A convenient way to define ‘disequilibrium’ is of course as the contrary of ‘equilibrium’. Unfortunately this leaves us with no unique definition as the word equilibrium itself has been used in the economic literature with at least two principal meanings. The first one refers to market equilibrium, i.e. the equality of supply and demand on markets. This is the meaning we shall retain in this entry, and therefore the disequilibrium analysis we shall be concerned with here is the study of nonclearing markets, also called non-Walrasian analysis by reference to the most elaborate model of market clearing, the Walrasian model.

The second meaning of equilibrium is somewhat more general. A typical definition is given by Machlup (1958) as ‘… a constellation of selected interrelated variables, so adjusted to one another that no inherent tendency to change prevails in the model which they constitute’. Dealing with disequilibrium in this second meaning would be a quite formidable (and actually extremely imprecise) task, which is why we want to limit ourselves in this entry to disequilibrium analysis in the first sense.

We should note that the entry RATIONED EQUILIBRIA presents concepts of equilibria in the second, but not in the first sense of the word, i.e. more specifically equilibria without market clearing or non-Walrasian equilibria.

The Essence of the Theory

Disequilibrium analysis is best appraised by reference to the standard equilibrium market clearing paradigm, corresponding to the notions of Marshallian or Walrasian equilibrium. There all private agents receive a price signal and assume that they will be able to exchange whatever they want at that price. They express demands and supplies, sometimes called ‘notional’, which are functions of this price signal. An equilibrium price system is a set of prices for which demand and supply match on all markets. Transactions are equal to the demands and supplies at the equilibrium price system.

Two characteristics deserve to be stressed: all private agents receive price signals and make rational quantity decisions with respect to them. But no agent makes any use of the quantity signals sent to the market. Also no agent actually sets prices, the determination of which is left to the ‘invisible hand’ or to the implicit Walrasian auctioneer. This logical hole of the theory was pointed out by Arrow (1959) when he noted there was ‘… a logical gap in the usual formulations of the theory of the perfectly competitive economy, namely, that there is no place for a rational decision with respect to prices as there is with respect to quantities’, and more specifically ‘each individual participant in the economy is supposed to take prices as given and determine his choices as to purchases and sales accordingly; there is no one left over whose job is to make a decision on price’.

Disequilibrium analysis takes this strong logical objection quite seriously, and its purpose is to build a consistent theory of the functioning of decentralized economies when market clearing is not axiomatically assumed. The consequences of abandoning the market clearing assumption are actually quite far-reaching: (i) The transactions cannot be all equal to demands and supplies expressed on markets. Rationing will be experienced and quantity signals will be formed in addition to price signals (ii) Demand and supply theory must be substantially modified to take into account these quantity signals. One thus obtains a theory of effective demand, as opposed to notional demand which only takes price signals into account (iii) Price theory must also be amended in a way that integrates the possibility of non-clearing markets, the presence of quantity signals, and makes agents themselves responsible for price making, (iv) Finally expectations, which in market clearing models are concerned with price signals only, must now include quantity signals expectations as well.

History

Though roots may be found earlier, an uncontestable grandfather of disequilbrium analysis in the sense we use here is of course Keynes (1936). He rightfully perceived that one of his main contributions in the General Theory was the introduction of quantity adjustments, and more specifically income adjustments, in the economic process, whereas the then dominant ‘classical’ economists focused on price adjustments only. As Keynes (1937) wrote ‘As I have said above, the initial novelty lies in my maintaining that it is not the rate of interest, but the level of incomes which ensures equality between savings and investment’.

Unfortunately for many decades things did not go much further: macroeconomists added the level of income in their equations, thereby allowing for unemployment. But concentration on the ‘equilibrium’ of the goods and money markets, exemplified by the dominant IS–LM model, obscured the ‘disequilibrium’ nature of the model. As for microeconomics, it was basically unaffected by the Keynesian revolution, and correlatively a growing gap developed between microeconomics and macroeconomics.

A few isolated contributions in the post-war period made some steps toward modern disequilibrium theories. Samuelson (1947), Tobin and Houthakker (1950) studied the theory of demand under conditions of rationing. Bent Hansen (1951) introduced the ideas of active demand, close in spirit to that of effective demand, and of quasi-equilibrium where persistent disequilibrium created steady inflation. Patinkin (1956, ch. 13) considered the situation where the firms might not be able to sell all their ‘notional’ output. Hahn and Negishi (1962) studied non-tâtonnement processes where trade could take place before a general equilibrium price system was reached. Hicks (1965) discussed the ‘fixprice’ method as opposed to the flexprice method.

A main impetus came from the stimulating works of Clower (1965) and Leijonhufvud (1968). Both were concerned with the microeconomic foundations of Keynesian theory. Clower showed that the Keynesian consumption function made no sense unless reinterpreted as the response of a rational consumer to a disequilibrium on the labour markets. He introduced the ‘dual-decision’ hypothesis, a precursor of modern effective demand theory, showing how the consumption function could have two different functional forms, depending on whether the consumer was rationed on the labour market or not. Leijonhufvud (1968) insisted on the importance of short-run quantity adjustments to explain the establishment of an equilibrium with involuntary unemployment.

These contributions were followed by the macroeconomic model of Barro and Grossman (1971, 1976), integrating the ‘Clower’ consumption function and the ‘Patinkin’ employment function in the first ‘disequilibrium’ macroeconomic model.

Then the main development was that of microeconomic concepts of non-Walrasian equilibrium proposed notably by Benassy (1975, 1976, 1977, 1982), Drèze (1975) and Younès (1975). These, which generalize the notion of Walrasian general equilibrium to non-market clearing situations, gave solid microeconomic foundations to the field. The main concepts are reviewed in the entry RATIONED EQUILIBRIA.

From then on, the field has developed quite rapidly, notably in the direction of macroeconomic applications and econometrics, as we shall outline below. We shall now review quickly the main elements of disequilibrium analysis. Longer developments can be found notably in Benassy (1982).

Non-Clearing Markets and Quantity Signals

A most important element of the theory is obviously to show how transactions can occur in a market in disequilibrium, and how quantity signals are generated in the decentralized trading process. To make things clear and intuitive, we shall start with the simple case of two agents, one demander and one supplier in a market which does not necessarily clear. They meet and express, respectively, an effective demand \( \tilde{d} \) and supply \( \tilde{s} \) (note that we do not use notional demands and supplies which are fully irrelevant in this context). We shall now indicate how transactions and quantity signals are formed in this example. Transactions will be denoted d* and s* respectively and they must of course satisfy d* = s*.

The first principle we shall use is that of voluntary exchange, i.e. that no agent can be forced to trade more than he wants on a market. This condition is quite natural and actually verified on most markets, except maybe for some labour markets which are regulated by more complex contractual arrangements. It is written in this example:

$$ {d}^{\ast}\le \tilde{d}\quad {s}^{\ast}\le \tilde{s} $$

which implies that:

$$ {d}^{\ast }={s}^{\ast}\le \min \, \left(\tilde{d},\tilde{s}\right) $$

Actually in this simple example, there is not reason why these two agents would exchange less than the minimum of demand and supply, as they would be both frustrated in their desires of exchange. This simple ‘efficiency’ assumption leads us to take the transaction as:

$$ {d}^{\ast }={s}^{\ast }=\min \, \left(\tilde{d},\tilde{s}\right) $$

the well-known ‘rule of the minimum’.

Now at the same time as transactions take place, quantity signals are set across the market: faced with the supply \( \tilde{s} \), and under voluntary exchange, the demander knows that he will not be able to purchase more than \( \tilde{s} \).Symmetrically the supplier knows that he cannot sell more than \( \tilde{d} \). Each agents thus receives from the other a quantity signal, respectively denoted as \( \tilde{d} \) and \( \tilde{s} \), which tells him the maximum quantity he can respectively buy and sell. In this example:

$$ \overline{d}=\tilde{s}\quad \overline{s}=\tilde{d} $$

and the transactions can thus be expressed as:

$$ {\displaystyle \begin{array}{l}{d}^{\ast }=\min \left(\tilde{d},\overline{d}\right)\\ {}{s}^{\ast }=\min\;\left(\tilde{s},\tilde{s}\right)\end{array}} $$

Let us move now to the general case (which is explored more formally in the entry on RATIONED EQUILIBRIA). Agents, indexed by i, exchange goods indexed by h. On each market h a rationing scheme transforms inconsistent demands and supplies, denoted \( {\tilde{d}}_{ih} \) and \( {\tilde{s}}_{ih} \), into consistent transactions, denotedand \( {d}_{ih}^{\ast } \) and \( {s}_{ih}^{\ast } \), which balance identically (i.e. total purchases always equal total sales). At the same time, and continuing to assume voluntary exchange, each agent receives a quantity signal, respectively \( {\tilde{d}}_{ih} \) or \( {\tilde{s}}_{ih} \) for demanders and suppliers, which tells him the maximum quantity he can buy or sell, and the rationing scheme is equivalently written:

$$ {\displaystyle \begin{array}{l}{d}_{ih}^{\ast }=\min \left({\tilde{d}}_{ih},{\overline{d}}_{ih}\right)\\ {}{s}_{ih}^{\ast }=\min\;\left({\tilde{s}}_{ih},{\overline{s}}_{ih}\right)\end{array}} $$

where \( {\overline{d}}_{ih} \) and \( {\overline{s}}_{ih} \) are functions of the demands and supplies of the other agents on the market. These quantity signals may result from the signals sent to each other by agents in decentralized pairwise meetings (as in the above two agents example) or result from a more centralized process (as in a uniform rationing scheme).

We thus see that on a market we may have unrationed demanders or suppliers, or rationed ones. The rationing scheme is called efficient if there are not both rationed demanders and rationed suppliers in the same market. An efficient rationing scheme implies the well-known ‘rule of the minimum’, according to which aggregate transactions equal the minimum of supply and demand. Such an assumption, which was very natural for our example with two agents, may not be valid if one considers a macroeconomic market, as not all demanders and suppliers meet pairwise. In particular it is well known that the property of market efficiency may be lost in the process of aggregating submarkets, whereas voluntary exchange remains. Note, however, that the concepts that follow do not require that property of market efficiency.

Now it is clear that the quantity signals received by the agents hould have an effect on demand, supply and price formation. This is what we shall explore now.

Effective Demand and Supply

Demands and supplies are signals that agents send to the ‘market’ (i.e. to the other agents) in order to obtain the best transactions according to their criterion. The traditional ‘notional’ or Walrasian demands and supplies are constructed under the assumption (which is actually verified ex-post in a Walrasian equilibrium) that each agent can buy and sell as much as he wants on each market. There is thus an equality between the signal the agent sends to the market (demand or supply) and the transaction he will obtained from it.

In disequilibrium analysis there is of course a difference between the signals sent (effective demands and supplies) and their consequences (the transactions actually realized). Effective demands and supplies expressed by an agent in the various markets are the signals which maximize his expected utility of the resulting transactions, knowing that these transactions are related to the demands and supplies by equalities of the type seen above, i.e.:

$$ {\displaystyle \begin{array}{l}{d}_{ih}^{\ast }=\min \left({\tilde{d}}_{ih},{\overline{d}}_{ih}\right)\\ {}{s}_{ih}^{\ast }=\min\;\left({\tilde{s}}_{ih},{\overline{s}}_{ih}\right)\end{array}} $$

The results of such expected utility maximization programmes may be quite complex, depending for example on whether quantity constraints are expected deterministically or stochastically, or whether agents act or not as price markers, as we shall see in the next section. In the case of deterministic constraints, there exists a simple and workable definition of effective demand, which generalizes Clower’s original ‘dual decision’ method: effective demand (or supply) on one particular market is the trade which maximizes the agent’s criterion subject to the constraints encountered or expected on the other markets. This definition thus naturally integrates the well-known ‘spillover effects’, which show how disequilibrium in one market affects demands and supplies in the other markets.

We shall immediately give an illustrative example of this definition, due to Patinkin (1956) and Barro and Grossman (1971), that of the employment function of the firm. Consider a firm with a production function y = F(l) exhibiting diminishing returns, and faced with a price p on the output market and a wage w on the labour market. The traditional ‘notional’ labour demand results from maximization of profit py – wl subject to the production constraint y = F(l), which yields immediately the usual Walrasian labour demand F′−1(w/p). Assume now that the firm faces a constraint \( \overline{y} \) on its sales of output (i.e. a total demand \( \overline{y} \)). According to the above definition the effective demand for labour \( \tilde{l} \) is the solution in l of the following programme:

$$ {\displaystyle \begin{array}{l}\mathrm{Maximize}\quad py- wl\quad \mathrm{s}.\mathrm{t}.\\ {}\quad y=F(l)\\ {}\quad y\le \overline{y}\end{array}} $$

the solution of which is:

$$ \tilde{l}=\min \left\{{F^{\prime}}^{-1}\left(w/p\right),\quad {F}^{-1}\left(\overline{y}\right)\right\} $$

We see that the effective demand for labour may have two forms: the Walrasian demand just seen above if the sales constraint is not binding, or, if this constraint is binding, a more ‘Keynesian’ form equal to the quantity of labour just necessary to produce the output demand. We see immediately on this example that effective demand may have various functional forms, which intuitively explains why disequilibrium models often have multiple regimes (see for example the three goods–three regimes model in the entry FIX-PRICE MODELS.

In the case of stochastic demand, the programme yielding the effective demand for labour becomes evidently more complex. One obtains some results quite reminiscent of the inventories literature as developed for example by Arrow et al. (1958) or Bellman (1957). See Benassy (1982) for the link between these two lines of work.

Price Making

We shall now address the problem of price making by decentralized agents, and we shall see that there too quantity signals play a prominent role. It is actually quite intuitive that quantity signals must be a fundamental part of the competitive process in a truly decentralized economy. Indeed, it is the inability to sell as much as they want that leads suppliers to propose, or to accept from other agents, a lower price, and conversely it is the inability to buy as much as they want that leads demanders to propose, or accept, a higher price. Various modes of price making integrating these aspects can be envisioned. We shall deal here with a particular organization of the pricing process where agents on one side of the market (usually the suppliers) quote prices and agents on the other side act as price takers. Other modes of pricing (bargaining, contracting) are currently studied, but have not yet been integrated in this line of work. As we shall see this model of price making is quite reminiscent of the imperfect competition line: Chamberlain (1933), Robinson (1933), Triffin (1940), Bushaw and Clower (1957), Arrow (1959), Negishi (1961).

Consider thus, to fix ideas, the case where sellers set the prices (things would be quite symmetrical if demanders were setting the prices), and in order to have only one price per market, let us characterize a market by the nature of the good sold and its seller (we thus consider two goods sold by different sellers as different goods, a fairly usual assumption in microeconomic theory since these goods differ at least by location, quality, etc…). On each ‘market’ so defined we thus have one seller, the price maker, facing several buyers. As we saw above, for a given price this seller faces a quantity constraint s, actually equal to the demand of the other agents on that market. But the price level is now a decision variable for the seller, and this quantity constraint (the others’ total demand) can be modified by changing the price: for example in general the seller who wants to sell more knows that, others things being equal, he should lower the price. The relation between the maximum quantity he expects to sell and the price set by the price maker is called the expected demand curve. If demand is forecasted deterministically, this expected demand curve will be denoted as:

$$ \overline{S}\left(p,\theta \right) $$

where θ is a vector of parameters depending on the exact functional form of that curve (for example elasticity and a position factor for isoelastic curves). If demand is forecast stochastically, the expected demand curve will have the form of a probability distribution on \( \overline{s} \) (i.e. total demand) conditional on the price.

For a given expected demand curve, the price maker chooses the price which will maximize profits, given the relation between price and maximum sales. For example, continuing to consider a firm with production function F(l), the programme yielding the optimum price is the following in the case of a deterministic expected demand curve:

$$ {\displaystyle \begin{array}{l}\mathrm{Maximize}\quad py- wl\quad \mathrm{s}.\mathrm{t}.\\ {}y=F(l)\\ {}y\le \overline{S}\left(p,\theta \right)\\ {}l\le \overline{l}\end{array}} $$

where \( \overline{l} \) is the constraint the firm possibly faces on the labour market, where it is a ‘wage taker’. Note that, according to our definition above, the effective demand for labour of this same firm would be given by the above programme, from which the last constraint would be deleted.

Both the price and quantity decisions of price makers depend on the parameters θ. Of course it would require quite heroic assumptions on the computational ability and information available to price setters to assume that they know the ‘true’ demand function (i.e. the ‘true’ functional form with the ‘true’ parameters). But the theory developed here gives a natural way of learning about the demand curve. Indeed, each realization p, s in a period is a point on the ‘true’ demand curve in that period (Bushaw and Clower 1957). Using the sequence of these observations, plus any extra information available (including for example the price of its competitors), the price maker can use statistical techniques to yield an estimation of the demand curve. Whether this learning would lead to the ‘true’ demand curve is still an unresolved problem.

Expectations

Of course, the modifications we outlined concerning the signal structure affect not only the current period, but the future periods as well, and as compared to traditional ‘competitive’ analysis, disequilibrium analysis introduces expected quantity signals in addition to expected price signals. Such an introduction allows for example to rationalize the traditional Keynesian accelerator (Grossman 1972). The introduction of such quantity expectations into the microeconomic setting was made in Benassy (1975, 1977b, 1982). Macroeconomic applications of the corresponding concepts can be found in Hildenbrand and Hildenbrand (1978), Muellbauer and Portes (1978), Benassy (1982, 1986), Neary and Stiglitz (1983).

Scope and Uses of Disequilibrium Analysis

We have briefly outlined the basic elements or building blocks of disequilibrium analysis. We saw that it generalizes the traditional theories of demand, supply and price formation to cases where, in the absence of an auctioneer, markets do not automatically clear. This theory is thus a quite general one, and the scope of its applications very broad. Up to now there have been in the literature three particularly active areas of development: (1) The construction of various concepts of equilibria with rationing, or non-Walrasian equilibria. These concepts, which generalize the traditional notion of Walrasian equilibrium to the cases where not all markets clear, show how mixed price-quantity adjustments can bring about a new type of equilbrium in the short run. (2) The development of numerous macroeconomic applications, which basically use the above concepts in the framework of aggregated macromodels, and derive policy implications, for example to fight involuntary unemployment. (3) Finally new econometric methods have been developed to deal with such models, as traditional methods were more suited to the study of equilibrium markets.

Microeconomic concepts of non-Walrasian equilibria are reviewed in the entry RATIONED EQUILIBRIA. We shall now very briefly outline the macroeconomic and econometric developments.

Macroeconomic Applications

Many contributions in the field started from a reconsideration of Keynesian models, and it is therefore no surprise that many macroeconomic applications have been made. The early model of Barro and Grossman (1971) has been followed by a huge macroeconomic literature, notably aimed at policy analysis and the study of involuntary unemployment. A very valuable feature of disequilibrium macromodels is that, like the microeconomic models, they endogenously generate multiple regimes in which various policy tools may have quite different impacts. These models are thus a particularly useful tool for synthesizing hitherto disjoint macroeconomic theories. One finds a number of macroeconomic applications in books by Barro and Grossman (1976), Benassy (1982, 1986), Cuddington et al. (1984), Malinvaud (1977), Negishi (1979). We may note that the same methods can also be used to study the problems of centrally planned economies (Portes 1981).

A few lessons can be drawn from these macrodisequilibrium models. The first is that, even though these models were at the very beginning aimed at bridging the gap with Keynesian analysis, they proved to be of more general relevance, and were able to generate non-Keynesian results as well as the traditional Keynesian results. Secondly, and more generally, whether or not a policy tool is efficient may depend very much on the ‘regime’ the economy is in. A famous example is the Barro and Grossman fixprice macroeconomic model, with its ‘Classical unemployment’ and ‘Keynesian unemployment’ regimes. Finally, it appears that the results of these models are quite sensitive to both the price formation mechanism on each market, as well as on the expectations formation mechanisms on both price and quantities (cf. for example, Benassy (1986), which experiments with various hypotheses).

This quite naturally leads to the need of further theoretical work, and to the necessity of empirically testing these models, an issue to which we now turn.

Disequilibrium Econometrics

In order to estimate microeconomic or macroeconomic disequilibrium models a whole new econometric technology has developed in recent years. Let us consider the very simplest case, that of a single market with a rigid price. The most basic system to estimate is then:

$$ {\displaystyle \begin{array}{l}{X}^d={a}_d{Z}_d+{\varepsilon}_d\\ {}{X}^s={a}_s{Z}_s+{\varepsilon}_s\\ {}X=\min \left({X}^d,{X}^s\right)\end{array}} $$

where Xd is quantity demanded, Zd is the set of variables affecting demand, ad is the vector of corresponding parameters and εd is a demand disturbance term (and symmetrically on the supply side). The market is assumed for the moment to function efficiently so that transaction X is the minimum of demand and supply Xd and Xs. The problem in estimating such a model, as compared with an equilibrium model, where by assumption

$$ X={X}^d={X}^s $$

is that only X is observed, not Xd or Xs. Techniques for dealing with these problems are reviewed in Quandt (1982). Of course this is the simplest possible model, and numerous extensions are now considered: (1) The prices may be flexible, either within the period of estimation, or between successive periods. The price equation must then be estimated simultaneously with the demand–supply system. (2) Since some applications are made on macroeconomic markets, the ‘minimum’ condition may not be satisfied, and is replaced by an explicit procedure of aggregation of submarkets. (3) Finally models with several markets in disequilibrium have been estimated, notably at the macroeconomic level.

Concluding Remarks

The development of disequilibrium analysis has clearly led to an enlargement and synthesis of both traditional microeconomics and macroeconomics.

Usual microeconomic theory in the market clearing tradition has been generalized in a number of directions: the study of the functioning of non-clearing markets and the formation of quantity signals, a theory of demand and supply responding to these quantity signals as well as to price signals, the integration of quantity expectations into microeconomic theory. This line of analysis further includes a theory of price making by agents internal to the system which also bridges the gap with the traditional theories of imperfect competition.

As for the corresponding macroeconomic models, they turn out to be a very useful synthetical tool, as they cover all possible disequilibrium configurations. They are more general than either traditional Keynesian macromodels, which considered only excess supply states, or than ‘new classical’ macromodels which postulate market clearing at all times. They are of course the natural tool to study problems such as involuntary unemployment.

Still richer developments lie ahead with further developments in the theories of price and wage formation in markets without an auctioneer. The methodology outlined here will permit us to derive the micro and macro consequences, as well as the consequences in terms of economic policy prescriptions. Much is also to be expected of the development of the associated econometric methods, which should allow us to choose the most relevant hypotheses, and to characterize specific historical episodes.

See Also