2. Recall the model of neighborhood sorting of Guerrieri, Hartley and Hurst. Let households of Type 3, for s = R, P have utility given by: warm) = [ozlnc+ (1 a)lnh] [A + Hon\" 0 0, (1) where c: is non-housing consumption. h: is consumption of housing services 3:: is the location where the household chooses to live. H (:13) is the externality associated with the fraction of high-income residents at :r. a. What is the role of the parameter A? b. Suppose that a Type-s household has income yg, with yR > yo and pays rent Ram) for each unit of housing services at their preferred location, 3:. Derive their demands for housing services, ham) and @(x) as functions of ys and RS(:B). c. Suppose there is an equilibrium with full segregation, explain why high income households who live relatively near low income neighborhoods pay lower rent and consume more housing. (1. Do you know which type of household lives near the periphery of the city? Why do they do so