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Mas-Colell, Whinston, and Green Proposition 6.C.1 (p. 187) says that for an expected utility maximizer with a Bernoulli utility function $u(\cdot)$ on amounts of money, saying that "the decision maker is risk averse" is equivalent to "$u(\cdot)$ is concave". However, these other assumptions matter. A concave utility function isn't enough. Diminishing ...

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