Coaseian Biodiversity Conservation and Market Power

Abstract

We apply a land-use approach to biodiversity conservation (BC) by assuming that the global public good ‘biodiversity’ is positively correlated with the share of land protected by land-use restrictions against the deterioration of habitats, ecosystems, and biodiversity. The willingness to pay for BC is positive in developed countries (North), but very low in developing countries (South). Taking the no-policy regime as our point of departure, we analyze two concepts of BC: the northern countries’ financial support of BC in the South, and the coordination of northern countries’ BC efforts. In each regime, governments may either take prices as given or may act strategically by seeking to manipulate the terms of trade in their favor. Our numerical analysis yields results with unexpected policy implications. If northern countries support BC financially in the South without coordinating their actions, the protected land, biodiversity and welfare increase so slightly that this BC policy is almost ineffective. The BC concept with a Coaseian flavor—in which northern countries support BC financially in the South and coordinate their action—is efficient if governments act non-strategically. Otherwise, the concept is an ineffective BC policy instrument, because the incentives for expanding the protected land the BC policy creates are so strong that biodiversity actually becomes excessive.

Appendix

1.1 Appendix A: Protected and Unprotected Land Markets

For simplicity, we treat the protected area $b_h$ as the governments’ policy parameter assuming that the land zones are imposed in a command and control fashion. It is straightforward to introduce competitive domestic markets, one for protected and one for unprotected land, to allocate the land to domestic firms. We determine the equilibrium on these markets as follows. After the government of country $h \in \Omega$ has divided total land into protected and unprotected land, the equilibrium prices for the goods X and Y are determined by (8). Denote by $p_{e}^i$ and $p_{e}^j$ the price of unprotected land use in the production of good X, $i \in \mathcal{N}$ and good Y, $j \in \mathcal{S}$, respectively. Consider the first-order conditions of profit maximization $p_x X_i'(e_i) =p_{e}^i$ and $p_y Y_i'(e_i) =p_{e}^j$, respectively. The first-order conditions clearly define the land prices, $p_{e}^i= p_x X_i'(e_i)$ and $p_{e}^j= p_y Y_i'(e_i)$.

Next, consider the market for ecosystem services in country h and define the prices $p_g=1$, $p_b^h$ and the profit of the firm in country h that produces green goods, $G_h(b_h) - p_b^h b_h$. The first-order condition of profit maximization determines the equilibrium price of protected land in country h: $p_b^h{:=} G_h'(b_h)$.

Finally, observe that the income of country $i\in \mathcal{N}$ and $j \in \mathcal{S}$, respectively, is given by

$$\begin{aligned} I_i:= & {} p_e^i e_i + p^i_b b_i +(g_i -p_b^i b_i)+\,(p_x x_i-p_e^i e_i)\nonumber \\= & {} g_i + p_x x_i= G_i(b_i) + p_x X_i (\ell _i -b_i), \end{aligned}$$

(A1)

$$\begin{aligned} I_j:= & {} p_e^j e_j + p^j_b b_j +(g_j -p_b^j b_j)+\,(p_y y_j - p_e^j e_j)\nonumber \\= & {} g_j + p_y y_j= G_j(b_j) + p_y Y_j (\ell _j -b_j). \end{aligned}$$

(A2)

1.2 Appendix B: Social Optimum

Maximizing the Lagrangian (24) yields the first-order conditions

$$\begin{aligned} \frac{\partial \mathcal{L}}{\partial x^d_h}= & {} V'_h - \lambda _x = 0, \quad \, h \in \Omega , \end{aligned}$$

(B1)

$$\begin{aligned} \frac{\partial \mathcal{L}}{\partial y^d_h}= & {} U'_h - \lambda _y = 0, \quad \, h \in \Omega , \end{aligned}$$

(B2)

$$\begin{aligned} \frac{\partial \mathcal{L}}{\partial g^d_h}= & {} 1- \lambda _g = 0, \quad \, h \in \Omega , \end{aligned}$$

(B3)

$$\begin{aligned} \frac{\partial \mathcal{L}}{\partial z_{i}}= & {} - \lambda _x X'_{i} + \lambda _z = 0, \quad \, i \in \mathcal{N}, \end{aligned}$$

(B4)

$$\begin{aligned} \frac{\partial \mathcal{L}}{\partial z_{j}}= & {} - \lambda _y Y'_{j} + \lambda _z = 0, \quad \, j \in \mathcal{S}, \end{aligned}$$

(B5)

$$\begin{aligned} \frac{\partial \mathcal{L}}{\partial z^d_{h}}= & {} \lambda _g G'_h + \sum _{\mathcal{N}} B_i' - \lambda _z = 0, \quad \, h \in \Omega . \end{aligned}$$

(B6)

The standard procedure of equating shadow prices with prices on perfectly competitive markets yields $\lambda _x = p_x$, $\lambda _y = p_y$, $\lambda _g =p_g$ and $\lambda _z = p_z$, and proves that the allocation in Regime $3^*$ is efficient.

1.3 Appendix C: Parametric Functions and Numerical Examples

Regime 1 The consumer’s demand for good X and Y is given by

$$\begin{aligned}&V'(x_h^d) = p_x \quad \iff \quad x_h^d = \frac{a_x -p_x}{\beta _x} \equiv x^d \quad \text{ for } \,\, h = \mathcal{N}, \mathcal{S}, \end{aligned}$$

(C1)

$$\begin{aligned}&U'(x_h^d) = p_y \quad \iff \quad y_h^d = \frac{a_y -p_y}{\beta _y} \equiv y^d \quad \text{ for } \,\, h = \mathcal{N}, \mathcal{S}. \end{aligned}$$

(C2)

Inserting the demands (C1), (C2) and the supplies $x_h =2 \alpha _{x} \sqrt{\ell - b_{\mathcal{N}}}$ and $y_h =2 \alpha _{y} \sqrt{\ell - b_{\mathcal{S}}}$ into the equilibrium conditions $(n+s) x^d = n x_{\mathcal{N}}$ and $(n+s) y^d = sx_{\mathcal{S}}$ we obtain

$$\begin{aligned} p_x = P^x(b_{\mathcal{N}}) = a_x - \frac{2 n \alpha _{x } \beta _x}{n+s} \sqrt{\ell - b_{\mathcal{N}}}, \quad p_y = P^y (b_{\mathcal{S}}) = a_y - \frac{2 s \alpha _{y} \beta _y}{n+s} \sqrt{\ell - b_{\mathcal{S}}}.\nonumber \\ \end{aligned}$$

(C3)

Inserting the parametric functions (25) into (10) and (11) we get

$$\begin{aligned} \alpha _{g} - \frac{p_x \alpha _{x}}{ \sqrt{\ell - b_{\mathcal{N}}}} + \gamma = 0, \quad \alpha _{g} - \frac{p_y \alpha _{y}}{ \sqrt{\ell - b_{\mathcal{S}}}} = 0 \end{aligned}$$

(C4)

for non-strategic action and

$$\begin{aligned}&\alpha _{g} - \frac{p_x \alpha _{x}}{ \sqrt{\ell - b_{\mathcal{N}}}} + \frac{\partial P^x}{\partial b_{\mathcal{N}}} \cdot \left( 2 \alpha _{x} \sqrt{\ell - b_{\mathcal{N}}} - \frac{a_x-p_x}{\beta _x} \right) + \gamma = 0, \end{aligned}$$

(C5)

$$\begin{aligned}&\alpha _{g} - \frac{p_y \alpha _{y}}{ \sqrt{\ell - b_{\mathcal{S}}}} + \frac{\partial P^y}{\partial b_{\mathcal{S}}} \cdot \left( 2 \alpha _{y} \sqrt{\ell - b_{\mathcal{S}}} - \frac{a_y-p_y}{\beta _y} \right) = 0 \end{aligned}$$

(C6)

for strategic action.

Regime 2 In Regime 2 the consumer’s demands are given by $x^d = \frac{a_x - p_x}{\beta _x}$, $y^d = \frac{a_y - p_y}{\beta _y}$ and the price functions by

(C7)

(C8)

For the parametric functions (25) the first-order conditions (18)–(20) turn into

(C9)

for non-strategic action and

(C10)

(C11)

for strategic action.

Regime 3 In Regime 3 the first-order conditions (18), (22) and (23) turn into

(C12)

for non-strategic action and

for strategic action.

1.4 Appendix D: Closed-Form Solution for Non-strategic Action

For non-strategic action we get the following closed-form solutions.

Regime 1 Solving (C4) we get

where and . The welfare levels of northern and southern countries are given by

Regime 2 Solving (C9) one gets

where and . Inserting (D1) and (D2) into (D8) and (D9) and solving for and yields

The welfare levels are

where and .

Regime 3 Solving (C12) and (C13), we obtain

where and . Inserting (D2) and (D3) into (D18) and (D19) and solving for and yields

The welfare levels are given by

where and .

Table 8 Equilibrium values in Example 1 ($\beta _x = 0.1$)

Table 9 Equilibrium values in Example 2 ($\alpha _y = 0.9$)

Table 10 Equilibrium values in Example 3 $(\beta _x=0.5)$