U " U "U '+U 'U "
R"(a) = —— > 0, and R"(α) = ——z——— < 0
U " U '2
zz
which indicate that the equilibrium land rent is increasing with the amount of preserved
open space at a decreasing rate.
For a community with preserved open space a, the equilibrium price per unit land
P(a) is the present value of the flow of equilibrium land rent net of property tax in an
infinite horizon, i.e., P(a) = (R(a)-P(a)τ)∕δ, where δ is the discount rate, and τ is the
property tax rate. Further, equilibrium land price P(a) can be solved as P(a) = R(a)∕(i+τ).
That is, equilibrium land price equals equilibrium land rent divided by the sum of the
discount rate and the property tax rate. Similarly, the equilibrium land price in the
community increases with preserved open space at a decreasing rate, P’(a) > 0, P”(a) ≤ 0.
This linkage between equilibrium land price and preserved open space shows how
property value would respond to open space preservation in a dynamic setting, which
constitutes the basis for using property tax increment to finance investment in open space.
The context for exploring the potential of using property tax increment to finance
open space preservation is set up by a community with a total land area L and a units of
preserved open space that may or may not be socially optimal. Suppose land in this
community, except those preserved as open space, is privately owned by decentralized
absentee landowners. The local land manager is concerned with the negative effect of
urban sprawl, and decides to preserve more open space to protect against the welfare loss
of local public. A practical question confronting him at the very beginning is how much
more open space land need to be acquired for preservation that is socially optimal. The
land manager, informed by policy analysts, knows that economic efficiency requires
preserving open space up to a level such that the marginal benefit of preserving open