Note on the continuity of demand correspondences

概要

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We may summarize the above results. 1. One can maintain the continuity and the compact valuedness of γ if one of the conditions categorized in Table 1 is satisfied. 2. Suppose that the conditions which ensure the continuity and the compact valuedness of γ are satisfied. (a) one can maintain the u. h. c. and the compact valuedness of the demand correspondence ξ (resp. ψ), and the continuity of the indirect utility function U(ξ(ω)) (resp. V(ψ(ω)) if the utility function U(χ) (resp. V(ω, χ)) is continuous. (b) If the utility function U(χ) (resp. V(ω, χ)) is continuous and quasi-concave with respect to χ, then ξ (resp. ψ) is convex-valued as well as u. h. c. and compact-valued. (c) If the utility function U (χ) (resp. V (ω, χ)) is continuous and strictly quasi-concave with respect to χ, then ξ (resp. ψ) is a continuous function.研究ノート
香川大学経済研究所の論文