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()?

c. Draw an example of what this agent's utility function might look like, using the origin as a reference point and assuming they are loss averse. Describe the key features of the graph (specifically the curvature and slope in the two domains).