2. Assume that there is a neighbourhood that contains one public high school, called School 1 (denoted by S1). Across town, there is a private school called School 2 (denoted by S2). Consider 2 high school aged students, Student A and Student B. Neither student is able to afford the private school tuition on their own. Student As utility is given by UA = S1 + 2S2, where S1 = 1, S2 = 0 if they are enrolled in their local public school, or S1 = 0, S2 = 1 if they are enrolled in the private school across town. Student B has not performed as well academically as Student A. Student B does not meet the admission requirements of School 2. This student attends School 1 and has a utility of UB = S1 = 1. a) The local school district pays the cost for both students to attend School 1. If neither students family is able to afford the cost of School 2 on their own, what will be the utility of each student as well as their combined utility? (7 points) b) Imagine that the school district decides to give Student As family a school voucher. This voucher would allow them to attend either School 1 or School 2. What decision would Student A make, what would be their utility, and what would be the combined utility of Student A and Student B? (7 points) c) Is the combined utility higher when Student A is given a school voucher? Explain why 2 or why not? (7 points) d) Imagine that Student B receives a utility benefit if Student attends the same school as them. This can be thought of as a peer effect or a positive externality. Student Bs utility is now UB = S1 + 2 I, where I = 1 if Student A attends School 1 and I = 0 otherwise. What is the combined utility of the two students if Student A chooses to attend School 1? (7 points) e) What is the combined utility if Student A chooses to attend School 2? (7 points) f) What decision would Student A make? (7 points) g) Is this the decision that results in the highest combined utility? Explain why or why not. (8 points)