Question

Professors and Students (2) Again, consider a city with 100 professors and 100 students and two ucighborhoods (A and B). There are 100 lots in each city so the namber of professors and students in each cities must add up to 100. A professor's indirect utility for living in a neighborhbod is given by: V i (I i , S i ,f i)=1.7(Ii−I i )−I i Where L 5 , and L F, are the mumber of students and protessors living in neighborhood i, respectively. A student's indirect utility for living in a neighborhood is given by: V i(I i S P P i ,I i )=1.5(I iS−I i )−L i

​ a. What are all of the equabbium point(s)? List the equilibria in terms of the number of students in neighborbood A. Aho, for each of the equilbria listed, state whether it is stable or unstable.

Answer 1

In this question, we are given the indirect utility functions for professors and students in two neighborhoods, A and B, and we need to find the equilibrium points and determine their stability.

Step-by-step explanation:

In this question, we are given the indirect utility functions for professors and students in two neighborhoods, A and B. The professor's indirect utility for living in neighborhood i is given by Vi(Ii, Si, fi)=1.7(Ii−Ii)−Ii. The student's indirect utility for living in neighborhood i is given by Vi(Ii, SP, Pi, Ii)=1.5(IiSP−Ii)−Li.

To find the equilibrium points, we need to set the utility functions equal to each other and solve for the number of students in neighborhood A. The equilibrium points occur when the number of students in each neighborhood adds up to 100. The stability of each equilibrium point can be determined by analyzing the slope of the utility functions.