(Expected utility maximization) Nick is a risk-averse person with a concave utility function u(w) = w, where w denotes wealth. His original wealth is w = $400. Nick believes that with probability 0.3, a burglary will happen at his home, which will cause him to suer a nancial loss of $250. (i) Facing this potential risk of burglary, he is now choosing among the following three mutually exclusive ways to cope with this potential risk. A. Do nothing. B. Purchase a complete coverage policy oered by an insurance company. If Nick purchases this insurance policy, the insurance company will compensate him for all of his nancial loss in the event that a burglary occurs. Currently, the insurance company charges a premium of $76 for this complete coverage policy. C. Install an alarm system that will reduce the probability of the occurrence of a burglary from 0.3 to 0.1. The cost of installing the alarm system is $39. Determine Nick's expected utilities under each of the possible scenarios. Which course of action would you recommend him to take? (ii) Now suppose that Nick's wealth and loss scenario are as given above, i.e., his wealth is $400 and with probability 0.3 he