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• W3126011554 abstract "An economic agent, who participates in a pure exchange economy is described by his needs, tastes, and endowments. If there are 1 commodities, these economic concepts are formalized as follows: the needs are described by a subset X c Rt; in choosing a commodity vector, the agent is restricted to the set X; the tastes are described by a binary relation < on X; x < y means that the commodity vector y is at least as desired as the commodity vector x; the endowments are described by a vector e in the commodity space R' (for more details see Chapters 2 and 4 of G. Debreu [6]). pure exchange economy is a finite family {(Xa, 'a, ea)}aeA of economic agents. Since the endowments ea typically are not a maximal element for <a in Xa, there is an incentive to exchange commodities in order to improve the initial position. The result of an exchange is a redistribution of the total endowments; it can be described by a function f ofA into R' such that for every a E A, fa e Xa and A fa = EA ea or, if we assume free disposal of all commodities, EA fa <_ EA ea. The economic analysis of pure exchange economies consists of specifying a certain class of redistributions as possible outcomes of the exchange process. Imagine a planner who cannot enforce his plan and who proposes a certain redistribution f. If there exists a subset B of agents and for every agent a in B a commodity vector ga Xa such that ga is preferred to fa by every member a in B and LB ga _< B ea, then the coalition B has the desire and the power to block the proposed plan f. It seems reasonable to exclude as possible outcomes all redistributions which can be blocked by any coalition. The remaining redistributions are called the core of the exchange economy. The core, if not empty, contains in general many redistributions. Suppose now that all agents agree to exchange commodities in fixed ratios. This agreement simplifies the exchange extremely. If p E R' is the price system (that is, Ph/Pk is the amount of commodity k one has to give for one unit of commodity h), the agent a = (X, <, e) will only consider vectors in his budget set {x e X|p x . p*e} and will choose a most desired vector in this set. redistributionf and a price vectorp is called a price equilibrium, ifthe commodity vectorfa is for every agent a most desired vector in his budget set. The existence of price equilibria can be shown under quite general conditions (Debreu [6])." @default.
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• W3126011554 title "Metric measure spaces of economic agents" @default.
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