Mortgage Interest Deductibility, Land Values and the Equilibrium Rate of Return on Capital: In the text, we suggested that the property tax can be thought of in part as a tax on land and in part as a tax on capital invested in housing. In the U.S., property taxes are typically levied by local governments—while the major piece of federal housing policy is contained in the federal income tax code which allows individuals to deduct (from income) the interest they pay on home mortgages prior to calculating the amount of taxes owed.
A. Whereas we can think of the property tax as a tax on both land and housing structures, we can think of the homeownership subsidy in the federal tax code as a subsidy on land and housing structures.
(a) If your marginal federal income tax rate is 25% and you are financing 100% of your home value, how much of your housing consumption is being subsidized through the tax code? What if you are only financing 50% of the value of your home?
(b) Suppose homeowners are similar to one another in terms of their marginal tax rate and how much of their home they are financing, and suppose that this implies a subsidy of s for every dollar of housing/land consumption. How would you predict the value of suburban residential land (assumed to be in fixed supply) is different as a result of this than it would have been in the absence of this policy?
(c) When s was first introduced, who benefitted from the implicit land subsidy: current homeowners or future homeowners?
(d) Now consider s as a subsidy on housing capital. Do you think houses are larger or smaller as a result of the federal income tax code?
(e) Suppose that the overall amount of capital in the economy is fixed and that capital is mobile across sectors. Thus, any given unit of capital can be invested in housing or alternatively in some other non-housing sector where it earns some rate of return. If the overall amount of capital in the economy is fixed, what happens to the fraction of capital invested in the housing sector?
(f) What would you predict will happen to the rate of return on capital in the non-housing sector? Explain.
(g) True or False: Even though only housing capital is statutorily subsidized, the economic incidence of this subsidy falls equally on all forms of capital (so long as capital ismobile between sectors).
B. Suppose we model owners of capital as a “representative investor “who chooses to allocate K units of capital between the housing sector and other sectors of the economy. With k1 representing capital invested in housing and k2 representing capital invested in other sectors, suppose f1(k1) = αk10.5 and f2(k+) = βk20.5 are the production functions of the two sectors.
(a) In the absence of any policy distortions, calculate the fraction of total capital (K) that is invested in the housing sector.
(b)What changes as a result of the federal income tax code’s implicit housing subsidy s.
(c) What happens to the marginal product of capital in the non-housing sector?
(d)What happens to the equilibrium rate of return on capital?
.(e) True or False: The general equilibrium subsidy incidence of the implicit subsidy of housing capital falls equally on all forms of capital.