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Economics of Migration and Job Search: Problem Set 3

1. Suppose workers prefer low s locations but firms prefer high s locations, what would the Roback model predict in terms of relative wages and rents between city 1 and

2 where s1 < s2 ? Use a diagram, explain the intuition and give an example of such amenities.

2. Now allow each individual to have idiosyncratic preference shocks.  The utility of person i for living in city c with skill level s, where s ∈ {h, l}, is

uics = βws(wcs−t)−βrsrc+βAsAc+eics

6cs

where wcs  is city c’s wage for skill level s, rc  is the local rent, Ac  is amenities, t is a common lump sum tax, β \s are preference parameters (note that these differ by skill level), eics  is a taste shock, independent and drawn from type-1 extreme value distribution. Suppose there are three cities. According to the data, the city population shares of high skilled people are: s1h  = 0.3, s2h  = 0.5, s3h  = 0.2; and those of low skilled people are: s1l  = 0.4, s2l  = 0.2, s3l  = 0.4.

(a) Calculate the mean utility 6cs in all locations.

(b)  [optional ] Now suppose people do not differ by skill level. Given 6c, explain how to decompose the mean utility into values for wage, rent and amenity.