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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, F_t = T ~^γ > 0, F_τ = 0 and F_τT = 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 F_t = T ~^γ > 0, F_τ = τ ~^ρ > 0 and F_t = 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 F_t = T ~^γ > 0, F_τ = -τ ~^ρ < 0 and F_tt = 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 F_t = ( T + τ) ^γ > 0, F_τ = (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 F_t = (T + τ ) ^^γ > 0, F_τ = -(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)=T^ατ^1-α, where F_T =αT^α-1τ^1-α >0, F_τ =(1-α)T^ατ^-α >0 and

F_τT =(1-α)αT^α-1τ^-α > 0

and increasing ALEP substitutability as

A.2.7 F(T,τ)=e^T-βτ, where F_T = e^T-βτ >0, F_τ = -βe^T-βτ <0 and
FτT =-βe^T-βτ <0.

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