Suppose that there are three types of workers: H, M, and L. Different types of workers have different wages: wH=9, wM=5, wL =1. There are three neighborhoods they can choose to live in: A,B,C. Different neighborhoods have different natural amenities: A =7, B = 4, C = 1. Total amenities a neighborhood offers depend on the natural amenities and average income of those living in the neighborhood: Ai = i*Ei(w) where i=A,B,C. The utility of type j workers living in neighborhood i is wj*Ai-Ri where Ri is the equilibrium rent in neighborhood i. Assume that each type occupies one and only one of the neighborhoods. Find all possible equilibrium location patterns (i.e., who live where). Justify your answer.