1. A salesperson can choose either high effort or low effort selling a water bottle. If she works hard. she can successfully sell the bottle with 100% probability. at an effort cost of 10. Ifshe does not work, she can sell it with probability one half. at a lower effort cost of 0. Assume the salesperson does not have any outside options. The salesperson's effort is not observable. Her compensation scheme is as follows: she receives a wage of 15 if she successfully makes the sales and receives a wage of 0 if unsuccessful. The salesperson's utility is her wage minus cost of efforts. a. What is the salesperson's welfare if she decides to work hard? 1:. What is the salesperson's welfare if she does not work? c. Under this compensation scheme. will the salesperson work hard or not work? A manager oversees the perfonnance of the salesperson and designs the compensation scheme. If the bottle is successfully sold. the manager receives a utility of 40. If the sale is unsuccessful. the manager receives a utility of 30. The manager's total payoff is her utility from sales minus the wage paid to the salesperson. :1. Suppose the manager now considers two compensation schemes. One is the above scheme: pay the salesperson 15 if successful and 0 otherwise (this is a high-powered incentive scheme]. The second scheme is to pay the salesperson 5 no matter what [a low-powered incentive scheme}. Which scheme should the manager choose? e. Briefly explain why xed salary works better than pay for performance in this scenario