Competitive Equilibrium
Competitive market equilibrium is the traditional concept of economic equilibrium, 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, a standard that other market structures are evaluated by.
A competitive equilibrium is a vector of prices and an allocation such that given the prices, each trader by maximizing his objective function (profit, preferences) subject to his technological possibilities and resource constraints plans to trade into his part of the proposed allocation, and such that the prices make all net trades compatible with one another ('clear the market') by equating aggregate supply and demand for the commodities which are traded.
A simple example is a society where there are only two products, bananas and apples, and 2 individuals, Jane and Kelvin. The price of bananas is Pb, and the price of apples is Pa.
The indifference curves J1 of Jane and K1 of Kelvin first intersect at point X, where Jane has more apples than Kelvin does, Kelvin has more bananas than Jane does, and they are willing to trade with each other at the prices Pb and Pa. After trading both Jane and Kelvin move to an indifference curve which depicts a higher level of utility, J2 and K2. The new indifference curves intersect at point E. The slope of the tangent of both curves equals -Pb/Pa.
And the MRSJane=Pb/Pa; MRSKelvin=Pb/Pa. The marginal rate of substitution of Jane equals that of Kelvin. Therefore the 2 individuals society reaches Pareto efficiency, where there is no way to make Jane or Kelvin better off without making the other worse off.
Read more about Competitive Equilibrium: The Competitive Equilibrium and Allocative Efficiency
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