A Hedonic Approach
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...
You are not authenticated to view the full text of this chapter or article.
Elgaronline requires a subscription or purchase to access the full text of books or journals. Please login through your library system or with your personal username and password on the homepage.
Non-subscribers can freely search the site, view abstracts/ extracts and download selected front matter and introductory chapters for personal use.
Your library may not have purchased all subject areas. If you are authenticated and think you should have access to this title, please contact your librarian.