Question

There are two types of residents in Brookline and Boston, professors and students. Professors have an income of Y = 200; students have an income of Y = 100. Both Brookline and Boston provide road repair services for their citizens. Professors value road repair more than students because they have nicer cars. In fact, the value of road repair to each individual takes the form (Y × R)/10 - R2/2. The per-resident cost of road repair is 5R. a) What is the marginal value of road repair for each type of individual?

Answer 1

The marginal value of road repair for professors is 19R, while for students it is 9R. This is derived by differentiating the given utility function with respect to R for each type of individual.

Step-by-step explanation:

The student's question pertains to the marginal value of road repair for professors and students in the context of their incomes and how each group values road services.

The given utility function for the value of road repair is (Y × R)/10 - R^2/2, where Y represents income and R is the amount of road repair.

To find the marginal value, we differentiate this function with respect to R. For professors, Y=200, the marginal value is (200 × R)/10 - R which simplifies to 20R - R or simply 19R.

For students, Y=100, it is (100 × R)/10 - R which simplifies to 10R - R, or 9R. Note that the marginal cost for road repair for all is given as 5R.