Simplify (11)
P(a +a0) ≥----10---[---aδ-Tr + (L - a0)]
(12)
P(a0) L -a0 -a τw(1 - e-δT )
Inequality (12) identifies the relationship among policy parameters, such as the financing
period T and property tax rate τ, residents’ bid price for land, and the incremental amount
a of open space, if preserving open space a is to be financed by property tax increment.
Note that this inequality is derived based on a balanced budget for an arbitrary amount of
open space a between 0 and L - a0, the total available land. For alternative settings of
policy context, (12) can be relied on to examine policy variables of interest. For
example, if local land managers know how land rent changes with preserved open space,
inequality (12) can be used to determine the amount of open space that can be financed
by property tax increment for given policy parameters. On the other hand, (12) can also
be used to identify the restriction on households’ bid price for land and other policy
variables if land managers intend to use tax increment to finance open space preservation.
To identify a weaker condition for using property tax increment to finance open
space a, we allow an infinite financing period, T = +∞. Correspondingly, (12) becomes
P(α + a0)
P(a0)
______1_
L - a0
_[ aδ + ( L — a 0)]
a τw
(13)
As before, we examine the property of the self-financed amount of open space by
comparing the locus of two independent functions of preserved open space involved in
inequality (13). Let Ψ(a) = P(a + a0)/P(a0), which represents the ratio of bid price per unit
land with and without preserved open space as a function of preserved open space, and
1 aδ 0
Φ(a) =-----0----[--+ (L - a )], which represents the critical value of the bid price
L - a0 - a τw
13