Partial Equilibrium Analysis versus General Equilibrium Analysis

The analytical apparatus of book V of the Principles is firmly rooted in Marshall’s math­ematical training, though here, unlike in the early manuscripts, the mathematics occupies a less prominent position, being confined to footnotes and appendices.

Whereas Walras identified economics with mechanics, Marshall pointed out the limits of the mechanical analogy (Marshall 1898: 39), however valuable it is to grasp the instan­taneous action of economic forces. In economics, alterations concern “the character as well as the magnitude of economical and social forces... the catastrophes of mechanics are caused by changes in the quantity and not in the character of the forces at work; whereas in life their character changes also” (Marshall 1898: 42, emphasis added). In the former case, the mechanical law of the composition of forces can work; in the latter, the mechanical analogy proves defective. Nevertheless, the latter must not be abandoned too “hastily”, as it helps cope with situations in which change takes place at different levels, mastering them one by one. By way of example, Marshall selects mechanical systems whose movement can be broken up into separate components, each with its own laws of motion, if any. They go from packing the parcels on the rack of a moving train (Marshall 1898: 38) to studying the movement of a pendulum “standing on an inclined ledge” (ibid.: 42), hanging in the troubled water of a mill-race, or held by a hand whose move­ments are “partly rhythmical and partly arbitrary” (Marshall 1920: 346). Economics has much to learn from such mechanical systems as “the economic pendulum does not swing back along the course by which it came” (Guillebaud 1961, II: 71). Unsurprisingly, to illustrate Marshall’s way of reasoning, Frisch (1950) invites the reader to look at the economy in terms of a succession of equilibria nested into one another, like a system composed of three pendula, one suspended from the other, with the heaviest, which stands for long period equilibrium, on top, and the lightest, representing temporary equilibrium, at the bottom (the middle pendulum stands for short-term equilibrium).

Partial equilibrium is the only way of dealing with economic change. Any disequilib­rium is characterized by the subset of variables it affects. The standard example is the fishing industry (Marshall 1920: 369-71). Day-to-day oscillations of the fish price, owing to the weather, do not call for any change on the supply side, and equilibrium is restored by variations in demand. A cattle plague, which raises the demand for fish for a couple of years, causes variations at a deeper level, inducing fishermen to set afloat boats not especially fit for fishing. If “the disuse of meat causes a permanent distaste for it”, dis­equilibrium will affect the shipbuilding industry. Each case has to be studied on its own, impounding the movements that still take place at the other levels in the ceteris paribus clause. Day-to-day oscillations still happen when we consider the effects of the cattle plague, or the dietary change, but have no influence on the equilibrium we are looking for. Similarly, long period movements happen while we look for the temporary or short period equilibrium price, but their influence is negligible.

The fishing industry shows that complex problems must be broken up to be subjected to scientific machinery: “the human mind has no other method than this; that a complex problem is broken up into its component parts” (Pigou 1925: 164). To treat variables as constants “is the only method by which science has ever made any great progress in dealing with complex and changeful matter, whether in the physical or moral world” (Marshall 1920: 380 n). Marshall’s ceteris paribus clause attempts to do this. It refers to the time period under consideration, without necessarily implying that the rest of the system is in equilibrium as it should (and could not) be if the clause were applied from a general equilibrium perspective.

The clause is rather hazardous in the long period, when slow movements that do not directly affect the market under consideration “may produce great effects... if they happen to act cumulatively”. Therefore “violence is required for keeping broad forces in the pound of Ceteris Paribus during, say, a whole generation, on the ground that they have only an indirect bearing on the question in hand” (Marshall 1920: 379 n). Time period analysis is how partial equilibrium works. The latter is not a sub-system which, if the ceteris paribus clause were removed, would end up in static general equilibrium. The stationary state is a fiction, a device useful “only to illustrate particular steps in the argu­ment, and to be thrown aside when that is done” (ibid.: 366 n).

Marshall’s economic analysis cannot be cut off from this conceptual framework, which makes sense of it. Though expressed in the language of marginal analysis that marked the new paradigm of economic science, his analytical tools perform different functions, as emerges almost at every step. Marshall’s concept of margin itself is instrumental and far from univocal, as it should be if it were taken for the cause of value. The margin “does not govern price, but... focuses the causes which do govern price” (Marshall, 1920: 428; see also ibid.: 411). Like a valve, it is the locus where the opposing forces can be measured, but these forces alone can be said to govern price.

The driving force that guides human action to equalize marginal uses is the “principle of substitution”. This too cannot be identified with the maximizing tool of the marginal- ist school, as it performs a supplementary function, dynamic or rather biological, mixing up “optimization within a given technology with a change of technology” (Loasby 1990: 121-2).

Marshall’s use of the concept of normal provides further proof of the incompatibility between his analysis and general equilibrium theory. Supply and demand curves reflect a “normal” way of working of the economic system: “every use of the term normal implies the predominance of certain tendencies which appear likely to be more or less steadfast and persistent in their action over those which are relatively exceptional and intermit­tent” (Marshall 1920: 34). This sets the reference point which, when brought into dis­equilibrium, will tend to re-establish itself. Perfect competition is ruled out as “the term [normal] has often to be applied to conditions in which perfectly free competition does not exist” (ibid.: 35) and “Normal does not mean Competitive” (ibid.: 347). This relativ­istic attitude is not due to any inconsistency, or unwillingness to follow the requirements of rigorous analysis. It is an ingrained habit, following from Marshall’s evolutionary approach. Any change that takes place is not from scratch. It happens in a given setting and ends up in a slightly different one, according to the principle of continuity - natura non facit saltum - that well describes how evolution was conceived to work, both in the natural and the human world, at least before the theory of punctuated equilibria. Single changes are slight, it is their cumulative effects that revolutionize the system. This is how Marshallian competition works. It does not immediately subvert every behavioural rule, habit, or custom it finds on its way. It does so slowly, until in the end the passive resist­ance of custom is overcome by the active force of competition (Marshall and Marshall 1881: vi-vii; see Schlicht, 2006: 302-3). In the meantime however, other rigidities, due to newly established routines, will have replaced the old ones, and the system is never perfectly competitive. Imperfections are essential to evolution: no imperfection, no evolution could be Marshall’s motto. Once “perfect adaptation” sets in, the system stops evolving and this is undesirable “for perfectly stable businesses would be likely to produce men who were little better than machines” (Marshall 1919: 195).

Marshall was at pains to insist that competitive markets are far from perfect, first because perfect competition “requires a perfect knowledge of the state of the market” and this is “an altogether unreasonable assumption” (Marshall 1920: 540). Marshallian competition is a lively force, based on guesses and expectations, far from its mechanical neighbour of general equilibrium theory. If productive routines make firms different from each other, consumers too have their own idiosyncratic preferences. Therefore, individual firms in a competitive market do not face the perfectly elastic demand curve of perfect competition theory. They compete starting from varying degrees of consum­ers’ fidelity and their market is made up of separate groups of buyers, which Marshall classifies under two headings, the particular and the general market (Marshall 1919: 182; 1920: 458-9). In the 1930s, market imperfections were considered a major innovation only because they had been removed from the standard version of Marshall’s theory.

Another anomaly of Marshall’s analysis is that he drew his diagrams with prices as functions of quantities. These diagrams do not indicate the optimal quantities that are demanded or supplied at a given price, but the maximum or minimum prices at which they can be sold or supplied. The Marshallian cross is drawn from the point of view of the producer, who tries to determine the price at which different quantities can be sup­plied and sold: “the cost of production per unit is deduced from the amount expected to be produced, and not vice versa” (Marshall 1920: 457 n). The same view was already stated in The Economics of Industry: “Every producer of a commodity calculates the price at which he will be able to sell it, and the Expenses of producing it. He thus deter­mines whether to increase or diminish his production” (Marshall and Marshall 1879 [1994]: 76). According to the advocates of the “marginalist revolution”, the classics had failed to see how demand governs value. In appendix I of The Principles Marshall openly criticizes Jevons’s opinion that “value depends on utility”, and sympathizes with the clas­sical doctrine that in the long run cost of production governs value.

To close this section, it may be appropriate to quote Leijonhufvud’s (2006: 226-7) remark that “nothing better illustrates our confusion than the universal habit of drawing Walrasian schedules in Marshallian space”.