A Hedonic Approach
New Horizons in Environmental Economics series
Appendix 1: Proof of time-series capitalization [*]
The time-series measure is: (r* Ϫr1)H1 ϭR. 1 (A1.1) The sum of rents from the land is distributed among consumers equally. This is called the uniform national dividend scheme (UNDS), which is a common assumption in a general equilibrium analysis since there are only homogeneous consumers in the society. Before the project implementation, the endowment is: sϭ(r1H1 ϩr2H2)/N. (A1.2) A consumer has a utility function u(x, l, z) where x is a composite good, l is area of land used and z is a level of amenity. A consumer maximizes the utility: max u(x, x,l l, z) under the income constraint of wage w, which is given exogenously, and endowment: px ϩrlϭwϩs (A1.3) where p and r are the price of a composite good and the unit rent (price) of land, respectively. The expenditure function is deﬁned as follows: E( p, r, z, u)ϭmin [( pxϩrl ); u(x, l, z)Նu]. x,l From Shepard’s lemma, the demand for goods is obtained as follows: xϭѨE/ѨpϭѨE( p, r, z, u)/ѨpϭEp lϭѨE/ѨrϭѨE( p, r, z, u)/ѨrϭEr. (A1.5) (A1.6) (A1.4) In the two regions, the utility should be equal because of the openness of regions: uϭu1 ϭu2. 127 (A1.7) 128 The economic valuation of the environment and public policy And the expenditures of both regions are: E(1, r1, z1, u)ϭE(1, r2, z2, u)ϭwϩs. (A1.8) The...
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