Appendix B. Theoretical basis for measuring social costs
Because landfill disposal creates external costs to nearby residents, market failure often occurs. While benefits provided by a new landfill site are shared by all citizens, harms from a landfill (e.g., reduction in housing values) concentrate on nearby residents (Kunreuther and Kleindorfer 1986; Mitchell and Carson 1986). In order to measure the community’s social costs for each target site, the City determines to measure willingness tor pay (WTP) for avoiding external effects from the proposed landfill. Environmental policy usually focuses on improvements in environmental quality rather than deliberate degradation of the environment (Pearce et al. 2006)
In order to obtain the resident’s WTP for avoiding the landfill, the City considers the hypothetical situation: (i) pre policy (with the landfill); and (ii) post policy that removes the landfill). Following Mitchell and Carson (1989), the assumptions are that: (i) planners have a policy option to restrict the landfill on the target site; and (ii) the residents have a property right only to the initial situation Q^' (the level of environmental quality with the landfill). The residents do not have the property right to the benefits by the post policy that improves environmental quality. The value that a resident places on environmental quality (Q) with the landfill is defined as (pre policy) (for the theoretical background from equations B-1 to B-9, see Roberts et al. 1991; Freeman 2003):
U^0=U^0 (X,Q^0) (B-1)
where U^0 is the level of utility with a landfill nearby, X is a vector of quantities of private goods, and Q^0 is the level of environmental quality with a landfill. The resident's level of utility without the landfill is given by (post policy):
U^1=U^1 (X,Q^1) (B-2)
where U^1 is the level of utility without the landfill, X is a vector of quantities of private goods, and Q^1 is the level of environmental quality without the landfill. Because the landfill site produces negative external effects (e.g., a decrease in housing values and environmental degradation), U^1 is greater than U^0.
In order to value this increase in environmental quality (Q^0 to Q^1) i.e., avoiding external effects from the landfill, the associated dual problem can be considered. The objective of the dual problem is to minimize total consumer expenditures needed to maintain a given level of utility. The hypothetical problem with the landfill is (B-3), and the current problem without the landfill is (B-4):
Minimize ∑_(j=1)^n▒P_j X_j subject to U^0=U^1 (X,Q^0) (B-3)
Minimize ∑_(j=1)^n▒P_j X_j subject to U^1=U^1 (X,Q^1) (B-4)
where P_j is the price vector of private good j, X_j is a vector of quantities of private good j, and ∑_(j=1)^n▒P_j X_j is the total consumer expenditures given utility with the landfill...