24
Appendix 1. Parametric specifications for amenity valuation function F(T,τ)
It was shown in section 2 that the precise role of the amenity valuation function
matters. This Appendix specifies various possibilities.
* ALEP independence can be described e.g. by an amenity valuation function
T 1-γ
A.2.1 F (T ,τ) =--+ K , where K is constant, Ft = T ~γ > 0, Fτ = 0 and FτT = 0.
1-γ
* Temporal independence for ALEP complements can be described e.g. by
T1-γ τ1-ρ
A.2.2 F (T ,τ) =--1--, where Ft = T ~γ > 0, Fτ = τ ~ρ > 0 and Ft = 0,
T τ τT
1-γ 1-ρ
and temporal independence for ALEP substitutes respectively as
T1-γ τ1-ρ
A2.3 F (T, τ ) =---, where Ft = T ~γ > 0, Fτ = -τ ~ρ < 0 and Ftt = 0.
1-γ 1-ρ
*Decreasing ALEP complementarity can be described e.g. by a valuation function
(T + τ)1-γ
A2.4 F (T, τ) =---------, where Ft = ( T + τ) γ > 0, Fτ = (T + τ) γ > 0 and
1-γ τ
FτT = -γ(T + τ)-(γ+1) <0
and decreasing ALEP substitutability as
(T - τ)1-γ
A2.5 F (T ,τ) = -(----)— , where Ft = (T + τ ) ^γ > 0, Fτ = -(T - τ )- γ > 0 and
1-γ τ
FτT =γ(T-τ)-(γ+1)>0.
* Increasing ALEP complementarity can be described e.g. as
A.2.6 F(T,τ)=Tατ1-α, where FT =αTα-1τ1-α >0, Fτ =(1-α)Tατ-α >0 and
FτT =(1-α)αTα-1τ-α > 0
and increasing ALEP substitutability as
A.2.7 F(T,τ)=eT-βτ, where FT = eT-βτ >0, Fτ = -βeT-βτ <0 and
FτT =-βeT-βτ <0.
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