General Equilibrium Effects of a Property Tax: In Chapter 19, we introduced the idea that the property tax is really composed of two taxes: a tax on land, and a tax on improvements of land which we can think of as capital invested in housing.
A. For purposes of this problem, we focus only on the part of the property tax that is effectively a tax on housing capital. Assume, unless otherwise stated, that capital can move freely between housing and other uses.
(a) Begin by drawing a graph with housing capital h on the horizontal axis and the rental rate of housing capital rh on the vertical. Draw demand and supply curves that intersect at r ∗h and illustrate the impact of the property tax t on the rental rate r sh (t ) earned by suppliers of capital when considering this market in isolation.
(b) Next to your graph from part (a), illustrate the demand and supply curves for non-housing capital prior to the imposition of the property tax on the housing market. Where must the equilibrium rental rate r ∗ be in relation to the pre-tax equilibrium housing capital rental rate r∗h ? Given that capital is mobile between the two sectors, can the after-tax “partial” equilibrium you identified for the housing market in (a) be the “general” equilibrium for the housing market once we take into account the mobility of capital across sectors?
(c) What does your answer to (b) imply for what will happen to the supply curve for capital in the housing and non-housing sectors?
(d) Illustrate the new general equilibrium that takes into account the movement of capital across sectors in response to the property tax. What happens to the rental rate of capital in the no housing sector?
(e) In what sense is a portion of the property tax burden shifted to non-housing capital?
(f) Are renters of housing capital better or worse off as a result of the general equilibrium shifting of some portion of the tax burden across sectors? Will they consume more or less housing compared to the initial partial equilibrium prediction?
(g) True or False: The property tax will result in smaller houses and more investment in business machinery—but, if we do not take the general equilibrium effect of the tax into account, we will underestimate both how much smaller the houses will be and how many more business machines there will be.
B. Suppose that demand and supply for capital are identical in the housing and non-housing sector — taking the form kd (r ) = (A −r )/α and ks (r ) = (B +r )/β (as in the example of part B of the text). In this example, let A = 1, B = 0, α = 0.00000015 and β= 0.00000001.
(a) Begin by determining the equilibrium rental rates r ∗ and r∗h for non-housing capital and housing capital —and think of these as interest rates. How much capital is being transacted in each sector?
(b) Next, suppose that a tax of t = 0.04 is imposed through the property tax in the housing sector. If you assumed that there was no connection of the housing sector to any other sector of the economy, what would happen to the interest rate rsh received by suppliers of housing capital and the interest rate rdh paid by demanders of housing capital.
(c) Next, suppose that capital is freely mobile across the two sectors. How much capital will flow out of the housing sector? (Hint: You can treat this just like any other problem involving trade between two sectors where the starting prices are not equal to one another. The flow of capital is then just defined exactly like X∗ derived in the text. To apply this formula, you need to redefine the demand (or supply) curve in the housing sector to include the tax t = 0.04—which simply shifts A down (or B up) by 0.04.)
(d)What happens to the new equilibrium interest rate that suppliers of capital can get in the economy? In what sense has a portion of the property tax been shifted to all forms of capital?
(e) What happens to the rental rate of capital paid by consumers in the housing sector?
(f) Describe the general equilibrium economic incidence of the tax.