In most Western democracies, it is settled law that governments cannot simply confiscate land for public purposes. Such confiscation is labeled a “taking”— and, even when the government has compelling reasons to “take” someone’s property for public use, it must compensate the landowner. But, while it is clear that a “taking” has occurred when the government confiscates private land without compensation, constitutional lawyers disagree on how close the government has to come to literally confiscating private land before the action constitutes an unconstitutional “taking”.
A: Any restriction that alters the way land would otherwise be used reduces the annual rental value of that land and, from the owner’s perspective, can therefore be treated as a tax on rental value.
(a) Explain why the above statement is correct.
(b) Suppose a land use regulation is equivalent (from the owner’s perspective) to a tax of t% on land rents to be statutorily paid by landowners (where 0< t < 1). How does it affect the market value of the land?
(c) I am about to buy an acre of land from you in order to build on it. Right before we agree on a price, the government imposes a new zoning regulation that limits what I can do on the land. Who is definitively made worse off by this?
(d) Suppose you own 1000 acres of land that is currently zoned for residential development. Then suppose the government determines that your land is home to a rare species of salamander— and that it is in the public interest for no economic activity to take place on this land in order to protect this endangered species. From your perspective, what approximate tax rate on land rents that you collect is this regulation equivalent to? Do you think this is a “taking”?
(e) Suppose that, instead of prohibiting all economic activity on your 1000 acres, the government reduces your ability to build residential housing on it to a single house. How does your answer change? What if it restricts housing development to 500 acres? Do you think this would be a “taking”?
B: Suppose that people gain utility from housing services h and other consumption x, with tastes described by the utility function u(x,h) = lnx +lnh. Consumption is denominated in dollars (with price therefore normalized to 1). Housing services, on the other hand, are derived from the production process h = k0.5Lα where k stands for units of capital and L for acres of land. Suppose 0 < α < 1.
Let the rental rate of capital be denoted by r , and assume each person has income of 1000.
(a) Write down the utility maximization problem and solve for the demand function for land assuming a rental rate R for land. as
(b) Suppose your city consists of 100,000 individuals like this—and there are 25,000 acres of land available. What is the equilibrium rental rate per acre of land (as a function of α)?
(c) Using your answers above, derive the amount of land each person will consume.
(d) Suppose the government imposes zoning regulations that reduce the coefficient α in the production function from0.5 to 0.25. What happens to the equilibrium rental value of land?
(e) Suppose that what you have calculated so far is the monthly rental value of land. What happens to the total value of an acre of land as a result of these zoning regulations assuming that people use a monthly interest rate of 0.5% to discount the future?
(f ) Suppose that, instead of lowering α from 0.5 to 0.25 through regulation, the government imposes a tax t on the market rental value of land and statutorily requires renters to pay. Thus, if the market land rental rate is R per acre, those using the land must pay tR on top of the rent R for every acre they use. Set up the renters’ utility maximization problem, derive the demand for land and aggregate it over all 100,000 individuals. Then derive the equilibrium land rent per acre as a function of t (assuming α = 0.5).
(g) Does the amount of land consumed by each household change?
(h) Suppose you own land that you rent out. What level of t makes you indifferent between the zoning regulation that drove α from0.5 to 0.25 and the land rent tax that does not change α?
(i) Suppose the government statutorily collected the land rent tax from the owner instead of from the renter. What would the tax rate then have to be set at to make the land owner indifferent between the zoning regulation and the tax?