Optimal Private and Public Harvesting under Spatial and Temporal Interdependence



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 1

and temporal independence for ALEP substitutes respectively as

T1τ1

A2.3  F (T, τ ) =---, where Ft = T ~γ > 0, Fτ = -τ ~ρ < 0 and Ftt = 0.

1 1

*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 (T)-(γ+1)>0.

* Increasing ALEP complementarity can be described e.g. as

A.2.6 F(T,τ)=Tατ1, where FT Tα-1τ1 >0, Fτ =(1)Tατ >0 and

FτT =(1)αTα-1τ > 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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