Final answer:
The equilibrium outcome in a city with a preference-based segregation model, where rich and poor individuals prefer to live with more rich people, is determined by solving for the intersection of the premium curves P(poor)= 0.9x² and P(rich)= 35x-0.1x².
Step-by-step explanation:
The student's question involves an economics concept of equilibrium in a market with a preference-based segregation model. In a hypothetical city with 200 people (100 rich, 100 poor) and two neighborhoods, people are willing to pay a premium to live with a higher percentage of rich people.
The equilibrium outcome would occur where the premium curves of the poor and the rich intersect. For the poor, their premium is represented by the equation P(poor)= 0.9x², and for the rich, it is P(rich)= 35x-0.1x², where x is the percentage of rich people above 50%. To find the equilibrium, we would set P(poor) equal to P(rich) and solve for x, which represents the percentage point above 50%.
However, without further information or computational resources, this response does not solve the equations to provide the equilibrium outcome. This concept is an example of how preferences and willingness to pay can shape the distribution of different income groups within a city's neighborhoods.