This paper is designed to study the core equivalence problem ininfinite dimensional commodity spaces by using nonstandard analysis,Let x be a superstructure,κ>card(x)a regular cardinal ,and ^*x a κ-saturated non...This paper is designed to study the core equivalence problem ininfinite dimensional commodity spaces by using nonstandard analysis,Let x be a superstructure,κ>card(x)a regular cardinal ,and ^*x a κ-saturated nonstandard extension of x.A nonstandsrd exchange economy model is established on a commeodity space ^*E.where E∈x is a standard normed Riesz space.in this model the set of consumers is a hyperfinite(really infinite)st,denoted by T={1,2，…，ω}，（ω∈^*N-N),and the preference of each consumer t is an internal binary relation,>t on his consumption set Xt such that x ≯x for any x∈Xt,Each consumption set Xi is assumed to satisfy that(1),int E+Xt∩ E+≠φ，and (2),y >x implies y ∈ Xt for any x ∈nx Xt and y∈ ns ^*E.It is that if the preferences are monotonic for almost all consumers,then the core of the economy coincides with the set of all competitive equilibria.It is also showed that when the set of comsumers who have monotonic preferences is nonnegligible,an allocation is an core allocation if and only if it issupported by prices,and if and only if it is strongly supported by prices.展开更多
文摘This paper is designed to study the core equivalence problem ininfinite dimensional commodity spaces by using nonstandard analysis,Let x be a superstructure,κ>card(x)a regular cardinal ,and ^*x a κ-saturated nonstandard extension of x.A nonstandsrd exchange economy model is established on a commeodity space ^*E.where E∈x is a standard normed Riesz space.in this model the set of consumers is a hyperfinite(really infinite)st,denoted by T={1,2，…，ω}，（ω∈^*N-N),and the preference of each consumer t is an internal binary relation,>t on his consumption set Xt such that x ≯x for any x∈Xt,Each consumption set Xi is assumed to satisfy that(1),int E+Xt∩ E+≠φ，and (2),y >x implies y ∈ Xt for any x ∈nx Xt and y∈ ns ^*E.It is that if the preferences are monotonic for almost all consumers,then the core of the economy coincides with the set of all competitive equilibria.It is also showed that when the set of comsumers who have monotonic preferences is nonnegligible,an allocation is an core allocation if and only if it issupported by prices,and if and only if it is strongly supported by prices.
