Question 4 [MIT] Consider a society S consisting of 2M students, and M schools each with place for 2 students. Each student has a preschoong human capital e,;, and will attain a post-schooling human capital In. The postschooling human capital of a student 2' with pre-schooling human capital 3,: attending school j is 3 1 kg; = (805 (lgm) 5 where 34\"., is the pre-schooling human capital of the student other than i attending school 3'. (Thus if two students each with pre-schooling capital of 2 enter a school, they each leave with post- school capital of 4.) a. Show that, to maximize the sum of post-schooling human capitals in society, 2168 kg, the two students with the highest preschooling human capital should be allocated to one school, then the next two students with the highest preschooling 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 post-schooling human capitals: each school chooses some cost of attendance (tuition) p,- and accepting all students who want to attend at this price. [SuggestiOm Consider a given student with preschool capital 2:. Find the inerease in his post- school income when he goes to school with a peer of ability y, and when he goes to school with a peer of ability 9 + A. How much is he willing to pay for the extra A? How does this willingness change with 3?] c. What could go wrong with this decentralization scheme? d. Now suppose that the post-schooling capital is given by I NIH i 1 i h, = 26,; +e_ E338 Can this allocation be decentralized in the same manner as in part b.'? If not, why not