# The Economic Valuation of the Environment and Public Policy

## A Hedonic Approach

####
- New Horizons in Environmental Economics series

## Noboru Hidano

## Extract

Appendix 3 Proof of equality conditions [*] PROOF OF THE EQUALITY CONDITIONS FOR THE SMALL DEGREE OF IMPROVEMENT CASE The small degree of improvement means that z2 Ϫz1 is small. And z2 is ﬁxed and not changed due to the project. Thus we can assume that the beneﬁt and cost of the project are a function of z1. From the overestimation theorem A2.29 Appendix 2, we get: B(z1)ϪC(z1)ϭN(x* ϩr2l *)ϪNE. (A3.1) And x*, l * can be expressed by the partial derivatives of the expenditure function using Shepard’s lemma. This left-hand side of the equation equals: N{Ep[1, r*(z1), z2, u*(z1)]ϩr2(z1) Er[1, r*(z1), z2, u*(z1)]ϪE [1, r2(z1), z2, u(z1)]}. (A3.2) The net beneﬁt of the project in terms of the equivalent variation V is: V(z1)ϭN{E [1, r2(z1), z2, u*(z1)] ϪE[1, r2(z1), z2, u(z1)]}. (A3.3) We can examine the following situation in order to prove the equality condition: B(z1 ) Ϫ C(z1 ) . z1→ z2 z2 Ϫ z1 lim Since: z1→ z2 (A3.4) lim [B(z1)ϪC(z1)]ϭ0, (A3.5) then using l’Hôpital’s theorem, lim B(z1 ) Ϫ C(z1 ) BЈ(z1 ) Ϫ CЈ(z1 ) ϭ lim ϭϪ lim BЈ(z1)ϪCЈ(z1) z2 Ϫ z1 z1→ z2 Ϫ1 z1→ z2 134 (A3.6) z1→ z2 Appendix 3 V(z1 ) ϭϪ lim V Ј(z1) z1→ z2 z2 Ϫ z1 z1→ z2 lim BЈ(z1 ) Ϫ CЈ(z1 ) ϭEpr[1, r*(z1), z2, u*(z1)]r*Ј(z1) N...

**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.