US data reveals poor and rich households are imperfectly sorted across municipalities within a state. In 2000 in the average state, 85% of the richest municipality and 20% of the poorest municipality had incomes above median state income. However, standard theories such as Tiebout (1956) imply that households are perfectly sorted in income across municipalities based on their demand for local public goods. Ignoring poor (rich) households in the rich (poor) municipality, as previous theories do, biases the predictions of these models. For instance, per household public spending levels and housing prices would be underestimated (overestimated) in poor (rich) municipality. This paper has two objectives: 1) Provide a quantitative theory, which is a simple generalization of Tiebout (1956), that is consistent with imperfect income sorting 2) Using this theory, analyze property tax competition policy and mixed income housing policy. To achieve first objective, I introduce probabilistic location choice, captured via lotteries along the lines of Prescott and Townsend (1984), into Tiebout (1956). The model calibrated to Rhode Island data, predicts 85% of the richest municipality and 12% of the poorest municipality had incomes above median state income. Moreover, differently from previous literature and consistently with data, model predicts imperfect income sorting among municipalities after controlling for rent share in income and imperfect income sorting among census tracts. Counterfactual experiments show that mixed income housing policy and property tax rate competition across municipalities decreases income sorting by 56% and 17% respectively.
    This paper provides a median voter theorem for an economy where heterogeneous income households can opt out of public education. Policy analysis of such economies proved difficult since majority voting equilibrium and decisive voter may not exist as argued in Stiglitz (1974). Differently from Stiglitz (1974) and consistently with empirical evidence, I model private schools as monopolistically competitive firms with decreasing average costs over enrollment. In my model, there are a finite number of different quality private schools each having a different tuition. Public school spending is financed by income tax revenue collected from all households. The tax rate is determined by majority voting. In my model when income tax rate increases, enrollment increases in public schools and decreases in private schools. This increases tuition and per pupil spending in private schools. With Cobb-Douglas utility, income effect is dominated by substitution effect for households choosing private schools and they favor increases in tax rate up to some cutoff. Preferences over tax rates turn out to be single peaked and therefore a majority voting equilibrium exists. Moreover median income household is the decisive voter. These results hold for any income distribution function and any finite number of private schools.