2.1 (15 points) Suppose the value a worker can create each week is $1000 if the worker is a high-ability one, and $500 if the worker is a lowability one. Workers can attend school, which, for the purpose of illustration, does not change the value each worker creates. However, years of school attended is publicly observable and veriable to every employer on the market. Every worker prefers higher wage and less school. But the utility function for a high-ability worker is given by UH = W 125w/E, where E is the years of schools attended. The utility function for a low- ability worker is given by UL = W 150E. (a) (10 points) Imagine employers offer the following wage scheme: \"your wage is $1000 if you attended schools for at least X years. Otherwise, your wage is $500.\" What is the maximal X such that employers can perfectly separate the two types of the workers through such wage scheme? (Hint: there are two IC conditions, one for low-ability workers, one for high ability workers. We solved the case of minimal education requirement in class, in which case ICL is binding. When solving the maximal education requirement, the ICH constraint should be binding. After you obtain your answer, verifying that ICL is also satised is optional, but it can help conrm your answer if you complete such step.) (b) (5 points) Because education in this model is a pure cost (it has no intrinsic value), the government may improve workers' welfare by imposing maximal education requirement. What would be the most efcient maximal education requirement the government can impose while still allowing education as a signaling device for a separating equilibrium? Round your number to the nearest (reasonable) integer. (Hint: the most e'icient maximal education requirement = the minimal years of education needed for a separating equilibrium.)