## Sunday, December 12, 2010

### Theory of Value, Chapter 5...

Chapter 5 of Debreu's Theory of Value is on economic equilibrium.  First some definitions...let xi be the vector of consumptions of for consumer i with i indexed from 1,...,m; yj be the vector of production for producer j with j indexed from 1,...,n; let wi denote the resource endowment of consumer i (the sum of these endowments over 1,...,m equals w or the total resources of the economy); finally, sij is consumer i's share in the profits of firm j. Net demand is x-y, excess demand is defined to be x-y-w.

The first few sections in the chapter define what an economy is, what market equilibrium is, and what attainable states of an economy are.  Basically attainable states of the economy are states where consumers are choosing a consumption bundle that is possible for them (i.e., satisfies their wealth constraint), producers are choosing a production that is possible for them, and that the market is in equilibrium (i.e., the net demand must equal the total available resources).  Economy equilibrium is then defined to be some subset of these obtainable states where consumers are maximizing utility and firms are maximizing profit.