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General equilibrium theory is a branch of theoretical microeconomics. It seeks to explain production, consumption and prices in a whole economy. This article considers neoclassical approaches to general equilibrium. Investigations into the interaction of markets arguably outside of neoclassical theory are taken to be outside the scope of this article. In particular,Classical and Marxist analyses of natural prices or prices of production, Wassily Leontief's Input-Output analysis, and John von Neumann's Linear Programming model of growth are not otherwise discussed.
General equilibrium tries to give an understanding of the whole economy using a bottom-up approach, starting with individual markets and agents. Macroeconomics, as developed by so-called Keynesian economists, uses a top-down approach where the analysis starts with larger aggregates. Since modern macroeconomics has emphasized microeconomic foundations, this distinction has been slightly blurred. However, many macroeconomic models simply have a 'goods market' and study its interaction with for instance the financial market. General equilibrium models typically model a multitude of different goods markets. Modern general equilibrium models are typically complex and require computers to help with numerical solutions.
Under capitalism, the prices and production of all goods are interrelated. A change in the price of one good, say bread, may affect another price, for example, the wages of bakers. If bakers differ in tastes from others, the demand for bread might be affected by a change in bakers' wages, with a consequent effect on the price of bread. Calculating the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the millions of different goods that are available.
The first attempt in Neoclassical economics to model prices for a whole economy was made by Leon Walras. Walras' 'Elements of Pure Economics provides a succession of models, each taking into account more aspects of a real economy (two commodities, many commodities, production, growth, money). Many think Walras was unsuccessful and the later models in this series inconsistent. Nevertheless, Walras first laid down a research program much followed by 20th century economists. In particular, Walras' agenda included the investigation of when equilibria are unique and stable.
Walras also first introduced a restriction into general equilibrium theory that some think has never been overcome, that of the tatonnement or grouping process.
The tatonnement process is a tool for investigating stability of equilibria. Prices are cried, and agents register how much of each good they would like to offer (supply) or purchase (demand). No transactions and no production take place at disequilibrium prices. Instead, prices are lowered for goods with positive prices and excess supply. Prices are raised for goods with excess demand. The question for the mathematician is under what conditions such a process will terminate in equilibrium in which demand equates to supply for goods with positive prices and demand does not exceed supply for goods with a price of zero. Walras was not able to provide a definitive answer to this question.
In partial equilibrium analysis, the determination of the price of a good is simplified by just looking at the price of one good, and assuming that the prices of all other goods remain constant. The Marshallian theory of supply and demand is an example of partial equilibrium analysis. Partial equilibrium analysis is adequate when the first-order effects of a shift in, say, the demand curve do not shift the supply curve. Anglo-American economists became more interested in general equilibrium in the late 1920s and 1930s after Piero Sraffa's demonstration that Marshallian economists cannot account for the forces thought to account for the upward-slope of the supply curve for a consumer good.
If an industry uses little of a factor of production, a small increase in the output of that industry will not bid the price of that factor up. To a first order approximation, firms in the industry will not experience decreasing costs and the industry supply curves will not slope up. If an uses an appreciable amount of that factor of production, an increase in the output of that industry will exhibit increasing costs. But such a factor is likely to be used in substitutes for the industry's product, and an increased price of that factor will have effects on the supply of those substitutes. Consequently, the first order effects of a shift in the supply curve of the original industry under these assumptions include a shift in the original industry's demand curve. General equilibrium is designed to investigate such interactions between markets.
Continential European economists made important advances in the 1930s. Walras' proofs of the existence of general equilibrium often were based on the counting of equations and variables. Such arguments are inadequate for non-linear systems of equations and do not imply that equilibrium prices and quantities cannot be negative, a meaningless solution for his models. The replacement of certain equations by inequalities and the use of more rigorous mathematics improved general equilibrium modeling.
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