Let L be a lottery with non-negative random outcome X having cdf F and density f and consider a decision maker having wealth w 0 and utility function u : [0, ) R given by u(x) = 3(x 1 3 1) (2)

1. Compute the certainty equivalence CE(w, X) of the above lottery L having random outcome X (hint: simplify this formula as much as possible!)

2. Compute the risk premium (w, X) of the above lottery L having random outcome X.

3. Show that the risk premium (w, X) is non-negative and a decreasing function of the wealth w of the decision maker. (Hint: you may use for any nonnegative random variable Y that the function h : [1, ) R given by h() = E(Y ) 1 is increasing!)

4. Is the decision maker in this lottery riskaverse or riskseeking?