A Hedonic Approach
New Horizons in Environmental Economics series
Appendix 2: Proof of the overestimation theorem [*]
The overestimation theorem is: Bϭ(r2 – r1) H1 ՆCϩN EVϭCϩV. Thus: (r2 – r1) H1 ϪCՆV. The hedonic measure is: Bϭ(r2 – r1) H1. (A2.3) (A2.2) (A2.1) PROOF A consumer has a utility function u(x, l, z), where x is a composite good, l is the area of land of a consumer, and z is an amenity. A consumer maximizes the utility: max x,l u(x, l, z) under the income constraint of wage w and endowment: pxϩrlϭwϩs. (A2.4) The sum of rents from the land is distributed among consumers equally. Thus the endowment is: sϭ(r1H1 ϩr2H2)/N (A2.5) where p and r are the price of a composite good and unit rent (price) of land, respectively. Expenditure function is deﬁned as follows: E( p, r, z, u)ϭ min [( pxϩrl ); u(x, l, z)Նu]. x,l 130 (A2.6) Appendix 2 From Shepard’s lemma,1 the demand for goods is obtained as follows: xϭѨE/ѨpϭѨE( p, r, z, u)/ѨpϭEp lϭѨE/ѨrϭѨE( p, r, z, u)/ѨrϭEr. 131 (A2.7) (A2.8) Now we turn to examine the equilibrium conditions without a project. In two regions, the utility should be equal because of the openness of regions: uϭu1 ϭu2. And the expenditures of the two regions are: E(1, r1, z1, u)ϭE(1, r2, z2, u)ϭwϩs. (A2.10) (A2.9) The total land demand of each region should be equal to...
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