Advances in Equilibrium Theory: Proceedings of the - download pdf or read online

By Donald G. Saari (auth.), Prof. C. D. Aliprantis, Prof. O. Burkinshaw, Prof. N. J. Rothman (eds.)

ISBN-10: 3540152296

ISBN-13: 9783540152293

ISBN-10: 3642516025

ISBN-13: 9783642516023

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Read Online or Download Advances in Equilibrium Theory: Proceedings of the Conference on General Equilibrium Theory Held at Indiana University-Purdue University at Indianapolis, USA, February 10–12, 1984 PDF

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Extra info for Advances in Equilibrium Theory: Proceedings of the Conference on General Equilibrium Theory Held at Indiana University-Purdue University at Indianapolis, USA, February 10–12, 1984

Sample text

Y is non-empty and closed, with non-zero outputs requiring non-zero inputs; the input requirement sets are strictly convex from below and admit free disposal. If producer factor prices, Pv' are strictly positive and factor markets are competitive, then the cost function is c (y ,pv) = Min{pv· u : u E V (y) }. u In our discussion, it will be convenient to characterize the production possibility set in terms of transformation functions, as we did in Theorem 1. The distance function is defined by F (y,v) = Maxo.

E •• aonve:x:ity of aonsumption sets. produation sets and preferences. The next examp1e shows that an optimum need not be an equi1ibrium. EXAMPLE 7. See Figure 8, where x is an optimum but not an equi1ibrium. FIGURE 8 Asimp1e, but neverthe1ess fundamental, theorem is: [XIl Under [al every optimum :x: is a quasiequiZibril4Tl üJith respeat to sorne p;l O. PROOF. Suppose that the 10ca1 non-satiation condition [al ho1ds for i=l. 34 Define V= {z: z >1 Xl} + on preferences ([h]) V m l: {Z: Y Since the production set i =1 Z EY and p.

X:B;. supports the aZZocation :c if pFO, A"J 0 and: (a) p·z;;. y for atz y E:/; (b) p. (:ci. - :Ci) ;;. ) - ui (:Ci)] for atz i and :ci. E B; . ) supports the aUocation :c. then: (a) :c is a pPice quasiequiZibPium ~th pespect to p; and (b) ). is a vectop of suppopting utiZity weights fop U at PROOF. (a) I f (b) Let x' o u(:c). xi ~i Xi' then ui(xi) ~ ui(xi)' be an allocation. Then ~ p. ,1 [u,1 1=1 (x') - u 1' (x 1! ) ] • 1 So, for all allocations x' •• Either of the conclusions of [XV] implies that x is a weak opti- mum.

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Advances in Equilibrium Theory: Proceedings of the Conference on General Equilibrium Theory Held at Indiana University-Purdue University at Indianapolis, USA, February 10–12, 1984 by Donald G. Saari (auth.), Prof. C. D. Aliprantis, Prof. O. Burkinshaw, Prof. N. J. Rothman (eds.)


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