Preference matching,income, and population distribution in urban and adjacent rural regions

We analyse the impact of preference matching and income on the distribution of the population in an aggregate economy of an urban and an adjacent rural region. It costs more (less) to live in the urban (rural) region. Individuals choose to live either in the urban or in the rural region. They differ in their incomes. These incomes are uniformly distributed on the unit interval. Our analysis leads to four results. First, when the cost differential parameter satisfies a condition, both regions are occupied in the equilibrium. Second, when this parametric condition holds, in any equilibrium in which the mean income of individuals varies across the two regions, every resident of the rural region has a lower income than every resident of the urban region. Third, there exists an income threshold and all individuals with higher (lower) incomes choose to live in the urban (rural) region. Finally, in the equilibrium with income sorting, it is possible to make everyone better off by slightly modifying their residential choices.