Advances in Mathematical Economics Volume 11 (Advances in by S. Kusuoka, A. Yamazaki PDF

By S. Kusuoka, A. Yamazaki

ISBN-10: 4431777830

ISBN-13: 9784431777830

ISBN-10: 4431777849

ISBN-13: 9784431777847

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Example text

46 C. Hara cation of this theorem is that the allocation of bads may also be delegated to the market mechanism. An implicit and yet important assumption underlying the first welfare theorem is that consumers are price takers. Without this assumption, the market mechanism need not bring about an efficient allocation, and the relevance of the first welfare theorem would be lost. The assumption of the price-taking behavior is justified in the form of the core convergence theorem or the core equivalence theorem.

For an economy ((A, A , ν), χ ), a feasible allocation f , and a price vector p ∈ P, define 5 Hildenbrand’s theorem establishes the existence of a free-disposal equilibrium, but if every member of some coalition with positive measure has a monotone preference relation, then a free-disposal equilibrium can be easily modified to a Walrasian equilibrium (where the feasibility constraint is satisfied with an equality rather than a weak inequality), by assigning excess supply to these consumers. On the other hand, Aumann’s [4] and Schmeidler’s [16] theorems assume that almost every consumer’s preference relation is monotone.

6. 9 implies that lim inf | f n | is µ-integrable. 9 entail that the multifunction w − ls f n admits at least a µ-integrable, measurable selection. 5 of [11]). 4 of [11], the multifunction w − ls f n is measurable. 34 C. Castaing et al. 5. The case of multifunctions with values in a dual space As in the previous sections ( , F, µ) stands for a complete probability space and E for a separable Banach space. The topological dual of E is denoted by E ∗ and the dual norm by . , C) and defined by d(y, C) = inf y − z z∈C y ∈ E ∗.

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Advances in Mathematical Economics Volume 11 (Advances in Mathematical Economics) by S. Kusuoka, A. Yamazaki


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