direction. Furthermore, the interdistance between open space should be greater than the
average distance in the chosen direction as long as the amenity effect of open space can
reach half of the average distance.
The comparison of the net social value of open space among these three types of
locations further confirms the optimal rule of evenly distributing open space amenity.
With this rule of even distribution, the optimal location of two areas of open space should
be in favor of locations in the y direction relative to the x direction because the
community is rectangle-shaped with the y dimension being longer than the x dimension,
and locating along the long dimension could more evenly distribute open space amenity
without more amenity falling outside the community. The comparison of the distribution
effect is not explicit between the y or x direction and the diagonal direction. Although the
diagonal is longer than the length of community, panel A shows the distribution of open
space amenity is not even, with the land at the end of the diagonal getting more amenity
than the land at the end of the other diagonal. Therefore, the comparison between y or x
direction and diagonal is ambiguous depending on how the amenity effect of open space
distributes as perceived by local residents.
Next, we simulate the size effect for four evenly distributed circular open space
(see figure 7 panel A). The open space are spatially located such that the interdistance
between open space in x and y directions are consistent with the peak-value distance
identified for two circular open space.
Panel B summarizes the area effect of the open space on the net value of
community land and property tax increment. Note the area of open space on x axis
indicates the total area of four circular areas of open space. Interestingly, the peak-value
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