A company decides whether and how to induce a manager to put in high effort to increase the chances that the project succeeds. Unfortunately, the manager's effort is unobservable. The value of a successful project is $1 million; the probability of success given high effort is 0.5; the probability of success given low effort is 0.25. The manager's utility is the square root of compensation (measured in millions of dollars), and his disutility from exerting high effort is 0.1. The reservation wage of the manager is $160,000. To induce high effort, the company plans to offer the manager a contract pair (y, x) - where y is the salary given for a successful project and x is the salary given for a failed project. The contract pair (y, x) should satisfy the voluntary participation constraint: "sqrt(y) + 'sqrt(x) - 2 sqrt( and the incentive compatibility constraint: 'sqrt(y) + 'sqrt(x) *sqrt(y) + "sqrt(x) Hint: Write a probability as a decimal number. For example, write 50% as 0.5. Also, use $1 million as a measurement unit. For example, write $160,000 as 0.16