Local Differences in Property Taxes: Since property taxes are set locally in the U.S., they differ across communities—with different communities therefore facing different taxes on housing capital. (Note: This exercise presumes you have already gone through exercise 20.9.)
A. Consider the “general equilibrium” effect of the property tax — i.e. the effect that results from the mobility of capital across sectors and is in addition to the initial “partial equilibrium” effect you predicted in part (a) of exercise 20.9.
(a) Does this general equilibrium effect become larger or smaller as the supply of non-housing capital becomes more elastic?
(b) Compare the following two cases: In case 1, only the local community i imposes a property tax t while in case 2, a national property tax t (of the same magnitude) is imposed across the whole country. Given your answer to (a), in which case are renters of housing capital in community i more affected?
(c) Now consider the case where all communities are imposing property taxes — but some are imposing higher property tax rates than others. We can then think of the national property tax system as having two components: First, there is an average property tax rate 
that is imposed across the country, and second, each community i has a supplemental local tax that may be positive or negative depending on whether it’s property tax rate lies above the national average or below. Treating the national average tax rate like case 2 in part (b), what do you think is the general equilibrium incidence of this portion of the U.S. property tax system?
(d) Now consider community i and suppose this community taxes property more heavily than the national average. Using your insight from case 1 in part (b), what do you think is the incidence of the portion of community i ’s tax that lies above the national average?
(e) How would your answer change for community j that taxes property at a rate below the national average?
(f) True or False: All else equal, community j will have larger houses than community i .
(g) True or False: The U.S. property tax system (in which local property tax rates vary across communities) results in a uniform decrease in the return on all forms of capital — with business decisions regarding non-housing capital being affected the same way across the country.
B. Suppose that the demand and supply for housing capital and non-housing capital are the same as in part B of exercise 20.9.
(a) Suppose that the local property tax system in the U.S. has resulted in an average property tax rate of  = 0.04. Use what you calculated in exercise 20.9 to determine the impact of this property tax system on the rate of return on capital for owners of capital.
(b) Suppose community i deviates from the national average—and sets a local property tax rate of ti = 0.05. What will be the rental rate received by housing capital suppliers — and what will be the rental rate paid by renters of housing capital in community i.
(c) Suppose community j deviates from the national average by setting a local property tax rate of only t j = 0.03. What will be the rental rate received by housing capital suppliers — and what will be the rental rate paid by renters of housing capital in community j?
(d) True or False: The entire difference in local tax rates between community i and community j is borne by renters; i.e. renters in community j pay a local rental rate that is less than the rate paid by renters in community i —with the difference equal to the difference in the local property tax rates.