Advances in Mathematical Economics Volume 19 by Shigeo Kusuoka & Toru Maruyama

Author:Shigeo Kusuoka & Toru Maruyama
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo

for sufficiently large k. Similarly,

for sufficiently large k. For such k, we have , where . Then, if c > 0 is sufficiently small,

which completes the proof. ■

Lemmas 1 and 3 ensure that the claim of Theorem 1 holds. This completes the proof of Theorem 1. ■

Appendix 2: Proof of Theorem 2

Define and . Then all are invertible0That is, all h, h k are bijective. Injectivity follows from the uniqueness of the inverse demand function. Surjectivity arises from the surjectivity and homogeneity of f and f k . and, for any , there exists a neighborhood U of q such that

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