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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 .
A relative price is the price of a commodity such as a good or service in terms of another; i.e., the ratio of two prices. A relative price may be expressed in terms of a ratio between the prices of any two goods or the ratio between the price of one good and the price of a market basket of goods (a weighted average of the prices of all other goods available in the market).
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.
All superlative indices produce similar results and are generally the favored formulas for calculating price indices. [14] A superlative index is defined technically as "an index that is exact for a flexible functional form that can provide a second-order approximation to other twice-differentiable functions around the same point."
This will tend to put downward pressure on the price to make it return to equilibrium. Likewise where the price is below the equilibrium point (also known as the "sweet spot" [3]) there is a shortage in supply leading to an increase in prices back to equilibrium. Not all equilibria are "stable" in the sense of equilibrium property P3.
Thus these too raise both equilibrium income and the equilibrium interest rate. Of course, changes in these variables in the opposite direction shift the IS curve in the opposite direction. The IS–LM model also allows for the role of monetary policy. If the money supply is increased, that shifts the LM curve downward or to the right, lowering ...
The overall system involves two state variables: price and capacity. Using the temporary equilibrium method, it can be reduced to a system involving only state variable. This is possible because each short-run equilibrium price will be a function of the prevailing capacity, and the change of capacity will be determined by the prevailing price.
In a first-price auction, the auctioneer receives the maximum of the two equilibrium bids, which is (/, /). In a second-price auction, the auctioneer receives the minimum of the two truthful bids, which is (,). In both cases, the auctioneer's expected revenue is 1/3.