Please answer the above

Consider a society 3 consisting of 2211 students, and ill/1' schools each with place Jfor 2 students. Each student has a pre-schooling human capital ed, and will attain a post-schooling human capital kg. The post-schooling human capital of a student 3' with pre-schooling human capital eg- attending school 3' is 3 1 hm = ()(4,j) where e_,;,j is the preschooling human capital of the student other than 2' attending school 3'. (Thus if two students each with preschooling capital of 2 enter a school, they each leave with post- school capital of 4.) a. Show that, to maximize the sum of postschooling human capitals in society, 23-65 hi, the two students with the highest pre-schooling human capital should be allocated to one school, then the next two students with the highest pre-schooling human capital should be allocated to another school and so on. b. Suppose that parents maximize wh p, where w is the wage-rate and p is their cost of schooling. Show that the following pricing strategy will maximise the sum of postschooling human capitals: each school chooses some cost of attendance (tuition) psi and accepting all students who want to attend at this price. [Suggestiom Consider a given student with preschool capital 3:. Find the increase in his post school income when he goes to school with a peer of ability 3;, and when he goes to school with a peer of ability 3; + A. How much is he willing to pay for the extra A? How does this willingness change with 6?] c. What could go wrong with this decentralization scheme? d. Now suppose that the postschooling capital is given by | NIH 1 l hi : 28+_ 583.28 2' Can this allocation be decentralized in the same manner as in part b.? If not, why not