2. Consider a town with two neighborhoods: A and B. Under the status quo, which we call neighborhood schools, there are two schools, one in each neighborhood, and all kids in a given neighborhood go to their neighborhood school.

The town is considering adding a selective enrollment school. If they do, the kids with the highest standardized test scores in each neighborhood will go to the selective enrollment school. This will benefit those kids, by giving them access to more advanced classes and a higher percentage of peer students who are performing at an advanced academic level. We denote the size of the benefit to these kids by b > 0 (which is some amount of utility). But it will hurt the

kids who remain in the neighborhood schools by decreasing their resources and removing some of their most academically talented peers. We denote the size of the cost to these kids by c > 0.

We think of there being four groups of people in this society. An are the kids from neighborhood A who will remain in the A neighborhood school no matter what, As are the kids from neighborhood A who will be admitted to the selective enrollment school if it is created, and likewise for Bn and Bs. Suppose that An an Bn combined make up 75% of the population, while As and Bs combined make up 25% of the population.

Utilities under each of the two policies are given by the following:

An As Bn Bs

Neighborhood Schools Selective Enrollment School

100 100c 100 100+b 100 100c 100 100+b

B)Identify some b and c (i.e. fill in actual numbers for them) such that neighborhood schools is the utilitarian optimum. (Remember that An and Bn are 75% of the total population and As and Bs are 25% of the total population.)