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Nina has a convex utility of wealth function, u(x)

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Nina has a convex utility of wealth function, u(x). She is contemplating two prospects, L and M, where L is a mean preserving spread of M. Which of the following statements is therefore true? a. Nina will prefer M to L. b. Nina will prefer L to M. c. Nina's ranking of L and M cannot be determined without more information. (1. Nina must be risk averse, but that is the most one can say. 1 1. Pierce has a concave utility of wealth function, u(x). Pierce prefers prospect X to prospect Y. Which of the following statements is therefore necessarily true for Pierce? a. CE(X) > CE(Y). 13- U(EV(XD > U(EV(YD c. EU(X) < EU(Y) d. Y is a mean preserving spread of X. 12. Which of the following statements is necessarily @ for some given (non-degenerate) risky prospect, X? a. An individual with convex utility of wealth will have a greater value of CE(X) than an individual with concave utility of wealth? b. When utility of wealth is linear, the numeric value (ignoring units) of CE(X) — EV(X) is equivalent to the numeric value of EU(X) — U(EV(X)). c. A doubling of all of X's outcomes will result in a doubling of X's expected value. (1. A doubling of all of X's outcomes will result in a doubling of EU(X) for a risk averse individual.