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- W1992863886 abstract "The purpose of this paper is to extend the theory on the local uniqueness of equilibrium prices initiated by Debreu (1970) [and pursued by E. and H. Dierker (1972), Smale (1974a), Hazewinkel(1972), Delbaen (1971), Hildenbrand (1972), Fuchs (1974), and others] to production economies of the constant returns variety. The problem is the familiar one: good theoretical reasons for the uniqueness of equilibria being unavailable, one settles for expecting that, at least, equilibria will be locally unique and will vary continuously with perturbations of the economy, i.e., that economies will be ‘regular’ (as e,, or e,,, not e,, in fig. 1). Still, if multiplicity of equilibria is possible, non-regular economies (as e, in fig. 1) are unavoidable and the best possible result is to establish their exceptionality (that is to say, to justify giving to regular economies its name) by showing, and this is certainly intuitive (see fig. I), that they are associated with degeneracies and constitute a ‘negligible’ subset of economies. The notion of ‘negligibility’ we will use is topological [by contrast to measure theoretical, see E. and H. Dierker (1972)]; namely, the space of economies will be a topological space and negligible sets will be the ones which closures have empty interiors. In a production context, where only a limited number of commodities may be factors of production, initial endowments redistributions (if at all allowable) do not give enough parameter variability and so, consumers’ or producers’ characteristics other than initial endowments have to be regarded as variable; the space of economies becomes then infinite-dimensional and forces the topological definition of negligible. Different approaches to production have been considered by Fuchs (1974) and Smale (1974b). However, constant returns to scale have so far been excluded from the theory in the case of Fuchs (1974), because supply functions are assumed to exist, and, in the case of Smale (1974b), because the class of constant" @default.
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- W1992863886 date "1975-03-01" @default.
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- W1992863886 title "On the continuity of equilibrium prices in constant-returns production economies" @default.
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- W1992863886 doi "https://doi.org/10.1016/0304-4068(75)90011-7" @default.
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