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

maximizing choice of numeraire good z and house size q at each location (x,y) for given
land rent R and travel cost t,

z = α(m - tD(x,y))                                            (24)

q = (1- α)(m - tD(x,y))∕R                                        (25)

Similarly, we can solve for the land rent function,

R(x,y) = [α^α(1-α)(¹^^α)A(x,y)^β(m-tD(x,y))∕V]^ιz(¹^^α)                    (26)

Therefore, the equilibrium land price

P(x,y) = [σ^α(l-σ)' ^l-αιA(x.y)^β(m-tD(x.y))ZV]^{11 l-αι}Z(δ ■ τ)               (27)

which describes how equilibrium land price varies spatially with respect to open space
amenity A(x, y), income m, distance to the CBD D(x, y), the exogenous level of utility V,
and preference parameters, α and β.

To examine the effect of the size, shape, and location of preserved open space, we
need to further specify the location-specific open space amenity in relation to the spatial
structure of open space. Unfortunately, precisely describing open space amenity is an
empirical question, and there is no theoretical a priori on their quantitative representation
except some empirical findings regarding the spatial pattern of land value. Generally,
empirical studies have agreed on that 1) the further from preserved open space, the lower
property or land value; and 2) the larger preserved open space, the higher property or land
value. Since land rent (or price) is a monotonic function of open space amenity on that
land, these empirical findings may help discover an empirically effective measure of
open space amenities that is consistent with people’s perception. We adopted with some
modification a function used by Wu and Plantinga (2003) to describe open space amenity
that is consistent with those empirical restrictions

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