Two decision makers, Jim and Saeromi, each currently have $50 in initial wealth. They face a choice between two options: (A) gain $X for sure, or (B) lose $50 with probability 1 2 and gain $350 with probability 1 2 . Jim has a Bernoulli utility function u = x, where x is 'final wealth'. We don't know Saeromi's Bernoulli function, but we do know that her coefficient of absolute risk aversion is always less than zero. Both people's preferences can be represented with the expected utility form.

a) For what values of X will Jim choose option A? How does this compare to the expected cash value of option B, and why?

b) What does it mean that Saeromi's coefficient of absolute risk aversion is less than zero? For what values of X do we definitely know that Saeromi will choose option B over option A? Explain.