3. A salesperson in a bookstore sells books for 50 each. The cost of the books to the store is 30 each. The number of books the salesperson sells in a week is equal to q=Ze+v where e represents the effort the salesperson puts in, and v is luck (on average 17 = 0). The salesperson is paid a base salary plus a commission on every book sold, so that her weekly earnings are equal to w=a+bq Utility depends on earnings and on the effort level (which can be any positive real number), and is given by U=w 2 which reects the fact that the salesperson does not like putting in effort. (a) Assume a = 50 and b = 10. If the salesperson maximizes utility, which level of effort will she choose, how many books does she sell, and what are her expected weekly earnings (i.e. assuming v = 0)? (b) With the parameters as in (a), calculate the expected prots of the bookstore, assuming the only costs are the cost of the books and the wage paid to the salesperson. (c) The employer experiments with letting the salesperson keep the entire mark-up on the book, i.e. 20. If the employer wants the salesperson to have the same utility as in (a), what will the value of a be? (d) What would the effort of the salesperson be under the parameters in (c), how many books does she sell, what are her expected earnings, and what are prots for the bookstore? (e) Explain why the quantity sold under the new scheme is greater than the quantity sold under the old one. What are some potential problems using this new scheme