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

theoretical model to incorporate these policy-related spatial considerations in a two-
dimensional coordinate system and assume the community has no preserved open space.
As will be shown below, incorporating the spatial aspects of open space dramatically
complicates the model such that a closed-form, tractable analytical solution is impossible
without further assumption. Consequently, we use a simulation approach to explore these
spatial effects, and expect the simulation results would reveal implications for the optimal
structure of open space in the context of tax increment financing.

Similar to the non-spatial model, the spatially explicit model maximizes the net
value of community land by investing in open space subject to the capacity of tax
increment financing.

Max π(a(x₀, y₀),s)=[∫∫P((x, y),a(x₀, y₀),s)dxdy-P(0)a(x₀, y₀)]      (22)

^a( ^x0. Уо),^s                                  •£

s.t. ∫₀^T[∫∫τP((x, y),a(x₀, y₀),s)dxdy-τP(0)L]we^-δtdt≥ P(0)a(x₀,y₀) (23)

Ω

where P((x,y), a(x₀,y₀), s) is location-specific equilibrium land price, depending on its
location (x,y relative to the location (x₀,y₀) of the preserved open space with an area α(x₀,
У0) and shape s, and Ω is the set of (x, У) within the community but not belonging to the
preserved open space a(x0, y0).

Assume the utility function of local residents is in the form of a Cobb-Douglas
function, U(z, q, A(x,y)) = z^αq^1-αA(x,y)^β, where A(x,y) is location-specific open space
amenity at (x,y) determined by the distance to the location (x0,y0) and the configuration of
open space a(x0,y0), and α and β are preference parameters with 0 < α <1 and β > 0.
Following the same steps as with the non-spatial model, we can derive the utility-

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