International Biodiversity Management with Technological Change

Abstract

This document examines a group of countries where the conservation of land benefits anybody through biodiversity. All countries produce the same good from labor and land and improve their productivity through abatement investment. The international agency performing biodiversity management is self-interested. Three cases of biodiversity management are compared: (i) laissez-faire, (ii) the regulation of land use, and (iii) subsidies to the conservation of land. The results are the following. Regulation promotes biodiversity, abatement and welfare. Because subsidies must be financed by distortionary taxes, the replacement of regulation by subsidies hampers biodiversity, abatement and welfare. Applied to NATURA 2000 in the EU, this suggests that regulation without any budget is the appropriate degree of authority for the Commission.

Appendices

Appendix A: Equations (21) and (22) and Function (23)

Noting (5) and (8), the function (15) has the partial derivatives:

(41)

(42)

The maximization of the expected utility (18) by (l _j ,b _j ) s.t. (9) and (12), given (τ,s,η,b,R _j ,R), is equivalent to the maximization of

$$E\int_T^\infty a^{\gamma_j}\frac{b^{\delta}}{1+\tau}\phi(l_j,b_j,s,\eta,\tau)e^{-\rho(\theta-T)}d\theta $$

s.t. (9) and (12), given (τ,s,η,b,R _j ,R). The value of this optimal program starting at time T is

(43)

The Bellman equation corresponding to the optimal program (43) is given by (cf. Dixit and Pindyck 1994)

$$ \rho \varOmega_j=\max\limits_{ (l_{j},b_j) \mbox{\scriptsize{ s.t. (9)}}}\varLambda^j(l_j,b_j, \gamma_j,\underline{b},s,\eta,\tau), $$

(44)

where

(45)

The first-order conditions corresponding to the Bellman equation (44) and (45) are ∂Λ ^j/∂l _j =0 and ∂Λ ^j/∂b _j =0. To solve the dynamic program, I assume that the value of the program, Ω _j , is in fixed proportion to the instantaneous utility at the optimum:

(46)

where φ _j is a constant and $l_{j}^{*}$ and $b_{j}^{*}$ are the optimal values of l _j and b _j . From (46) it follows that

$$ \varOmega_j(\gamma_j+1,\underline{b},s,\eta, \tau)/\varOmega_j(\gamma_j,\underline{b},s,\eta,\tau)=a. $$

(47)

Inserting (46) and (47) into the Bellman equation (44) and (45) yields

(48)

Noting (41), (42), (45), (47) and (48), the first-order conditions corresponding to the maximization (44) are given by

(49)

(50)

In the system consisting of the international agency budget (11) and the first-order conditions (49) and (50) for all countries j∈[0,1], there is symmetry throughout j∈[0,1]. This implies l _j =l and b _j =b for j∈[0,1]. From this, (1), (5), (6), (13), (14), (15) and (17) it follows that

(51)

This implies (20). Inserting (51), l _j =l and b _j =b back to (49) and (50) yields (21) and (22).

Noting l _j =l, b _j =b, (15), (43), (46) and (51), the expected utility of country j, (18), can be written as follows:

Appendix B: Equations (25) and (26)

The average serial number of technology in the economy is given by

$$ \gamma=\int_{0}^1\gamma_jdj. $$

(52)

Given the Poisson property of the improvement of technology in countries j∈[0,1] (cf. Sect. 2.2), one obtains the following. In a small period of time dt, the probability that abatement investment will lead a jump from γ to γ+1 is given by λzdt, while the probability that abatement investment will remain without success is given by 1−λzdt. Noting (9), this defines a Poisson process χ with

$$ d\chi= \begin{cases} 1 & \mbox{with probability }\lambda (1-l)dt, \cr 0 & \mbox{with probability }1-\lambda(1-l)dt, \end{cases}\quad l\doteq\int_{0}^1l_jdj, $$

(53)

where dχ is the increment of the process χ.

Because there is perfect symmetry throughout countries j∈[0,1] in the system (2), (53), (21) and (22), there is l _j =l=l ^P and b _j =b=b ^P for j∈[0,1] in equilibrium. Because there is one-to-one correspondence from (η,s) to (l ^P,b ^P), one can replace the subsidies (η,s) by (l ^P,b ^P) as the international agency’s policy instruments. Thus, the international agency maximizes (24) by (l ^P,b ^P) s.t. technological change (53). Noting (5), (17) and (52), one obtains the value function of this maximization as follows:

Noting (8), this leads to the first-order conditions

These equations imply (25) and (26).

Appendix C: The Lobbying Game

Following Dixit et al. (1997), a subgame perfect Nash equilibrium for this game is a policy ζ and a set of contribution schedules R ₁(ζ),…,R _J (ζ) such that the following conditions (i)–(iv) hold:

• (i) Contributions R _j are non-negative but no more than the contributor’s income, Γ _j ≥0.

• (ii) The policy ζ maximizes the international agency’s welfare (27) taking the contribution schedules R _j as given.

• (iii) Country j cannot have a viable strategy R _j (ζ) that yields it a higher level of utility than in equilibrium, given the others’ contributions.

• (iv) Country j provides the international agency at least with the level of utility as in the case in which it offers nothing (R _j =0), and the international agency responds optimally given the contribution functions of the other countries.

Appendix D: Equation (37)

Given η=0, (7), (8), (13), (14), (17), (19) and (20), the international agency budget constraint (11) becomes