John, the owner of a family business, notices that when he works hard (a1) during the year the net income before manger compensation is $1,764 for 70% of the time, and $441 for 30% of the time. John recently had some issues and couldnt work hard. Because he shirked (a2) the net income has been $1,764 for 40% of the time and $441 for 60% of the time. To remediate, John decides to hire Oliver as a manager. Oliver is both risk and effort-adverse with utility equal to the square root of the amount of money received. His disutility of effort is 3.5, if he works hard, and 2.1 if he shirks. His reservation utility is equal to 7. Required (Take calculations to two decimal places). a. John suggests a salary of $85, Oliver accepts the offer. Which act would he take a1 (Work Hard) or a2 (Shirk)? b. John is not convinced that the contract offered to Oliver is the best possible contract. He decides to hire a consultant who advises him to offer a contract with a salary proportional to the net income (before manager compensation). Why does the consultant think that such a contract is better compared to the fixed salary offered in point a)? What proportion of net income should the consultant recommend? Show your computations. c. John is risk neutral, with utility equal to the amount of profit received after any managers compensation. Is John expected utility higher (or lower) under the contract offered in b) compared to the contract offered in point a)? Show you computations. d. Which act would Oliver take if offered the contract in point b)? Show your computations