In Metropolis, there are three types of houses: expensive, medium, and cheap. All households – regardless of what type of house they have – have the same marginal benefit curve for open space, which is a public good. Households can sort into different municipalities if they wish to.

a) Suppose that the provision of open space is financed with a head tax. What is the equilibrium number of municipalities? Briefly explain why.

b) Suppose instead that the provision of open space is financed with a property tax based on the market value of the house.

i) What is the equilibrium number of municipalities?

ii) Would households who have expensive houses want to live in the same municipality as households who have cheap houses? Why or why not?

c) Suppose instead that the provision of open space is financed with a square-foot tax, e.g., $2 per square foot of living space per year. Under what circumstances will there be only one municipality in equilibrium?