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_________________________________________________________________ Contents (A) Scarcity and Utility in the Classical Schema The crux of the Neoclassical theory of value is the notion of subjective scarcity. The Neoclassical answer to the famous "water-diamond" paradox is that diamonds are naturally more valuable than water not because diamonds are costlier to produce (the Classical answer), but rather because diamonds are more scarce than water. Some may object to this distinction: if diamonds are very costly to produce, then one should expect to see somewhat less of them around, thus the cost-of-production and rarity arguments seem to boil down to the same thing. Adam Smith seems to imply this when he writes: "[T]he value of [precious] metals has, in all ages and nations, arisen chiefly from their scarcity, and that their scarcity has arisen from the very small quantities of them which nature has any where deposited in one place, from the hard and intractable substance with which she has almost every where surrounded those small quantities, and consequently from the labour and expence [sic] which are every where necessary in order to penetrate and get at them." (A. Smith, 1776: p.563). But this is not quite true for Neoclassicals. The Neoclassical notion of scarcity is not merely that something is "rare", but rather that it is perceived as rare by consumers. To take Lionel Robbins's (1932: p.46) famous example, bad eggs may be "rare", but if people do not desire bad eggs, then even one bad egg is already "too many" in their eyes and thus will not have much value. In contrast, if people's desire for diamonds is very great indeed, then in their perception, even a large number of diamonds may be "too few" in their eyes, thus they will have a high price. Consequently, the Neoclassical concept of scarcity is quite distinct from the Classical notion: the subjective element of desire is an integral part of the story. There are thus two essential ingredients of Neoclassical value theory: (1) that the relative values of things arise from their relative scarcity and (2) that subjective desires are an integral part in determining the relative scarcity. Both of these notions have an old history predating 1871-4, but they were not always wedded together. Some economists believed that rarity gave rise to value without thinking too hard about whether rarity was a subjective or objective thing; in contrast, others have thought that subjective notions such as utility and demand were important in determining price, but did not really connect it to scarcity. (A) Scarcity and Utility in the Classical Schema The Classicals -- Adam Smith, David Ricardo, John Stuart Mill, Karl Marx, etc. -- believed in neither of these ideas. Following the pattern set by Richard Cantillon (1755), they argued that subjective desires and scarcity may be important factors in determining market (or temporary or short-run) prices, but they insisted that the natural (or equilibrium or long-run) prices were determined solely by relative costs of production (usually, relative labor costs). The Classicals perceived rarity to be an aberration: if goods can be produced -- i.e. created -- then there is no inherent scarcity of them. Consequently, scarcity prices were what Ricardo called "monopoly prices" -- i.e. the prices which arose only "when by no possible device their quantity can be augmented; and where, therefore, the competition is wholly on one side -- amongst the buyers." (Ricardo, 1817: p.165) and thus "their price is limited only by the extent of the power and will of purchasers" (ibid.) But this is not the natural, long-run price. "The exchangeable value...of a commodity which is at a monopoly price is nowhere regulated by the cost of production." (Ricardo, ibid.) Thus, scarcity may play a role in the short-run (when quantities are fixed), but not in the long-run. They had granted that rarity might be a determinant of value in a few cases, "rare statues and pictures, scarce book and coins, wines of a peculiar quality" (Ricardo, 1817: p.6) -- goods which cannot be produced and thus whose value is regulated by "monopoly prices". But these cases were so exceptional that they could be safely ignored. At best, as our earlier quotation from Smith indicates, they were willing to discuss scarcity as a foundation of value only insofar as it arose from high costs of production. Certainly, whatever lip service they paid to scarcity, they did not incorporate it into their central theoretical schema. Utility was a slightly different story. The Classicals confused utility of a good with its usefulness. They agreed that a good must have usefulness if it is to be produced. The mercantilist Nicholas Barbon was perhaps the first to explicitly claim that price was influenced by utility: "the Value of all Wares arise from their Use; Things of no Use, have no Value, as the English phrase is, They are good for nothing." (Barbon, 1690: p.13). In this, he was followed up by John Locke (1692) and John Law (1705). Richard Cantillon (1755) -- like all the Classicals thereafter -- acknowledged that a good must have utility in order to be produced. But utility itself did not determine the relative prices of the goods. It is relative costs of production that will determine the natural prices of goods. Utility merely determines that a good will be produced, period. That's where its role both begins and ends. Utility is of no further use beyond that. Why did the Classicals cut utility's role so short? The reason is that utility seemed to run into trouble when confronted with the old water-diamond paradox set forth by John
Law (1704: p.4) and made famous by Adam Smith
(1776: p.44-5). As Smith noted, water is useful to humans, diamonds are useless to humans, thus water should have a higher "use-value" or "utility" than diamonds. But clearly, water commands a lower "exchange-value" than diamonds. Thus, like
Aristotle before them, the Classicals gave up on the utility-value connection: it seems as if utility simply could not be incorporated successfully into a theory of natural price. At best, utility (like scarcity) will have a prominent role to play in Classical
theory only for the temporary case of short-run market prices. Indeed,
Cantillon (1755) was the first to suggest a clear supply and demand mechanism for the determination of market prices which includes both utility and scarcity (inexplicably, a lot of Anglo-Saxon literature tends to credit Sir James
Steuart (1767) for this). But for long-run natural prices, neither utility nor rarity have a role in the Classical schema. The Classicals were not amused: David Ricardo (1817: Ch. 20) and John Stuart Mill (1845, 1945) took both Say and Lauderdale to task for their heresy. For instance, Ricardo writes:
However, we should note that the resistance of the Classicals was not mere pig-headedness or simply a reiteration of Smith's "use-value" confusion. As particularly expressed by J.S. Mill (1845), if one was to acknowledge the role of both demand and supply in long-run price-determination, one is effectively mixing together mathematically heterogeneous things which cannot be juxtaposed upon each other.
Although insisting on the importance of subjective utility in price determination, Law, Say and Lauderdale were less clear about the role of rarity in all of this. This is understandable given the traditional difficulty of distinguishing a costly item from a rare item. Objectively-determined rarity had been of central importance in the work of Bernardo Davanzati (1588), Juan de Lugo (1642) and Pierre de Boisguilbert (1695), but the connection with utility was not immediately and clearly made. The first explicit recognition of scarcity, i.e. subjectively-determined rarity, as the source of value is contained in the remarkable work of Ferdinando Galiani (1751). Galiani's brilliant performance was followed up by the anti-Physiocrat philosopher, Abbé Condillac (1776). Condillac explicitly employed both utility and rarity in determining scarcity and value and was willing to confront the Classical solution directly. As he wrote, "a thing does not have value because of its cost, as some suppose; but it costs because it has value." Condillac's argument was reiterated in a relatively obscure note by the ambiguous Physiocrat, Jacques Turgot (1769). It is evident, then, that Say's groping for a subjectivist theory of price was not isolated. There was already a somewhat long history in France and Italy. Under Say's own influence, this Franco-Italian tradition sustained itself in these countries throughout the 19th Century. The ground-breaking work of French proto-marginalist economists such as Louis Auguste Say (1822) (J.B. Say's brother), Auguste Walras (1831) (L. Walras's father), Augustin Cournot (1838) and Jules Dupuit (1844) can thus be seen as natural outgrowths of a long tradition and not merely a series of brilliant isolated sparks of insight. It was upon this tradition that Léon Walras was to draw in composing his 1874 masterpiece.. In Germany, another ambivalent follower of Smith and popular textbook writer, Johann Friedrich Rau (1827) did not discard the role of demand entirely -- indeed he showed how demand-and-supply diagrams can be used to determine price explicitly! In addition, the weight of the German Historical School ensured that the Classical Ricardian theory never penetrated very deeply in Germany either. Together, this can perhaps explain the German-language contributions to the utility-cum-scarcity tradition, such as F.B.W. Hermann (1832), Hans von Mangoldt (1863) and, above everything, Hermann Heinrich Gossen (1854). Carl Menger was thoroughly soaked in Rau and Hermann before trying his hand in 1871. In Great Britain, where the Ricardians reigned supreme, the subjective scarcity notion had more trouble catching on. Nonetheless, the idea had been hatched by Nassau Senior (1836) and his associates at Oxford and Dublin -- Richard Whately (1832), William F. Lloyd (1837) and Mountiford Longfield (1834). These fledgling Neoclassicals did not mince their words when confronting the Classicals. As Whately asserts heretically, "It is not that pearls fetch a high price because men have dived for them; but on the contrary, men dive for them because they fetch a high price." (Whately, 1832: p.253). These tentative efforts in Britain, however, were smashed by John Stuart Mill's Principles of Political Economy (1848), a weighty restatement of the Classical Ricardian doctrine. It was with Lloyd, Whately and company in mind that Mill went on to assert that "Happily, there is nothing in the laws of Value which remains for the present or any future writer to clear up; the theory of the subject is complete" (Mill, 1848: Ch. III.1). Despite Mill's abrupt interception, the grumbling continued. By the 1860s, the Classical Ricardian doctrine had came under siege, not only from the usual suspects (e.g. Carlyle, Ruskin, Cliffe Leslie) but, more importantly, from their own. The gutting of the wages fund doctrine by Thornton, Sidgwick and Walker, and the wide-ranging assault on the "vulgar economists" by Karl Marx, had dented the confidence of Classical theory. As a consequence, a window of opportunity opened in Britain during this time for outcasts such as Richard Jennings (1855), William E. Hearn (1864), Fleeming Jenkin (1870) and Henry Dunning Macleod (1857, 1881), to pursue subjective scarcity and/or supply-and-demand mechanisms in their work. Thus the claim that William Stanley Jevons was working in a vaccum in 1871 with little more than Bentham to draw upon, is not strictly correct. [Note: Emil Kauder (1957) has argued that the reason for the retarded acceptance of subjective scarcity theory in English economics and the predominance of labor-cost theories was due to differing philosophical and religious traditions. Protestant Britain was wary of the hedonistic conception of utility, and the labor-cost theories seemed quite more compatible with its work-oriented Puritanical traditions. Thus it is in Catholic countries, like France and Italy, where sensualism is not altogether dead, that we find the great expounders of subjective scarcity theory. This is an interesting hypothesis, but it does not perfectly fit with the facts and certainly overlooks more straightforward explanations.] (C) The Holy Grail: Marginal Utility Discussions of utility, scarcity and the mechanism of demand and supply, however suggestive, were not well-integrated in the efforts of the early proto-Neoclassical economists. The great missing ingredient was the connection between utility and demand. Auguste Walras (1831) and Mountiford Longfield (1834) attempted an explicit connection, but their theories ended tied up in knots. As was to be discerned later, the key to successful integration was marginal utility -- specifically, diminishing marginal utility. The concept of diminishing marginal utility -- i.e. that equal increments of a good yield diminishing increments of utility -- was already widely known. Daniel Bernoulli (1738) had employed this concept to solve the St. Petersburg Paradox. The utilitarian Jeremy Bentham (1789, 1802) had certainly stated the idea. Lloyd (1833), Senior (1836), Jennings (1855) and Hearn (1864) were well aware of diminishing marginal utility as well. The question was one of connecting it to demand, which these writers failed to do clearly. (i) Auguste Cournot The idea of a demand function itself was proposed by Charles D'Avenant (1699), who even attempted to estimate one for wheat (on the basis of data allegedly provided by Gregory King (1696)). The first concrete expression of a demand function was accomplished by Pietro Verri (1760). Thereafter silence reigned until the enormous leap of Augustin Cournot (1838). Cournot did not bother with the niceties of utility; his concern was focused on demand functions directly which he considered to be deducible from empirical fact. He was the first to express the demand function in algebraic form as D = F(p) and the first to draw demand-and-supply functions in price-quantity space (Cournot, 1838: p.92, Fig. 6). This, of course, was not all: in addition to demand functions, Cournot introduced the concepts of marginal revenue, marginal cost, the concept of the profit-maximizing firm, monopoly, duopoly, perfect competition and, of course, his famous "reaction functions". But marginal utility was nowhere in sight. As he argued, the "accessory ideas of utility, scarcity, and suitability to the needs and enjoyments of mankind...are variable and by nature indeterminate, and consequently ill suited for the foundation of a scientific theory" (Cournot, 1838: p.10). (ii) Jules Dupuit The first successful connection between marginal utility and demand was accomplished by the French engineer Jules Dupuit (1844). His remarkable effort at developing a cost-benefit analysis of public works led him to draw the demand curve in price-quantity space. Unlike Cournot, Dupuit did not rest his demand curve on empirical intuition but rather identified the demand curve as the marginal utility curve itself. Dupuit's basic idea was this: as quantity rises, the marginal utility of the good declines. Consequently, one should also say that as the quantity rises, the willingness of a person to pay for that good declines. Thus, the concept of diminishing marginal utility should translate itself into a downward-sloping demand function. Of course, Dupuit's logic was suspect in at least one place: marginal utility is particular to an individual, while market demand is an aggregate, so something must be said about the interpersonal comparability of utility in order to proceed with the connection. Dupuit skimped on this. Nonetheless, the important point was that the connection was made between demand and utility. Dupuit, however, did not draw a supply curve and thus did not get price-determination into his story. [Dupuit went on to define "relative utility" (what later became known as Marshall's "consumer surplus") as the area under the demand/marginal utility curve above the price and used it as a measure of the welfare effects of different prices -- yielding his famous conclusion that public welfare is maximized when the price (in his case, the toll rate on a bridge) is zero.] (iii) H.H. Gossen The final step came from Hermann Heinrich Gossen (1854). Unlike Dupuit, Gossen clearly distinguished the marginal utility curve from the demand curve. Gossen posited that demand is derived from the utility-maximizing choices of the consumer. Gossen's "Three Laws" can be stated as follows:
Of Gossen's three laws, the second is perhaps the most remarkable. The idea that, at the margin, the consumer substitutes between goods so that he obtains the same marginal utility (in terms of money) across goods yields the downward-sloping demand curve for each of the goods. To see this, merely note that when the price of a good rises, the marginal utility in terms of money (MUi/pi) declines and thus, by Gossen's first law (diminshing marginal utility), less of that good will be bought. The foundations of the Marginalist Revolution were thus in place. H.H. Gossen's (1854) work had already anticipated much of the Marginalist Revolution. However, this "ingenius idiot", as Schmoller called him, was an unknown man -- a retired Prussian civil servant -- whose work was entirely neglected. His work was only accidentally discovered in 1878 during a search by Jevons for fellow travellers. As such, the works of Jevons, Menger and Walras came forth without the benefit of Gossen's insights. (i) William Stanley Jevons William Stanley Jevons developed his results on marginal utility (which Jevons called "final degree of utility") independently and first announced them in an abstract of a 1862 lecture (published in 1866). The publication of Fleeming Jenkin's (1870) diagrammatic representation of the demand-and-supply mechanism led Jevons to quickly write and publish his own 1871 treatise, Theory of Political Economy in order to establish priority. Jevons couched his construction in the context of pure exchange. Specifically, assuming two goods (call them x1 and x2) and two agents (call them A and B), then in equilibrium, Jevons proposed that:
where MUih is the marginal utility of good xi to household h. The term dx1 is the amount of good x1 given by agent A to agent B and dx2 is the amount of good x2 given by agent B to agent A. Thus, for agent A, the marginal utility of good x1 after amount dx1 has been surrendered divided by the marginal utility of good x2 after amount dx2 has been gained, is inversely related to the exchange ratio dx2/dx1. The analogous reasoning applies for agent B. Thus: "The ratio of exchange of any two commodities will be the reciprocal of the ratio of the final degrees of utility of the quantities of commodity available for consumption after the exchange is completed." (Jevons, 1871: p.95). Through the medium of a market, the exchange ratio can be expressed as prices, i.e. -dx2/dx1 = p1/p2, so that this can be rewritten as:
so not only does Gossen's Second Law hold for every single consumer, but it also holds across consumers. However, Jevons got somewhat tangled up in this derivation. In particular, he was not quite sure how to get from dx1/dx2 to p1/p2 or back again. It is important to note that Jevons did not assume price-taking behavior nor any kind of auctioneer, and thus did not construct a "supply-and-demand" model.. He wanted the exchange ratios to emerge from a process of exchange, and this landed him into some difficulties. Jevons believed it was easier to determine exchange ratios in bilateral exchange than in competitive situations - thus he tried to reduce his "market" situation into one of simple bilateral exchange. He did so with the help of two pieces of scaffolding: (1) by constructing "trading bodies" ( Jevons, 1871: p.88-90), so that the enormous mass of heterogeneous traders in markets could be reduced to a pair of what would today be called "representative agents" that would exchange with each other; (2) then via arbitrage-theoretic reasoning -- in his famous "Law of Indifference" (Jevons, 1871: p.90-5) -- he goes on to argue that, by definition, dx1/dx2 = p1/p2. Ten years later, Francis Ysidro Edgeworth (1881) was to show that Jevons's instincts should be reversed: determining the exchange ratio between two bilateral trading bodies, Edgeworth argued, is in fact more difficult than determining the exchange ratio when there are numerous, heterogeneous agents in a competitive market situation. Edgeworth's demonstration of the indeterminacy of exchange ratios in bilateral exchange was captured in his famous notion of the "contract curve" and the "core". His famous conjecture, that indeterminacy is eliminated when the number of traders increases ("perfect competition"), however, was not picked up immediately. Jevons established equilibrium in pure exchange, but, not having a good theory of production, was unable to construct the familiar "supply-and-demand" theory with variable output levels. His resolution was considerably unsatisfying. Jevons argued, as Gossen had before him, that labor supply was governed by disutility of labor: the greater the amount of work, the greater the marginal disutility of labor. Consequently, he went on to argue, by Gossen's Second Law, that the marginal utility of consuming a good must be equal to the marginal disutility of producing it. In other words, the quantity of a good produced is determined by the intersection of a downward-sloping marginal utility of consumption curve and an upward sloping marginal disutility of labor curve. With the quantity of the good thus determinate, Jevons's next step was quickly and sloppily reasoned: once the supply of the good is given, then we can apply the pure exchange scenario we had before to determine the price of the good. This entire story is summarized by Jevons in a famous "catena":
The first line seeks to explain the output-determination process we have just summarized: namely, how higher or lower wages shift around the the marginal utility of income/disutility of labor curves so that output level, i.e. supply, changes. The second line merely states that once we have supplies of goods determined, we know what marginal utility of those goods will be; finally, the third line summarizes the pure exchange process. This is confusing. The immediate temptation is to remove all the intermediate steps and reduce the catena to the simple claim that "cost of production determines value", a complete restatement of the Classical theory of Ricardo and Mill! Obviously, Jevons did not quite want to put it this way. Wages ought not to be hanging in the air by themselves. Unlike Classical theory, Jevons argued, the value of labour "is determined by the value of the produce, not the value of the produce by that of the labour." (Jevons, 1871: p.166). Thus, years later, Alfred Marshall would invert Jevons's catena into its proper order:
Without deriving demand and supply functions from his marginal utility/disutility schedules, Jevons discussion is quite confusing. It was Alfred Marshall (1890: Ch. 3; Math. App.), that got Jevons' out of this knot by deriving it formally. Now, as stated, MUi/pi is the marginal utility of dollar spend on good xi. By Gossen's Second Law, MUi/pi = MUj/pj for all goods i, j. Consequently, we can define the marginal utility of income (what Marshall called the marginal utility of money) as:
Jevons, as we know, was clearly aware of this and even offered the identity MUi = piMUY in his work (Jevons, 1871: p.146). But how is one to construct a demand function? Marshall's process is to follow Jevons in assuming that the marginal utility of income MUY is a constant. Doing so, we immediately recognize that differentiating with respect to quantity demanded xi:
so that:
as, by the rule of diminishing marginal utility, dMUi/dxi < 0, then dxi/dpi < 0, so a rise in the price of good xi leads to a decrease in demand for it. Thus, the demand curve is downward-sloping. [Note: the constancy of the marginal utility of income is a dubious assumption, discussed more fully elsewhere. Effectively, what it does to eliminate the famous "income effect" of a change in price (note that this is not the same as saying that all other prices are held constant! rather, intercommodity effects are neutralized). However, this also implies that as pi rises and xi falls, total expenditure on this good, pixi, is unchanged, i.e. the demand function is unit elastic. Marshall was uncomfortable with this assumption, thus he cautioned that this was only approximately true, provided that the expenditure by a consumer on any particular good is only "a small part of his total resources" (Marshall, 1890: p.279). The derivation of demand from utility without the constant marginal utlity of income assumption had to wait until Vilfredo Pareto (1892)] (ii) Carl Menger Carl Menger's (1871) contribution was more clear, but less formal. Although he did not name it explicitly, he introduced the concept of diminishing marginal utility in general discussion. He just referred to the decreasing "importance of the satisfaction of needs" and used numerical examples (Menger, 1871: p.127) to illustrate the idea. [Note: the term "marginal utility", Grenznutzen, was only introduced by Friedrich von Wieser (1889); in his work, Menger uses the term "utility" in the same misleading sense Adam Smith did, i.e. in terms of objective "use-value"]. As a result, Menger comes to the Marginalist conclusion:
Menger did not bother to derive a demand function, but his discussion of exchange, in many ways, supersedes that of Jevons. In particular, he defined prices as "only incidental manifestations of [exchange], symptoms of an economic equilibrium between the economies of individuals." (Menger, 1871: p.191). Prices, then, are formed by market processes of exchange and the nature of the process can vary depending on a variety of factors, notably in the degree of competitiveness. In his famous Chapter 5, Menger outlines the process of price-formation from a bargaining process between two individuals, under monopoly, duopoly and, finally, competition. Although he was not consistent (e.g. at one time recognizing the indeterminacy of prices in bilateral exchange, and then retreating from this elsewhere), Menger's analysis of the market process was highly suggestive and marked the approach of the Austrian School in years to come. Two other points insisted upon by Menger are worth mentioning. Firstly, his distinction between economic goods and non-economic (i.e. free) goods was given central importance (Menger, 1871: p.94-109). He underlined the fact that one cannot assume that goods have prices; whether a good is free or not is a result of the final equilibrium configuration and thus is endogenous to the problem. Secondly, Menger (1871: p.149-74) outlined the important theory of imputation. As only utility can confer value, then the value of factors of production ("goods of higher order") which have no utility in and of themselves must be determined by the prices of outputs ("goods of lower order"). This is the heart of the Neoclassical treatment of production as "indirect exchange". (iii) Léon Walras The contribution of Léon Walras (1874) outshines both Jevons, Menger and all other predecessors in clarity, rigor and insight. It is in Walras where we find the most careful, complete and visionary statements of the Marginalist Revolution. As Schumpeter expressed it, with characteristic lack of restraint:
The details of Walras's general equilibrium system are given elsewhere,, so we shall note only a few of his contributions here. Walras adopted the notion of marginal utility and the scarcity theory of value from his father, Auguste Walras (1831). However, Auguste Walras did not manage to connect the two concepts. Already in his early work, we find the young Léon Walras following his father in claiming that the value of goods depends on both utility and rarity ("rareté"). Walras then was holding on to an objective definition of rarity, defining a good as rare if "it is offered to general demand in a limited quantity" (Walras, 1860: p.8). It was only in an 1873 article preceeding his Elements (1874) that Léon Walras took the leap and made the connection by noting that "rareté is personal or subjective" (Walras, 1874: p.146). Walras used the term rareté for "marginal utility". At least for the case of bilateral trade, this is an extremely fortuituous use of language -- for what does marginal utility of a particular good represent other the intensity with which that good is needed and thus the degree to which its absence is felt? If my marginal utility for eggs is greater than yours, then eggs are perceived by me as being more scarce than they are perceived by you. Walras's use of the term rareté keeps the fundamental Neoclassical idea of subjective scarcity at all times in the forefront of our minds and does not let it slip out of sight. However, moving beyond exchange between two parties, the connection becomes more tenuous: scarcity is a market-wide phenomenon; marginal utility is an individual phenomenon, and thus his use of the term rareté for marginal utility may be confusing in the case of economy-wide exchange. The rest of Walras's work is sheer brilliance. Recognizing the multi-good nature of exchange, all of Walras's analysis proceeds with multiple markets. No oversimplifying ceteris paribus assumptions are made. Alone among the early Marginalists, Walras provided a proper derivation of the demand curve from utility functions via the use of household budgets (Walras, 1874: Ch. 8, 11.). If anything is demanded, something else must be offered in exchange; consequently the aggregate value of what is offered must equal the aggregate value of what is demanded. As a result, for any bundle of goods demanded x = [x1, x2, .., xn] and for a given set of endowments e = [e1, e2, .., en], it must be that:
Walras's recognized that the need for a numeraire good enabled him to fix one price, e.g. p1 = 1. In this case:
where p2, p3, etc. are the prices of goods x2, x3, etc. in terms of the price of good x1. Now, Walras used an additively separable utility function so that the utility of a bundle x can be written as:
where ui(xi) is the utility from good xi. Substituting the budget constraint into the first of these separate utilities:
which, upon maximization, yields for any good xi the following first order condition:
or letting MUi = ¶ ui/¶ xi, then we obtain the result:
for every i = 1, .., n. This is Gossen's Second Law once again. As we have n goods, we have n-1 such equations. The addition of the aggregate budget constraint equation implies we have a total of n equations. What about unknowns? As prices are given, then all we have to do is determine the amounts demanded/supplied by agents, x1, .., xn. With an equal number of equations and unknowns, we are there and can express our resulting individual demand functions as:
for i = 1, .., n. He aggregates these into market demand/supply functions by horizontal summation over households. Equilibrium is achieved when market demand is equal to market supply in each market. Walras goes on to his unique discussion of the stability of equilibrium via his tatonnement price adjustment process, to which we refer elsewhere. Finally, Walras goes beyond the other pioneering Marginalists in proceeding, in later chapters, to incorporate production, capital and money into his general equilibrium model in a complete and consistent manner. [Note: William Jaffé (1976) has noted that "instead of climbing up from marginal utility to the level of his general equilibrium system, Walras actually climbed down from that level to marginal utility". This seems evident from reading Walras. As such, at least in Walras's case, one might be tempted to play down the influence of the French utility-cum-scarcity tradition in favor of the other French tradition of "grand systems" of general equilibrium (cf. Cantillon, 1755; Quesnay, 1759, Turgot, 1766; Isnard, 1781).] (E) Consolidation: the Great Flood The works of Jevons, Menger and Walras were met with different reactions. Jevons's Theory received various notices and reviews, some of them sympathetic, many of them hostile (Alfred Marshall's (1872) review was noticeably lukewarm). At any rate, one could not fail to notice it. Even textbooks written in the Classical tradition, such as John E. Cairnes (1874) and Henry Sidgwick (1883), were forced to make some note or other about Jevons's new theory. In contrast, a complete silence surrounded Léon Walras's Elements -- the only notice of the existence of this book were Walras's own follow-up publications, most of them also duly ignored. Walras became aware of Jevons's existence in 1874 and gracefully acknowledged his priority. They took to each other immediately and made a joint effort to spread the word. Something akin to a division of labor ensued: Jevons went off digging up illustrious predecessors in order to enhance the pedigree of the new doctrine while Walras endeavored to establish communication with virtually every important economist of the day. Jevons's task proved to be more rewarding: in his efforts, he helped unearth Cantillon, Cournot and Gossen out of their obscurity. In contrast, Walras just found shut doors and impatient listeners. Only a handful of the economists he contacted responded positively to the new ideas. In frustration, he turned to contemporary mathematicians, only to be dismissed once again. Menger, who did not exactly cooperate with the Jevons-Walras efforts, went on his own crusade. His 1883 Investigations provoked prominent German-speaking economists such as Gustav Schmoller into a bruising debate on methodology. This Methodenstreit enhanced general awareness of Menger's new theory, but it also bogged him down. In the end, it was somewhat self-defeating: although his fame and reputation were greatly increased in Austria, the entire university system in Germany itself was closed to him and his followers. The Marginalist Revolution really began only to take off in the 1880s with the publication of the works of a younger generation which had begun to read up on their works. The wide dissemination of the work of two close disciples of Menger, Friedrich von Wieser (1884, 1889) and Eugen von Böhm-Bawerk (1886, 1889), gave the theories of the Austrian School wider attention. The mathematical tone of Jevons's and Walras's own works attracted a slew of technically-gifted young economists throughout the world. Among these we can count the Englishmen Francis Ysidro Edgeworth (1881) and Philip H. Wicksteed (1888), the Austrians Rudolf Auspitz and Richard Lieben (1889), and, a little later, the American Irving Fisher (1892) and the Swede Knut Wicksell (1893). The trickle of the 1880s turned into the flood of the 1890s, particularly after the joint discovery of the marginal productivity theory of distribution by the American economist John Bates Clark (1890, 1899), Knut Wicksell (1893), Philip H.Wicksteed (1894) and Enrico Barone (1895). The Marginalist Revolution then went into high gear with the publications of Maffeo Pantaleoni (1889), Vilfredo Pareto (1892, 1896-7, 1906), Knut Wicksell (1898, 1901, 1906) and Giovanni B. Antonelli (1886). Details on the consolidation of the Neoclassical theory of value by these economists are found elsewhere. Nonetheless, the most significant event of the 1890s was the publication of Alfred Marshall's Principles of Economics (1890). This is notable not so much for the research or insights which it generated, but rather because it was the first really successful Neoclassical textbook. It was through Marshall that the Marginalist Revolution became palatable to contemporary economists -- Marshall's extremely conciliatory attitude towards the displaced Classical School was the sugar that permitted it be swallowed by fellow academics. Through its wide adoption as a university textbook, Neoclassical theory was delivered to a wider public. The infamous "demand-and-supply" diagram with the reversed axes that has since become the standard staple of economics textbooks was a centrepiece of Marshall's book. In other countries, the works of Knut Wicksell, Maffeo Pantaleoni, Etienne Antonelli and others gained wide textbook usage, but in English-speaking countries, despite several efforts at displacement (e.g. by Wicksteed (1910)), the successive editions of Alfred Marshall's Principles remained the dominant text at least until the 1930s. [Note: Alfred Marshall irritatingly continued to insist time and time again that he had basically formed most of his ideas before he had read Jevons's 1871 volume (cf. Marshall notes and letters in Pigou, 1925), and thus that he should be counted as one of the original "revolutionaries". He pointed to two 1879 articles printed for "private circulation" as evidence of his habit of coming up with new ideas, but not rushing them to publication. However, most historians of economics have concluded that Marshall claims to originality have no basis. It is quite apparent that Marshall did derive most of his own theory after reading Jevons. For further notes on Marshall and his role in the Marginalist Revolution, see Whitaker (1975), Maloney (1985) and Mirowski (1990). In contrast, we should note that John Bates Clark (1885) did arrive at his utility-based theory of price while quite ignorant of the work of Jevons, Menger and Walras -- and thus Clark, but not Marshall, should be given high marks for originality.] (F) Aftermath: the Great Drought Although sharing the same underlying Neoclassical theory of value, the different emphasis, approaches and methods of the various pioneering Marginalists on details such as production, money, capital, dynamics, etc. led to the segmentation of the Neoclassical school into various largely independent "schools of thought", rather than consolidation into a "monolothic" Neoclassical edifice. The Cambridge Neoclassicals followed Marshall's approach, the Austrian School followed Menger Böhm-Bawerk and Wieser, while the Chicago School followed a combination of both Marshall and the Austrians. Naturally, the Stockholm School followed Wicksell, and and one can even divide the Lausanne School further intosubsequently distinct Walrasian and Paretian traditions. However, this segmentation should be treated with caution. Some Neoclassical economists, such as Jevons, Wicksteed and Fisher failed to belong to or develop behind them any clear "school of thought". Furthermore, there was a good degree of cross-pollination among schools -- for instance, the influence of the Austrians on the Swedes (and vice-versa) is well-documented. Finally, there were occasions when several economists attempted to hammer the disparate contributions of the different schools of thought together into a single, all-encompassing "Neoclassical" theory. Such efforts are discernable, for instance, in the 1930s, 1960s and the 1980s, although not always successful. Finally, we should note that the "Marginalist Revolution" had severer growing pains than this brief account indicates. Initiated in 1871-4, it only began to be noticed in the 1880s and by the late 1890s it was already running out of steam. In the early part of the twentieth century, the Marginalist Revolution was, in fact, retreating on many fronts. The great splash in the 1880s excited both support and opposition and, as a result, it advanced quickly and generated great professional debates that helped it become better known. However, a mere two decades later, we begin to notice that Neoclassicism seemed more and more to have become a peripheral "fringe" movement in the economics profession as a whole. The reasoning for the Neoclassical retreat in the 1900s is largely because, to many contemporaries, it seemed to be descending into "quackery". Originally, the Neoclassicals had promised that their approach would provide a more sound, "scientific" explanation of economic phenomona than the alternative Classical, Institutional or Historical approaches. However, its Achilles' heel was the very notion of "marginal utility". Marginal utility, let us be frank, is hardly a scientific concept: unobservable, unmeasurable and untestable, marginal utility is a notion with very dubious scientific standing. As Stigler notes, "Had specific tests been made of the implications of theories, the unfruitfulness of the ruling utility theory as a source of hypotheses in demand would soon have become apparent" (G.J. Stigler, 1950). However, it was given the benefit of the doubt in the 1880s by contemporary economists as a tentative hypothesis that was helpful to economic analysis, but which, hopefully, could be dispensed with later. But it quickly became apparent that rather than being a small part of the Neoclassical paradigm, it was increasingly becoming the "all" of Neoclassicism. Everything was beginning to be reduced with almost religious devotion into this nebulous hedonistic concept and thus seemed less and less "scientific". As Henry L. Moore, an early disciple of Walras, wrote:
The indulgence contemporary economists had granted to the Neoclassical marginal utility hypothesis in the 1880s was largely withdrawn by the 1900s. In contemporary eyes, Neoclassicals were "quacks": they had promised a "scientific" approach and instead yielded up a "religious" approach to economics. Contemporary economists echoed with approval the merciless ridicule that Thorstein Veblen heaped upon Neoclassical quackery. As Jacob Viner was to lament in 1925:
By and large, economists throughout the world withdrew from Neoclassicism and moved back into what seemed like "more serious science": i.e. the empirical approach of the Institutional and Historical schools. There were a few isolated exceptions: at Cambridge, Chicago and Vienna, Neoclassical dominance was maintained through the early part of the 20th Century. At the University of Cambridge (UK), Neoclassicism survived because it was a pretty self-contained place anyway -- "everything is in Marshall", they believed (although things changed considerably after Sraffa's 1926 attack, and particularly, after Keynes's 1936 General Theory). The University of Chicago survived as a Neoclassical bastion in good part because of it was composed of a few strong personalities -- esp. Frank Knight, Jacob Viner, Henry Schultz -- who were gripped by siege mentality (witness their extensive journal forays in defense of Neoclassical methodology). The third exception was the University of Vienna -- which was also energized by a siege mentality and wilful personalities. However, the Austrian Neoclassicals held on there only until the end of the First World War, when they were finally dispersed. Consequently, for nearly thirty years, Neoclassical economics was effectively moribund, being slowly pushed forward by a handful of economists hidden away at Cambridge, Chicago and a few other scattered places . This state of affairs changed drastically during the 1930s, when the Neoclassicals began rolling back in. The most significant institutional event was the "reconquest" of the London School of Economics by Lionel Robbins in the early 1930s -- and a parallel "half-conquest" of Harvard by Joseph Schumpeter and Wassily Leontief. The formation of the Cowles Commission and the Econometric Society put the Neoclassicals back in touch with each other and the research energy that emerged was remarkable. Paradoxically, Hitler's armies contributed to this process: by expelling many economists from Central Europe, they effectively forced them to reassemble together at places like the LSE, Cowles and other institutions. But it was the theoretical achievements of the 1930s on the part of a handful of a few young technically-minded economists that saved Neoclassical economics. The Hicks-Allen "ordinalist" revolution and Paul Samuelson's "revealed preference" approach helped remove much of the quackery that stained utility theory. It gained an empirical plausibility which had been missing before -- or at least, in the words of one contemporary economist, it was no longer "repugnant to our logic to suppose that [experiments] can be made" (Ricci, 1933: p.15). Welfare economics, firstly via A.C. Pigou and then through the hands of Harold Hotelling, Oskar Lange, Maurice Allais and the L.S.E. economists (John Hicks, Abba Lerner, etc.), demonstrated that there was still something quite useful in the hypothesis. At any rate, Cassel's resurrection of the Walrasian general equilibrium system, the consolidation of the Neoclassical theory of production, the empirical efforts of Shultz and Douglas, and even Hayek's foray into macroeconomics were all done on the basis of demand functions -- without utility -- thereby demonstrating that there remained huge swathes of Neoclassical theory were not too reliant on that dubious hedonistic concept. All these theoretical developments helped lend "scientific" teeth to Neoclassicism that were previously missing. The rest of the story is too well-known. After the fervor of the 1930s -- the "Paretian revival" as we have chosen to call it -- Neoclassical theory managed to displace virtually all other theories and approaches from economics. Thus, the "Marginalist Revolution" was not something that just happened in the 1870s, but, in fact, it took at least six decades to entrench itself. Cheekily, some historians have preferred to call the early period merely the "Marginalist Insurrection". Some would argue it took even longer to attain its monopoly over the economics profession. At least four other important paradigmatic challenges were hatched during the 20th Century which slowed down the Neoclassical ascendancy or at least prevented its complete dominance: Monopolistic Competition, the Keynesian Revolution, Classical-Sraffian counter-revolution and the rise of Game Theory. By the 1980s, the first three had been "beaten back" by the Neoclassicals with different degrees of success; Game Theory, however, has proven to be a far more resilient beast and might conceivably yet undo considerable parts of Neoclassical theory, and perhaps the Marginalist Revolution as a whole, in the future.
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