2.2. (15 points) In the recorded lecture we reviewed the following screening problem: suppose a software engineer can be either high or low-ability. An employer's total prot increase by 10 (thousand dollars) when a high-ability engineer completes a task, and by 5 (thousand dollars) when a low- ability one completes a task. Highability engineers have utility function UH = W 0.4T2, where W is yearly wage (in thousand dollars) and T is number of tasks performed. Meanwhile, low-ability engineers have utility function UL = W 0.5T2. That is, both types of engineers prefer higher wage and fewer tasks. However, high-ability engineers have a lower marginal cost of performing an additional task. The employers cannot observe the type of each engineer. (a) (10 points) Suppose the employers design the following \"screening\" contract: \"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 10 (thousand dollars) per task\". What is the minimal number of task X such that this screening contract achieves a separating equilibrium? Round your answer to the nearest (reasonable) integer. (Hint: follow the recorded lecture and set up the IC condition for both the low-ability and the high-ability engineers. To find the minimal X, the IC condition for low-ability engineers needs to be binding) (b) (5 points) In part (a), what is the maximal number of task X such that this screening contract still achieves a separating equilibrium? Round your answer to the nearest (reasonable) integer. (Hint: if X is too high, the high-ability engineer would prefer to choose the lowwage, fewtask combination designed for low-ability engineers. Like how you solve problem 2. 1 (a), this means you need to set the IC condition for highability engineers to be binding. You may nd the following result useful: 0.4T}? 10TH + 10 = 0.4[(TH 12.5)2 131.25].)