History of economic analysis 1010 of entering into these developments, I shall conclude by noticing. Mathematical Analysis for Economists, passim). A still more telling instance is Professor Hicks’s ‘Distribution and Economic Progress,’ Review of Economic Studies, October 1936. One of the most