By John Eatwell, Murray Milgate, Peter Newman (eds.)
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Additional resources for General Equilibrium
Peleg and Yaari present a trading model without production. The commodity space s is the space of all real sequences. In order to discuss continuity the space must be given a topology, in this case, the product topology. Thus a sequence of points converges if it converges in every coordinate, that is, x' -+ x, S = 1,2, ... , if x·( i) -+ x( i) for i = 0, 1, .... The space is presented as a sequence of real numbers but by grouping terms it may equally well represent a sequence of vectors, for example, commodity bundles occurring in successive time periods.
One theorem of Radner extends the existence of an equilibrium of plans and price expectations to this context. His assumptions are: (1) Consumers satisfy the usual conditions on convexity, non-satiation, and positive endowments. (2) Consumers own the shares of firms and each consumer owns shares in every firm. (3) Producers have closed, convex production sets with free disposal. The total production set satisfies the condition that the negative of a producible vector of commodities is not producible.
This was the vision of Walras, perhaps guided by the theory of static equilibrium of mechanical forces which he found in Poinsot. Another direction of abstraction in general equilibrium theory in its classic expressions has been to ignore the effects of processes which do not pass through the market. In particular each consuming unit is described as interested only in its own consumption in the theory of Pareto optimality and as uninfluenced in its choices by the choices made by other households.