standardized marginal cost per unit remaining land eventually increases to infinity with
open space, g(a) will cross f(a) at least once if g(0) > f(0), i.e.,
P (a 0)
P(a 0)
2
>--------∩^∙
L-a0
Therefore, if residents’ standardized WTP at the time of the land manager’s preservation
decision is sufficiently large so as to go beyond 2∕(L - a0), preserving more open space
would improve the welfare of land owners by raising the total value of community land∙
P'(a0) 2
indicates preserving open space is more likely to
The condition —ʒ-ʌ >-----
P(a0) L -a0
be welfare-improving for a community with a large amount of land L that preserved a
small amount a0 of open space∙ This is because on one hand, the standardized marginal
cost per unit remaining land 2/(L - a0) is very low, on the other hand, local residents
would pay more money to preserve open space, as revealed by P'(a0)∕P(a0)∙
We derive the following proposition∙
Proposition 1 If local residents prefer preserving open space, and if the utility
function of local residents is concave in preserved open space, there is an optimal (or
incremental) amount of open space that is socially efficient if local residents’
(standardized) current willingness to pay for preserved open space is greater than
2
L - a 0 ’
III. Tax Increment Financing for Optimal Open Space Preservation
The second question confronting the land manager is the possibility of using property tax
increment to finance the socially efficient incremental amount of open space∙
Economically, we are interested in the interaction between economic conditions of social
efficiency and tax increment financing∙
11
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