General equilibrium

The extension from this partial equilibrium in a single market to general equilibrium reflects  the idea that it may not be legitimate to speak of equilibrium with respect to a single commodity when supply and demand in that market depend on the prices of other goods.On this view, a coherent theory of the price system and the coordination of economic activity has to consider the simultaneous general equilibrium of all markets in the economy. This of course raises the questions of (i) whether such a general equilibrium exists; and (ii) what are its properties.


An exchange economy is an economy without production.There are a finite number of agents and a finite number of commodities. Each agent is endowed with a bundle of commodities.We want to know whether there exist prices such that when everyone tries to trade their desired amounts at these prices, demand will just equal supply, and also what the resulting outcome will look like – whether it will be efficient in a well-defined sense and how it will depend on preferences and endowments.

Each agent chooses consumption to maximize her utility given her budget constraint.


We now define a Walrasian equilibrium for the exchange economy. A Walrasian
equilibrium is a vector of prices, and a consumption bundle for each agent, such
that (i) every agent’s consumption maximizes her utility given prices, and (ii)
markets clear: the total demand for each commodity just equals the aggregate
endowment.