Beth is an expected utility maximizing risk-averse individual with the utility function u(w) = w 0.5 and initial wealth of $100. There is a lottery...

Beth is an expected utility maximizing risk-averse individual with the utility function u(w) = w0.5 and initial wealth of $100. There is a lottery that pays $21 with probability 0.5 and $0 with probability 0.5. (a) Suppose Beth already owns the ticket to this lottery, in addition to her initial wealth. Find the smallest price Ps such that Beth would be willing to sell the ticket for this price. (b) Now suppose she does not initially own the ticket, and has to consider whether to buy one. Find an equation that implicitly defines the highest price Pb that she would be willing to pay to buy the ticket. You do not have to explicitly solve for Pb