A Hedonic Approach
Appendix 5: Short-run case [*]
OVERESTIMATION THEOREM IN THE CASE WHEN CONSUMERS IN REGION 2 CHOOSE THEIR LAND AREA OPTIMALLY When we consider the short-term case, the land area for an individual consumer cannot be chosen optimally by the consumer because the lot size of land in both regions is ﬁxed. But if the land area is chosen optimally by a consumer in Region 2 without the project, then the overestimation theorem holds. First we introduce a conditional expenditure function as follows: EC( p, r, z, u)ϭ min [( pxϩrl ); u(x, l, z)Նu]. x (A5.1) In the two regions, the utility should be equal because of the openness of the regions: u ϭu1 ϭu2. And the expenditures of both regions are: EC(1, r1, z1, u)ϭE(1, r2, z2, u)ϭwϩs sϭ(r1H1 ϩr2H2)/N (A5.3) (A5.4) (A5.2) because, in Region 2, the land area is chosen optimally by a consumer. The overestimation theorem is: Bϭ(r2 – r1) H1 ՆCϩN EVϭCϩV Thus: (r2 – r1)H1 ϪCՆV. (A5.6) (A5.5) PROOF OF OVERESTIMATION THEOREM The hedonic measure is: (r2 – r1)H1 ϭB. 141 (A5.7) 142 The economic valuation of the environment and public policy BϪCϭr2H1 ϪN [E(1, r2, z2, u )Ϫw]ϩr2H2 ϪC ϭwNϪNE(1, r2, z2, u)ϩr2(H1 ϩH2 )ϪC ϭwNϪNE(1, r2, z2, u)ϩr2HϪC BϪCϭwNϪNE(1, r2, z2, u)ϩr2(N1l1 ϩN2l2)ϪC ϭN1 wϩr2l1 Ϫ C C ϩN2 wϩr2l2 Ϫ ϪNE(1, r2, z2, u)...
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