part?b?? No.iv and No.v. plz?

Suppose you are faced with the following decision under uncertainty. You are considering buying a signed Connor McDavid Jersey. Your purchase is based solely on the hope of reselling the jersey in one year after McDavid has another season to show off his abilities. You currently have $200. The strength of the resale market for Edmonton Oilers Memorabilia varies dramatically with the performance of the team and Connor McDavid. Therefore, you face an uncertain outcome. Two outcomes can arise, the Oilers and McDavid can have a bad season (w_1) or a good season (w_2). If the Oilers and McDavid have a bad season, you can resell the jersey for only w_1 = $50. If the Oilers and McDavid have a good season, you can resell the jersey for w_2 = $650. Suppose you believe that the Oilers will have a bad season with probability p_1 = 0.75 and the probability of a good season is p_2 = 1 - p_1 = 0.25. Suppose there is no time discounting associated with payoffs (i.e., $1 today equals $1 in one year). What is the expected income and variance of this lottery? Suppose your utility function for receiving income x is given by: u(x) = alpha Squareroot x where alpha > 0 is a constant. Should you stick with the $200 with certainty or should you take the potential lottery? Does this answer depend on the value of a? Explain. Illustrate this problem graphically. Does Jensen's Inequality hold? Illustrate why or why not. How would your answer to part (i) change if w_2 = 1400 and alpha = 2? Suppose alpha = 2 and w_2 = 650 (the original problem). Compute the risk-premium of this lottery. Illustrate the Risk Premium Graphically. Now treat the probability p_1 as an arbitrary constant. Suppose alpha = 2 and w_2 = 650 (the original problem). Is there a feasible value of p_1 where you would accept this lottery over the certain payoff of $200? (Recall p_2 = 1 - p_1)