Suppose that the demand for housing in an urban area can be expressed as R 10;000

Suppose that the demand for housing in an urban area can be expressed as R ¼ 10;000 Q;

where R is annual rent and Q is quantity of housing units.The supply of housing is a function of the market value, V, of a unit, or V ¼ 50;000 þ 2:5 Q:

Assume that the real rate of discount is 6% and that the annual property tax is 2% of the value of a unit.

a. What are the market equilibrium quantity, annual rent, and market value?

b. Assume that the annual property tax is increased to 4% of market value. What happens to quantity, annual rent, and market value? How much of the increase in the tax is borne by the consumers of housing (tenants), and how much is borne by the owners of the housing?

c. Perform the graphical analysis mentioned in the text in which the supply of housing is fixed and the households are perfectly mobile across urban areas. What is the effect of reducing the property tax rate? Show using your diagrams.