Suppose a person's utility function is \(U(W)=\) \(3 W^{3}-40 W^{2}+180\), where \(W\) is wealth. Their initial wealth is 6 . If invested, that amount could rise or fall.

a. If it is equally likely that wealth could remain unchanged or fall to 2, compare the expected utility of the loss with the utility of having certain wealth equal to the expected wealth. Is the person risk averse?

b. If it is equally likely that wealth could remain unchanged or rise to 10 , compare the expected utility of the gain with the utility of having certain wealth equal to the expected wealth. Is the person risk preferring?

c. What can you say about this person's risk preference? Draw their utility curve.