As we have mentioned several times, the usual property tax is really two taxes: one levied on land value (or on land rents) and the other levied on the value of the “improvements” of land—or the rents from capital investments. The typical property tax simply sets the same tax rate for each part, but in an increasing number of places, governments are reforming property taxes to levy a higher rate on land than on improvements. Such a tax is called a split-rate property tax.
A. Suppose you are in a locality that currently taxes rental income from capital at the same rate as rental income from land. Assume throughout that the amount of land in the community is fixed.
(a) Which portion of your local tax system is distortionary and which is non-distortionary?
(b) Next, suppose that your community lowers the tax on capital income and raises it on land rents — and suppose that overall tax revenues are unchanged as a result of this reform. Do you think the tax reform enhances efficiency?
(c) Your community has a fixed amount of land—but capital can move in and out of your community and therefore changes depending on economic conditions. Do you think the land in your community will be more or less intensively utilized as a result of the tax reform—i.e. do you think more or less capital will be invested on it?
(d)What do you think happens to the marginal product of land in your community under this tax reform? What must therefore happen to the rental value of land (before land rent taxes
are paid)?
(e) Suppose half of your community has land that is relatively substitutable with capital in production— and the other half of your community has land that is relatively complementary to capital in production. Might it be the case that land values go up in part of your community and go down in another part of your community as a result of the tax reform? If so, which part experiences the increase in land values despite an increase in the tax on land rents?
(f ) Will overall output in your community increase or decrease as a result of the tax reform? Under what extreme assumption about the degree of substitutability of land and capital in production would local production remain unchanged?
(g) True or False: The more substitutable land and capital are in production, the more likely it is that the tax reform toward a split-rate property tax (that taxes land more heavily) will result in a Pareto improvement.
B. Suppose we normalize units of land so that the entire land area of a particular locality equals one unit. Economic activity is captured by the constant elasticity of substitution production function y = f (k,L) = (0.5L−1 +0.5k−1)−1. The government collects revenues through a property tax that taxes land rents at a rate tL and the rental value of capital at a rate tk — resulting in total tax revenue of TR = tLR +tk r̅K where R is the rental value of the 1 unit of land in the locality, r̅ is the interest rate in the local economy and K is the total capital employed in the locality. (Note that we have defined capital units such that the interest rate is equal to the rental rate of capital).
(a) Suppose that this locality is sufficiently small so that nothing it does can affect the global economy’s rental rate r —i.e. the supply of capital is perfectly elastic. If the locality taxes the rental value of capital at rate tk , at what local interest rate r̅ would investors be willing to invest here?
(b) Suppose that land is utilized optimally given the local tax environment—which implies that the marginal product of capital must equal r̅ . Define the equation that you would have to solve in order to calculate the level of capital invested in this locality.
(c) Suppose r = 0.06. Solve for the level of capital K invested on the one unit of land of this locality (as a function of tk ).
(d) Can you determine the rental value of land? (Hint: Derive the marginal product of land and evaluate it at the level of capital you calculated in the previous part and the 1 unit of land that is available.)
(e) Now consider the case where the local tax system is (tL , tk ) = (0,0.5). Derive the total capital K invested in the locality, the land rental value R, the value of land P (assuming that future income is discounted at the interest rate r = 0.06), the production level y and the tax revenue TR. (You may find it convenient to set up a simple spreadsheet to do the calculations for you).
(f ) Repeat this for the tax system (tL , tk ) = (0.05,0.3637), the tax system (tL , tk ) = (0.1,0.1748) and the tax system(tL , tk ) = (0.1353,0). Present your results for K, R, P, y and TR in a table (and keep in mind that r̅ changes with tk even though r remains at 0.06.) (Hint: All three systems should give the same tax revenue.)
(g) Use your table to discuss how the shift from a tax solely on capital (i.e. structures) toward a revenue-neutral tax system that increasingly relies on taxing land rents impacts the local economy. Which of the rows in your table could look qualitatively different under different elasticity of substitution assumptions?