Consider the problem of optimal salary scheme design. Suppose that a bank principal (she) wants to hire a bank manager (he) to manage an investment project. The manager can shirk or work diligently. He can exert two levels of unobservable effort, high and low, with costs ch = 2 and c1 = 1. The output that can be observed is positively associated with effort and the high output is xh = 20 and the low output is xl = 10. The probability of generating different outputs is also positively associated with effort and has the relation ph = 0.8 > pt = 0.4. The principal cannot observe the manager's effort but can verify the output and decide that the salary depends on the output. Assume that the principal is risk-neutral. The manager has the utility function of u(x) = In(x) for any payment x > 0 with a dis-utility of zero for not working. Let s, be the salary associated with the high output and s, the salary associated with the low output. (a) Formulate the problem as a constrained maximisation problem and explain the objec- tive function and the incentive-compatible constraints in detail. (b) Derive the relationship between the two salaries s, and sy and calculate the two optimal salaries.