space is equal to the marginal cost. Denote the cost of preserving a units of open space
by C(a) = P(a0)a, where P(a0) is the equilibrium price for land in this community with a0
units of preserved open space, and is the price at which more land will be purchased if
further preservation is needed. Denote the benefit of preserving a units of open space by
B(a), its measure, however, is not as explicit as the cost. Since the utility of local
residents, under the assumption that local residents can costless migrate between
communities, is exogenous, an appropriate policy objective for the local land manager is
to maximize the total value of community developable land in the interest of land owners
(Brueckner 1982, 1983). Therefore, the benefit of preserving open space can be
expressed as B(a) = P(a + a0)(L - a0 - a), where P(a + a0) is the equilibrium land price
after a units of open space have been preserved, and L - a0 - a is the area of the
remaining land after preservation. Consequently, the marginal benefit equal to the
marginal cost yields
P’(a + a0) (L - a0 - a) - P(a + a0) = P(a0) (2)
Equation (2) can be used to determine the optimal increment of open space to be
purchased, which, however, may be equal to zero, i.e., no more preservation is need for
given people’s preference. An interesting question is under what conditions preserving
more open space would be socially efficient, which is directly related to subsequent
investigation of conditions under which the socially efficient amount of open space can
be financed by property tax increment.
Move P(a* + a0) in (2) to the right hand side, and divide both sides by (L - a0 - a*)
P'(a* +a0)=
1
(L - a0 - a*)
(P(a* +a0)+P(a0))
(3)