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A characterization of quasi-concave functions |
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| Authors: | Kiyoshi Otani |
| Institution: | Department of Economics, Tokyo College of Economics, 1-7 Minami-cho Kokubunji, Tokyo 185, Japan |
| Abstract: | This paper provides a simple and short proof that the following two properties are equivalent under ▽f(x) ≠ 0: (A) ▽f(x) h = 0 implies hT▽2f(x) h ? 0 for any x; (B) f(x1) ? f(x0) implies f(tx1 + (1?t)x0) ?f(x0) for 0? t ? 1. |
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