Suppose that agents have utility over their final level of wealth, and that they are expected utility maximizers.

a. Suppose an agent is offered a choice between the gamble (0.4,50;0.6,0) - that is, a 40% chance of winning $50, a 60% chance of getting $0 - and $15 for sure. Suppose further that the agent chooses the $15. What mathematical property does this imply about their utility function? Are they risk averse, risk neutral, or risk seeking?

b. Suppose the same agent as in (a) prefers (0.4,-50;0.6,0) tolosing$15 for sure. What would this, together with the result in (a), imply about the agent's utility function U()?