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

A(x,y) = 1 + e^-Yd^{(x,y|xo,yo,s)}a(xo,yo)                        (28)

where d(x,y|x0, y0, s) denotes the distance from any location (x,y) to the open space at
(x0,y0) with shape s, and γ is the dissipating parameter of open space amenity.

By this specification, open space amenity decreases with the distance from and
increases with the size of preserved open space. The shape s affects amenity level
through its effect on local accessibility of open space measured by the distance from each
land parcel to the edge of preserved open space. Substituting the amenity function into
equation (27), we derive

P((x,y)∣a(x0,y0),s) = [α^α(1-α)(^1-α)(1 + e^-γd(^x,ylx0^,yθ,s)a(xo,yo)) ^β(m-tD(x,y))∕V]^ιz(^1-α)∕(δ+τ) (28)
Without loss of generality, we suppress the difference in the distance of each land parcel
within a community to the CBD, and use P(0) to represent equilibrium land price without
preserved open space. As a result, the equilibrium land price function can be expressed
as product of land price without open space P(0) and open space amenity A(x,y),

P((x,y), a(xo,yo), s, P(0)) = P(0)(1 + e ^d ' ' ' ' aιx ,y И ^βz(^1-α)                   (29)

We use this land price function to simulate the effect of some common spatial
configurations of open space on the net value of community land and the capacity of tax
increment financing for a rectangle-shaped (4ooom×8ooom) community, centered at
coordinate origin, with x ranging from -2ooom to 2ooom, and y ranging from -4ooom to
4ooom. This community can also be considered as a district in a city that uses property
tax increment to finance preserving open space. Table 1 presents the value of parameters
we used for simulation.

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