Entry-level computer engineers in Seattle can be either high or low ability. Demand for engineers is perfectly competitive. Employers cannot distinguish the ability of any single engineer from another. An employer's total profit increase by 12 (thousand dollars) when a high-ability engineer completes a task, and by 5 (thousand dollars) when a low-ability one completes a task. High-ability engineers have utility functionUH = W - .5T^2, where W is wage (in thousand dollars) andTis number of tasks performed. Meanwhile, low-ability engineers have utility functionUL = W - T^2

(a) (10 points) Suppose the employers design the following contract: "if you perform 5 tasks, you will be paid 5 (thousand dollars)per task; if you perform X number of tasks (X > 5), you will be paid 12 (thousand dollars)per task". Find Xmin, theminimalnumber of task X such that this contract achieves aseparatingequilibrium? (Leave your answeras it is. No rounding of Xminrequired)

(b) (5 points) Suppose the employers revises the contract as follows: "if you perform 10 tasks, you will be paid 5 (thousand dollars)per task; if you perform X number of tasks (X > 10), you will be paid 12 (thousand dollars)per task". Find Xmax, themaximalnumber of task X such that this contract still achieves aseparatingequilibrium? (Leave your answeras it is. No rounding of Xmaxrequired)