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Concept
Competitive equilibrium
Summary
Competitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium, introduced by Kenneth Arrow and Gérard Debreu in 1951, appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices. Competitive markets are an ideal standard by which other market structures are evaluated.
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.
An allocation matrix . For every , is the vector of commodities allotted to agent .
These elements should satisfy the following requirement:
Satisfaction (market-envy-freeness): Every agent weakly prefers his bundle to any other affordable bundle:
if then .
Often, there is an initial endowment matrix : for every , is the initial endowment of agent . Then, a CE should satisfy some additional requirements:
Market Clearance: the demand equals the supply, no items are created or destroyed:
Individual Rationality: all agents are better-off after the trade than before the trade:
Budget Balance: all agents can afford their allocation given their endowment:
This definition explicitly allows for the possibility that there may be multiple commodity arrays that are equally appealing. Also for zero prices. An alternative definition relies on the concept of a demand-set. Given a price function P and an agent with a utility function U, a certain bundle of goods x is in the demand-set of the agent if: for every other bundle y.
Official source
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