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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.
This lack of equilibrium arises from the firms competing in a market with substitute goods, where consumers favor the cheaper product due to identical preferences. Additionally, equilibrium is not achieved when firms set different prices; the higher-priced firm earns nothing, prompting it to lower prices to undercut the competitor.
That is, if we consider a sufficiently small change in some exogenous parameter, we can calculate how each endogenous variable changes using only the first derivatives of the terms that appear in the equilibrium equations. For example, suppose the equilibrium value of some endogenous variable is determined by the following equation:
Market equilibrium computation is interesting due to the fact that a competitive equilibrium is always Pareto efficient. The special case of a Fisher market, in which all buyers have equal incomes, is particularly interesting, since in this setting a competitive equilibrium is also envy-free. Therefore, market equilibrium computation is a way ...
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 ...
It is named after the German economist Heinrich Freiherr von Stackelberg who published Marktform und Gleichgewicht [Market Structure and Equilibrium] in 1934, which described the model. In game theory terms, the players of this game are a leader and a follower and they compete on quantity. The Stackelberg leader is sometimes referred to as the ...
It follows that the market value of total excess demand in the economy must be zero, which is the statement of Walras's law. Walras's law implies that if there are n markets and n – 1 of these are in equilibrium, then the last market must also be in equilibrium, a property which is essential in the proof of the existence of equilibrium.