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A separation theorem with applications to Edgeworth equivalence in some infinite dimensional setting

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We provide an Edgeworth Equivalence result for a pure exchange economy with a measure space of agents and a separable ordered Banach space as commodity space. In particular, we first establish a necessary and sufficient condition for the Equivalence to hold, by means of an ad hoc separation theorem, which allows us to extend the classical finite-dimensional proof of this result. Our setting does not require nor transitivity neither completeness of preferences. Finally, using the sufficient part of the previous result and assuming negative transitivity of preferences, we show that the Edgeworth Equivalence holds under a suitable properness ([ro]-uniform weak properness) of preferences.
Rocznik
Strony
227--243
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Dipartimento di Matematica e Informatica, Università de Perugia, Via Vanvitelli 1, 06123, Perugia, Italy
  • Dipartimento di Matematica e Informatica, Università de Perugia, Via Vanvitelli 1, 06123, Perugia, Italy
Bibliografia
  • [1] C. Aliprantis, R. Tourky and N. Yannelis, Cone conditions in general equilibrium theory, J. Econ. Theory, 92 (2000), 96-121.
  • [2] R. J. Aumann, Market with a continuum of traders, Econometrica, 32 (1964), 39-50.
  • [3] T. F. Bewley, The equality of the core and the set of equilibria in economies with infinitely many commodities and a continuum of agents, Internat. Econ. Rev., 14 (1973), 383-394.
  • [4] D. J. Brown and O. Burkinshaw, Edgeworth equilibria, Econometrica, 55 (1987), 1109-1137.
  • [5] C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, 580, Springer-Verlag, Berlin (1977).
  • [6] G. Chichilnisky, P. J. Kalman, Application of functional analysis to models of efficient allocation of economic resources, J. Opt. Theory Appl., 30 (1980), 19-32.
  • [7] B. Fuchssteiner and H. König, New version of the Hahn-Banach Theorem, General inequalities, Beckenbach Ed., Birkäuer, Basel (1980), 255-266.
  • [8] F. Hausdorff, Set theory, translated by J. R. Aumann, Chelsea, New York (1957).
  • [9] F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal., 7 (1977), 149-182.
  • [10] W. Hildenbrand, Core and equilibria of a large economy, Princeton University Press, Princeton, New York (1974).
  • [11] K. Kuratowski, Topology I, translated by J. Jaworowski Academic press, New York and London (1966).
  • [12] S. J. Leese, Multifunctions of Souslin type, Bull. Austr. Math. Soc., 11 (1974), 395-411.
  • [13] A. Martellotti and A. Salvadori, A minimax theorem for functions taking values in a Riesz space, J. Math. Anal. Appl., 133 (1988), 1-13.
  • [14] A. Martellotti and A. R. Sambucini, On the comparison between Aumann and Bochner integrals, J. Math. Anal. Appl., 260 (2001), 6-17.
  • [15] A. Martellotti and A. R. Sambucini, Multivalued integrals of non convex integrands, Internat. J. Pure Appl. Math., 5 (2003) 11-28.
  • [16] A. Mas Colell, The price equilibrium existence problem in topological vector lattices, Econometrica, 54 (1986), 1039-1053.
  • [17] K. Podczeck, On Core-Walras (Non-)Equivalence for Economies with a Large Commodity Space, (2001), forthcoming in Econ. Theory.
  • [18] K. Podczeck, Core and Walrasian Equilibria when agents’characteristics are extremely dispersed, Econ. Theory, 22 (2003), 699-725.
  • [19] P. Pucci and G. Vitillaro, A representation theorem for Aumann integrals, J. Math. Anal. Appl., 102 (1977), 149-182.
  • [20] A. Rustichini and N. Yannelis, Edgeworth’s conjecture in economies with a continuum of agents and commodities, J. Math. Econ., 20 (1991), 307-326.
  • [21] A. Rustichini and N. Yannelis, What is perfect competition?, in Equilibrium theory in infinite dimensional spaces, (M. Ali Khan - N. Yannelis Ed.) Springer-Verlag, Berlin (1991).
  • [22] R. Tourky and N. C. Yannelis, Markets with Many More Agents than Commodities: Aumann’s "Hidden" Assumption, J. Econ. Theory, 101 (2001), 189-221.
  • [23] N. Yannelis and W. Zame, Equilibria in Banach lattices without ordered preferences, J. Math. Econ., 15 (1986), 85-110.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0002-0106
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