1. Consider this simple example of the Rothschild and White model. There are fivestudents and three universities, each of which can enroll at most two students.The table below shows the amount of human capital that each student wouldaccumulate at each university and the cost of the resources that would be usedto generate this human capital.StudentABCDEH1371248H2491049H371013610Y1061168Y246666Y3581137a. How would a social planner choose to allocate students to universities tomaximize social surplus (total human capital created minus the costs ofgenerating this human capital)?b. What tuition levels would each university charge each student in order toimplement the allocation from part (a) in a decentralized way while makingzero profits?2. You are asked to consult on the curriculum design of a high school system. Youare choosing between a system that teaches all students the same subjects (amix of vocational and college preparation classes) for all but their last year inhigh school and then lets them choose to take either vocational or collegepreparation courses in their final year and a system that tracks students intoeither vocational or college preparation classes for their entire high school careerbased on their decision at the beginning of high school. This question is based onthe Malamud paper.a. Discuss the differences in the level of preparation for post-high-schoolstudies or careers of students under each system.b. Discuss the differences in the amount of switching from one track to doingsomething unrelated after high school (e.g. following the college prep trackin high school then working as a mechanic for several years after highschool graduation) under each system.c. What type of students will do better under the first system? What type ofstudents will do better under the second system? Which system do youexpect to be better for students overall?3. You want to measure the impact on housing prices of the quality of the local highschool football team.a. Write a hedonic pricing regression equation that would allow you tomeasure this effect while controlling for other important determinants ofhousing prices.b. You are concerned that football team quality may be correlated withunobserved characteristics of houses. Describe how you could use aregression discontinuity approach to resolve this problem.