# The Economic Valuation of the Environment and Public Policy

## A Hedonic Approach

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- New Horizons in Environmental Economics series

## Noboru Hidano

## Extract

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 135 (A3.7) r*(z1), z2, u...

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