ratio δ∕(τw) is greater than 1, the necessary condition for the socially efficient amount of
P'(a0) 1 δ
open space to be self-financed may be defined by — >------(1 +--). Note that
P(a0) L - a0 τw
these two conditions only guarantee the existence of the socially efficient amount a* and
the self-financed amount at, but remain neutral on the relative magnitudes of a* and at.
Therefore, as long as the standardized residents’ current WTP for open space, or the
marginal change rate of the equilibrium land price with respect to preserved open space,
1δ 2
is great than the larger of------(1 +--) and------- there exists at least a self-financed
L - a- τw L - a-
amount at of open space, and may exist a socially efficient amount a* that can also be
covered by increased tax revenue, depending on the relative magnitudes of at and a*.
Unfortunately, the relative magnitude of at and a* is not explicit. We proceed by
examining the condition required of residents’ WTP under which the socially efficient
amount a* of open space can be fully covered by property tax increment, i.e., a* < at. We
define the following system for the set Γ such that ∀a*∈Γ is socially efficient and can
also be fully financed by property tax increment: 1) the socially efficient amount a* of
P'(a + a*) 1
open space, ——--— = —---
P(a- + a* ) (L - a-
amount at of open space,
P(a)
-ʒr(l +--—ɪ) ; 2) the maximum self-financed
* -*
a*) P(a- + a*)
P(a0 + at )
P(a0)
1 atδ
------0----- [--+ (L - a0)]; 3) the self-financing
L - a-- at τw
condition,
P(a + a0)
P(a0)
1 .(∣δ
0 0 [ _
L - a - a τw
+ (L - a0)] for a < at; 4) the socially efficient
amount a* being self-financed, a* ≤ at.
Conditions 3) and 4) lead to
P(a* + a0)
P(a0)
1
0 0 *
L-a -a
[aδ + ( L — a0)]
τw
(14)
16