community, the net social value reaches its maximum of $7.8889 × 107 at 402 acres. This
comparison demonstrates the interaction between area and location, and implies that the
ring-shaped open space could be more efficient in terms of higher net social value and
lower size of open space when located farther or the radius of the ring is larger within
certain distance. This result is consistent with intuition since the larger the radius of ring,
the larger the perimeter and thus more developable land exposed to open space amenity
for a given amount of open space. Because of this value effect, the capacity of tax
increment financing is larger when the radius is 900m with the size of around 1440 acres
than when the radius is 300m with the size of around 1275 acres. Panel C reveals a very
different peak-value size for the cross-shaped open space, where the peak-value area is
around 300 acres with a maximum net social value of $7.8435 × 107.
Combining these results with the case of circular open space, we do find the shape
of open space could affect the net social value of open space as well as the capacity of tax
increment financing. Which shape of open space is preferred depends on the policy
objective of local jurisdiction and other constraints. In our simulation example, the ring
shape, among other shapes, maximizes, at least for the given preference, the net social
value of open space without incurring extra cost for financing these investments.
However, the ring-shaped open space may not be most efficient in terms of the net social
value per unit investment because the cross-shape can reach a similar net social value
with a smaller amount of open space preserved.
Nonetheless, a central large open space like a community park may be relatively
easy to set aside and socially desirable with less administration and/or transaction cost
and other political, legal, and fiscal constraints. For example, although requiring less
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