The unknowns are the prices of all factors and all commodities and the quantities purchased and sold of factors and commodities by each consumer and each producer. In principle a simultaneous-equation system has a solution if the number of independent equations is equal to the number of unknowns in the system. This approach has been followed by the founder of general equilibrium analysis Leon Walras.

The most ambitious general equilibrium model was developed by the French economist Leon Walras In his Elements of Pure Economics Walras argued that all prices and quantities in all markets are determined simultaneously through their interaction with one another. For example, each consumer has a double role: he buys commodities and sells services of factors to firms. Thus for each consumer we have a set of equations consisting of two subsets: one describing his demands of the different commodities, and the other his supplies of factor inputs.

Similarly, the behaviour of each firm is presented by a set of equations with two subsets one for the quantities of commodities that it produces, and the other for the demand for factor inputs for each commodity produced. In a general equilibrium system of the Walrasian type there are as many markets as there are commodities and factors of production. In a commodity market the number of demand functions is equal to the number of consumers, and the number of the supply functions is equal to the number of firms which produce the commodity.

In each factor market the number of demand functions is equal to the number of firms multiplied by the number of commodities they produce. The number of supply functions is equal to the number of consumers who own ex hypothesis the factors of production. A necessary but not sufficient condition for the existence of a general equilibrium is that there must be in the system as many independent equations as the number of unknowns.

Thus the first task in establishing the existence of a general equilibrium is to describe the economy by means of a system of equations, defining how many equations are required to complete and solve the system. For example, assume that an economy consists of two consumers, A and B, who own two factors of production, K and L These factors are used by two firms to produce two commodities, X and Y. It is assumed that each firm produces one commodity, and each consumer buys some quantity of both. It is also assumed that both consumers own some quantity of both factors but the distribution of ownership of factors is exogenously determined.

Since the number of equations is equal to the number of unknowns, one should think that a general equilibrium solution exists. In this model the absolute level of prices cannot be determined. With this device prices are determined only as ratios: each price is given relative to the price of the numeraire. If we assign unity to the price of the numeraire, we attain equality of the number of simultaneous equations and unknown variables the number of unknowns is reduced to 17 in our example. However, the absolute prices are still not determined: they are simply expressed in terms of the numeraire.

This indeterminacy can be eliminated by the introduction explicitly in the model of a money market, in which money is not only the numeraire, but also the medium of exchange and store of wealth. Even if there is equality of independent equations and unknowns, there is no guarantee that a general equilibrium solution exists. The proof of the existence of a general equilibrium solution is difficult.

Leon Walras was never able to prove the existence of a general equilibrium. In Arrow and Debreu provided a proof of the existence of a general equilibrium in perfectly competitive markets, in which there are no indivisibilities and no increasing returns to scale. Furthermore, in Arrow and Hahn proved the existence of a general equilibrium for an economy with limited increasing returns and monopolistic competition, without indivisibilities.

Apart from the existence problem, two other problems are associated with an equilibrium: the problem of its stability and the problem of its uniqueness. These problems can best be illustrated with the partial-equilibrium example of a demand-supply model. Assume that a commodity is sold in a perfectly competitive market, so that from the utility-maximising behaviour of individual consumers there is a market demand function, and from the profit-maximising behaviour of firms there is a market supply function.

An equilibrium exists when at a certain positive price the quantity demanded is equal to the quantity supplied. At such a price there is neither excess demand nor excess supply.

The latter is often called negative excess demand. Thus an equilibrium price can be defined as the price at which the excess demand is zero the market is cleared and there is no excess demand. The equilibrium is stable if the demand function cuts the supply function from above.

In this case an excess demand drives price up, while an excess supply excess negative demand drives the price down figure The equilibrium is unstable if the demand function cuts the supply function from below. In this case an excess demand drives the price down, and an excess supply drives the price up figure In figure It is obvious that at P e 1 there is a stable equilibrium, while at P e 2 the equilibrium is unstable.

Finally in figure In fact the three basic questions related to the existence, stability and uniqueness of an equilibrium can be expressed in terms of the excess demand function.

## General Equilibrium Theory (With Diagram)

To see this we redraw below figures For each of these cases we have derived the relevant excess demand function by subtracting Q s from Q D at all prices. From the redrawn diagrams in conjunction with the corresponding ones There are as many equilibria as the number of times that the excess demand curve E P intersects the vertical price-axis figure The equilibrium is stable if the slope of the excess demand curve is negative at the point of its intersection with the price-axis figure Note that the presence of a catalyst does not shift the equilibrium; it only causes the reaction to reach equilibrium faster.

This is due to the fact that catalysts only lower activation energies. Dynamic equilibrium is useful in predicting whether the forward or reverse reaction is spontaneous or nonspontaneous. To explain how this works, three quantities must be introduced: the equilibrium constant, K; the reaction quotient, Q; and the Gibbs Free Energy for a certain reaction, dG r. The equations for K and Q are given below:. When dG r is negative, the forward reaction is spontaneous and the reverse reaction nonspontaneous. When dG r is positive, the forward reactions is nonspontaneous and the reverse reaction spontaneous.

This is due to Q's deviation from K and Le Chatelier's principle at standard temperature. Macro-economic analysis, even though partially captured by the mathematical methodology that has invaded virtually all aspects of economics, nevertheless has maintained a high content of institutional structure and a basic concern for dynamics. The causality implicit in the macroeconomic models and the predictions based upon them depend directly on a host of macroeconomic accounting assumptions.

These deal with how household production is evaluated; what constitutes savings; how capital stock is evaluated; how depreciation is measured; what constitutes unemployment; how is inflation measured and many other factors usually involving both deep conceptual problems in the treatment of time and uncertainty. They also deal with fundamental economic and mathematical problems in obtaining optimal scalar or one number representations of phenomena which at best are multidimensional, or do not even have good numerical representation. An example of the measurement difficulties is provided when one tries to correct the growth of productivity for changes in the variety, quality and mixture of goods produced.

If the conceptual problems, however deep were merely confined to the academies they would not matter very much. They would increase employment for university professors and make little difference to the functioning of society as a whole. Unfortunately a cast of living index, or an inflation index or a measurement of the level of unemployment may be used to influence vital political decisions.

Academic economists are also citizens and as such they cannot avoid the responsibilities which must be assumed when one index is selected over another. Many of the basic problems with the national income accounts have been covered in the paper in this journal by Richard Ruggles, 1 the emphasis here is in on microeconomics.

Microeconomic theory since the s has developed in a considerably different manner from macroeconomics. The domain of study of microeconomics is vast and is split into many sub-disciplines. The theory of the firm, consumer choice, oligopoly theory and industrial organization maintained a high empirical content until the recent invasion of game theory, the central development in the study of the basic logic of markets, production and trade took a different turn.

The mathematics showed the conditions required for existence of such a price system but provided no indication as to how the prices were to be attained. Furthermore it was shown that in general the prices which would clear all markets efficiently were not necessarily unique. The few verbal commentaries in the book intimated that the mathematics represented the appropriate formulation of the concepts of a competitive price system which were present in the work of many economists from the earliest times.

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In particular this could be taken to represent the full formalization of the writings of Walras The development of general equilibrium theory was a great step forward in the mathematization of a central concept of economic theory. It showed the delicacy of the many conditions needed to permit the functioning of an efficient price system. It also showed the power of new and elegant mathematical applications to the social sciences. But the development of a science calls for more than mathematics and logic.

The relevance of and closeness of the abstractions to the functioning economy and the nature of the questions which can and cannot be answered by the theory developed must be considered with care.

## Principles of Chemical Equilibrium - Chemistry LibreTexts

General equilibrium theory is admirably suited to illustrate basic relationships in equilibrium but offers few if any insights into process. Time and uncertainty have essentially disappeared from this apotheosis of the price system. But it is time and uncertainty which are the concerns of everyday economic life and the problems of how to account for the influence of time and uncertainty in the ongoing economic process are central to the development of accounting.

Koopmans has noted general equilibrium theory is essentially pre-institutional in character. The ability to formulate and answer in a sophisticated way many deep problems about the relationship between prices and efficient production has been of great significance in laying the groundwork for an economics that accommodates process. But this strength should not serve to hide the gap between verbal descriptions of competition and the highly non-institutional and process-free description of preferences, ownership and technological relations that make up the basic elements of general equilibrium theory.

Many of the important developments in mathematical economics in the past twenty years have been directed towards finding mathematical generalizations which weaken assumptions on preferences, take care of boundary equilibria or cast light upon production conditions A certain amount of work has been done on the stability of equilibrium points under perturbations in excess supply and demand conditions; but few general results are known concerning the dynamic of socio-economic feedback mechanisms for the formation of price.

The next step in the development of microeconomics is in building full process models showing the formation of prices via the market or showing the manipulation of prices via a centralized economic planning agency. But any attempt to do this calls far the specification of updating mechanisms of the economy regardless of any equilibrium considerations and it is precisely the recognition of the need for the description of the updating implicit in economic process that has been central to the development of accounting.

The accountant takes the institutions as a fact of life. A successful post-general equilibrium theory must have them as a logical necessity of process. The growth of specific institutions undoubtedly depends on a host of factors involving history, chance, culture and technology pertaining to each society. Ideologies often use scholarly theories as part of the social process of legitimization.

The elegance, level of abstraction and apparent generality of general equilibrium theory appears to provide an intellectual justification for the extreme proponents of laissez faire. The market will take care of everything. It would be a great blessing if this were true. Unfortunately the truth lies elsewhere. The careful economic theorist with no immediate political cause to legitimize can simultaneously see the great intellectual contribution of the theory and its limitations.

An understanding of the limitations may help to bring it closer to reality and in doing so may also explain why many of the definitions of the microeconomist differ from the accountant and businessman concerned with the processes of every day production and trade.

The limitations of the general equilibrium model are as follows: It is basically non-institutional. Although equilibrium conditions are specified, no explanation of price formation is given. The general equilibrium model is static. The model is essentially timeless. Although one may make a simple pro forma change of notation which treats goods in different time periods as different goods, hence replaces an optimization problem in M dimensions by one in MT dimensions where M is the number of goods and T the number of the periods; this mathematical extension picks up only a few of the substantially new phenomena involved in the consideration of time and process in an economy.

The horizon is infinite and the agents appear without context at the start and disappear at the end. The many problems posed by uncertainty in an actual economy are avoided by the same type of device that was used to extend the model to several periods. Suppose that an economy trades in M commodities and that it can be in any one of K states of nature.

We may consider an economy with trade in MK commodities which may be regarded as options. The proofs of the existence of an efficient price system were independent of the number of competitors indicating that the mathematical model though appropriate for the study of efficient prices is not necessarily appropriate for the study of competitive price formation. The general equilibrium model was not designed to study economies with an intermix of monopolistic, oligopolistic and competitive elements yet every economy has this mix. It is an inadequate model for the study of non-symmetric information conditions, yet disclosure of costs and other competitive information are of critical importance to the economy.

It has no satisfactory explanation of unemployment. In essence it offers an ideological opportunity to claim that there is no such thing as unemployment because in the best of all possible worlds without governmental or other institutional constraints the markets would adjust so that all who wished to work could find a job at the appropriate price.

## 3.6 Equilibrium and Market Surplus

Bankruptcy plays no role. There is neither birth nor deaths of firms.

Yet a basic understanding in accounting is the need to differentiate ongoing enterprise evaluations from liquidation evaluations. Furthermore the elementary dynamics of economic process in a world with credit illustrates the proposition that the system may attain a state where prior commitments cannot be met. In such an instance bankruptcy laws become a logical necessity not merely an institutional fact. The general equilibrium model does not need markets, banks or other credit or financial institutions, as trust is implicitly perfect.

Firms are not institutions. Production is described by production correspondences available to all who have the resources.

### Who Sets the Price?

It is as though the only items necessary to bake a cake were the ingredients and a recipe free to and immediately understood by all. The firm as an entity with an internal organization and a management with goals of its own is not included in this abstraction. In the Debreu model there is really only one major actor - the consumer, and one shadow actor - the producer. The consumer has his own preference ordering and tries to maximize his own welfare. The producer is a shadowy manager of a firm which may be owned by stockholders other than himself. Even though his interests may conflict with others he is modeled as a profit maximizing perfect fiduciary who flows through the profits to a non-voting 2 group of stockholders.

The definition of profit depends upon the whole finite period being considered. In macroeconomic models and in economic life we frequently distinguish investors, savers, speculators, brokers, bankers, consumers, manufactures, retailers and others. It is important to ask at what level of abstraction do or should these distinctions appear. The general equilibrium model is essentially static in the sense that time is handled by merely enlarging the number of variables and renormalizing Wold, Work on sequences of economies Green, and the infinite horizon have modified this.

Even so in the work of Arrow and Debreu and Debreu , no explicit mechanism for the formation of price is given, i. It is not surprising that at this level of theorizing one cannot distinguish a competitive economy with prices arising from competitive behavior from a socialist economy with controlled prices.