A Hedonic Approach
Appendix 4: Model and proof of the overestimation theorem in the case of heterogeneous consumers [*]
A Hedonic Approach
We assume that there are two types of consumers who are identiﬁed by superscripts 1 and 2. Consumer 2 lives in both Regions 1 and 2. The regions are identiﬁed using subscripts. Consumer 1 only lives in Region 1. Then the hedonic measure may overestimate the real gross beneﬁt. Without an amenity improvement project: E 2(1, r1, z1, u2)ϭE 2(1, r2, z2, u2)ϭw2 ϩs2 E 1(1, r1, z1, u1)ϭw1 ϩs1 ՅE 1(1, r2, z2, u1) H1 ϭN 1E 1(1, r1, z1, u1)ϩN 2 E 2(1, r1, z1, u2) r 1 r H2 ϭN 2E 2(1, r2, z2, u2). 2 r The number of consumers i in Region j is N ji : N 2 ϩN 2 ϭN 2 1 2 N 1s1 ϩN 2s2 ϭr1H1 ϩr2H2. (A4.5) (A4.6) (A4.1) (A4.2) (A4.3) (A4.4) If we implement a project to increase the level of amenity in Region 1 from z1 to z2 at cost C: E 1(1, r*, z2, u1*)ϭw1* ϩs1* E 2(1, r*, z2, u2*)ϭw2* ϩs2* H1 ϩH2 ϭN 1E 1(1, r*, z2, u1*)ϩN 2E 2(1, r*, z2, u2*) r r N 1s1* ϩN 2s2* ϭr*(H1 ϩH2)ϪC. In this heterogeneous case, the overestimation theorem is: BϪCϪVՆDՆ0 139 (A4.11) (A4.7) (A4.8) (A4.9) (A4.10) 140 where: The economic valuation of the environment and public policy D ϭN1[E1(1, r2, z2, u1)ϪE1(1, r1, z1, u1)...
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