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Market equilibrium computation (also called competitive equilibrium computation or clearing-prices computation) is a computational problem in the intersection of economics and computer science. The input to this problem is a market , consisting of a set of resources and a set of agents .
In most simple microeconomic stories of supply and demand a static equilibrium is observed in a market; however, economic equilibrium can be also dynamic. Equilibrium may also be economy-wide or general, as opposed to the partial equilibrium of a single market. Equilibrium can change if there is a change in demand or supply conditions.
A competitive equilibrium (CE) consists of two elements: A price function . It takes as argument a vector representing a bundle of commodities, and returns a positive real number that represents its price. Usually the price function is linear - it is represented as a vector of prices, a price for each commodity type.
For example, if the MRS xy = 2, the consumer will give up 2 units of Y to obtain 1 additional unit of X. As one moves down a (standardly convex) indifference curve, the marginal rate of substitution decreases (as measured by the absolute value of the slope of the indifference curve, which decreases).
Partial equilibrium, as the name suggests, takes into consideration only a part of the market to attain equilibrium. Jain proposes (attributed to George Stigler ): "A partial equilibrium is one which is based on only a restricted range of data, a standard example is price of a single product, the prices of all other products being held fixed ...
This means that the equilibrium price depends positively on the demand intercept if g – b > 0, but depends negatively on it if g – b < 0. Which of these possibilities is relevant? In fact, starting from an initial static equilibrium and then changing a, the new equilibrium is relevant only if the market actually goes to that new equilibrium ...
The conceptual framework of equilibrium in a market economy was developed by Léon Walras [7] and further extended by Vilfredo Pareto. [8] It was examined with close attention to generality and rigour by twentieth century mathematical economists including Abraham Wald, [9] Paul Samuelson, [10] Kenneth Arrow and Gérard Debreu. [11]
From consumer equilibrium for an individual, the book aggregates to market equilibrium across all individuals, producers, and goods. In so doing, Hicks introduced Walrasian general equilibrium theory to an English-speaking audience. This was the first publication to attempt a rigorous statement of stability conditions for