Tax Increment Financing for Optimal Open Space Preservation: an Economic Inquiry

~

where P(a⁰ + a) is the post-preservation equilibrium land price independent of spatial

location such that π∫^r0 P(A(a⁰ + a, r))dr² =π∫^r0 P^~(a⁰ + a)dr² .
ra 1                                                     ra1

Similarly,

∫^r0 P(A(a⁰,r))2πrdr = πP^~(a⁰)(r₀² - r_a²₀)
ra0

where P^~(a⁰) is the pre-preservation average equilibrium land price independent of
spatial location. If we still assume the total area of community land is L, the total value
of the remaining land after preservation becomes P^~(a⁰ + a)(L - a⁰ - a), and the total
value of the land before preservation is P^~(a⁰)(L - a⁰) . Therefore, the spatial model of
tax increment financing of socially efficient open space transforms into
~

Max π = P(a⁰ + a)(L - a⁰ - a) - P(A(a⁰,r₀))a                  (20)

a

s.t. ∫ [τP^~(a⁰ + a)(L - a⁰ - a) -τP^~(a⁰)(L - a⁰)]we^-δtdt ≥ P(A(a⁰,r₀))a (21)
0

which is exactly the same as the non-spatial model except that the equilibrium land price
is replaced by some spatial average value. Therefore, the basic conclusion based on the
non-spatial model would not change except the non-spatial equilibrium land price
replaced by the spatial average land price.

Practically, to evaluate the condition for the self-financed, socially efficient
amount of open space for communities with given parameters requires estimation of the
marginal change rate of equilibrium land price, or residents’ WTP, at both pre- and post-
preservation levels of preserved open space. The equilibrium land price may exhibit a
spatial pattern rather than a spatially homogenous rate of capitalization when
communities or cities are sufficiently large, but often when tax increment financing is

21

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