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.



More intriguing information

1. Implementation of a 3GPP LTE Turbo Decoder Accelerator on GPU
2. The name is absent
3. Influence of Mucilage Viscosity On The Globule Structure And Stability Of Certain Starch Emulsions
4. The name is absent
5. AGRICULTURAL TRADE LIBERALIZATION UNDER NAFTA: REPORTING ON THE REPORT CARD
6. The name is absent
7. Menarchial Age of Secondary School Girls in Urban and Rural Areas of Rivers State, Nigeria
8. The name is absent
9. The name is absent
10. Popular Conceptions of Nationhood in Old and New European