Subsidizing Green Deserts in Southern Chile: Between Fast Growth and Sustainability of Forest Management

Abstract

The expansion of the forest industry in Chile has generated a significant impact on the ecological and socio-cultural balance in central and southern Chile since its strong development in the 1980s. Like every human activity, and especially those of industrial character, it is necessary to constantly assess both the positive and negative impacts it generates as a consequence. Forest public policies enacted during the 1980s seem to have been successful in helping to develop a strong forest sector that has been deemed as one of the engines of economic development in Chile for the last 40 years. But from the point of view of ecological economics and the environmental sciences there is a growing awareness that these policy reforms have had a significant impact on the environment and the ecosystem services it provides, which in turn has a direct negative relationship with the welfare of the people living in communities nearby the forest plantations. Therefore, the negative impact of these policies can be considered as a cost to society. However, no prospective evaluation has been made about the welfare enhancing characteristic of the structural reforms in the forests sector developed in Chile. In this chapter a simple static model of two sectors, one for conservation the other for resource extraction, is constructed. Against this background forest policy reforms of the 1980s are contrasted to evaluate their effect on conservation, cash income for consumption, ecosystem services provision and welfare enhancing characteristics. It will be shown that until a certain extent the extractive sector can help to achieve a necessary minimum income (and in so doing minimum standards of consumption) even though these policies had adverse effects in conservation and ecosystem services provision. Conditions under which social benefits of the policies subsidizing the forest sector are rather low while social costs are high are presented.

Appendix

1.1 Basic Results

The concentered model is

(A.1)

And the first order condition is:

$$\begin{aligned} \frac{\partial L}{\partial {z}_c}&=-\beta \left(p\Big(T-{z}_c\right)+w{z}_c\Big){}^{\beta -1}\left(p-w\right){z_C}^{\theta \left(1-\beta \right)}\\&\quad +{\left(p\left(T-{z}_C\right)+w{z}_C\right)}^{\beta}\theta \left(1-\beta \right){z}_C^{\theta \left(1-\beta \right)-1}=0 \end{aligned}$$

(A.2)

Rearranging Eq. (A.2) we get that

$$ -\frac{\beta \left(p-w\right)}{p\left(T-{z}_C\right)+w{z}_C}+\frac{\theta \left(1-\beta \right)}{z_c}=0 $$

(A.3)

and from Eq. (A.3)

$$ {z}_C^{\ast }=\frac{\theta \left(1-\beta \right) pT}{\left(\beta +\theta \left(1-\beta \right)\right)\left(p-w\right)} $$

(A.4)

if we collect preference’s parameters in

$$ \alpha =\beta +\theta \left(1-\beta \right) $$

(A.5)

Combining (A.4) and (A.5), and noting by (A.5) that α > β, gives the optimal allocation to conservation in Eq. (4.9) in the text

$$ {z}_C^{\ast }=\frac{\left(\alpha -\beta \right) pT}{\alpha \left(p-w\right)} $$

Note in the first order condition in (A.3) that the second term in the left-hand side gives the marginal benefits of increasing conservation, which does not depend on returns to each sector p, w, but only depends on the marginal damage of ecosystem services lost (1 − β) and how productive the ecosystem is in terms of ecosystem services provision θ. The first term on the left-hand side shows the opportunity cost of conservation in terms of reduced income for forest production, which is positive if the return to the forest sector p is higher than the returns captured trough the ecosystem services provision w. The optimal allocation to conservation occurs where both effects cancel each other out.

The optimal allocation of land to the forest sector can be determined by inserting ${z}_C^{\ast }$ in the total land restriction in Eq. (4.3)

$$ {z}_F=T-{z}_c $$

$$ {z}_F=T-\frac{\theta \left(1-\beta \right) pT}{\left(\beta +\theta \left(1-\beta \right)\right)\left(p-w\right)} $$

$$ {z}_F^{\ast }=\frac{T\beta p-\left(\beta +\theta \left(1-\beta \right)\right) wT}{\left(\beta +\theta \left(1-\beta \right)\right)\left(p-w\right)}, $$

This expression is equal to the optimal allocation of land to the extractive sector (i.e. forest) in Eq. (4.10) in the main text if Eq. (A.5) holds:

$$ {z}_F^{\ast }=\frac{T\beta p-\alpha wT}{\beta \left(p-w\right)} $$

Note that ${z}_F^{\ast}\ge 0$ if

$$ \frac{p}{w}\ge \frac{\alpha }{\beta } $$

(A.6)

Since α > β, this condition requires that the return to the extractive sector (either forest, agriculture, mining etc.) must be higher than the collected value for ecosystem services payment, (tourism, use of fresh water, etc.). As we show below, this expression is equivalent to the restriction in Eq. (4.5) c ≥ wT.

The total environmental quality q is calculated from Eqs. (4.4) and Eq. (4.9)

$$ {q}^{\ast }={z}_C^{\theta } $$

$$ {q}^{\ast }={\left(\frac{\left(\alpha -\beta \right) pT}{\alpha \left(p-w\right)}\right)}^{\theta }. $$

Cash income for consumption is calculated inserting the optimal values of land conservation Eq. (4.9) and forest land in Eq. (4.10) in the budget constraint (4.2):

$$ {c}^{\ast }=p{z}_F^{\ast }+w{z}_C^{\ast } $$

$$ {c}^{\ast }=p\frac{T\beta p-\alpha wT}{\alpha \left(p-w\right)}+w\frac{\left(\alpha -\beta \right) pT}{\alpha \left(p-w\right)} $$

$$ {c}^{\ast }=\frac{T\beta {p}^2-\alpha wpT+\left(\alpha -\beta \right) wpT}{\alpha \left(p-w\right)} $$

$$ {c}^{\ast }=\frac{T\beta {p}^2- w\beta pT}{\alpha \left(p-w\right)} $$

$$ {c}^{\ast }=\frac{T\beta p\left(p-w\right)}{\alpha \left(p-w\right)} $$

$$ {c}^{\ast }=\frac{T\beta p}{\alpha } $$

(A.7)

Note that if (A.6) holds, then

$$ {c}^{\ast}\ge wT $$

(A.8)

This means that even if the whole land is destined to conservation activities that would not be enough to satisfy minimum levels of consumption and some extractive activities are necessary.

1.2 Effects of a Negative Tax (Subsidy)

$$ \frac{\partial {z}_C^{\ast }}{\partial p}=\frac{\left(\alpha -\beta \right) T\alpha \left(p-w\right)-\alpha \left(\alpha -\beta \right) pT}{{\left(\alpha \left(p-w\right)\right)}^2} $$

$$ \frac{\partial {z}_C^{\ast }}{\partial p}=\frac{-\alpha \left(\alpha -\beta \right) wT}{{\left(\alpha \left(p-w\right)\right)}^2}<0 $$

$$ \frac{\partial {z}_F^{\ast }}{\partial p}=\frac{T\beta \alpha \left(p-w\right)-\alpha \left( T\beta p-\alpha wT\right)}{{\left(\alpha \left(p-w\right)\right)}^2} $$

$$ \frac{\partial {z}_F^{\ast }}{\partial p}=\frac{\alpha wT\left(\alpha -\beta \right)}{{\left(\alpha \left(p-w\right)\right)}^2}>0 $$

$$ \frac{\partial {q}^{\ast }}{\partial p}=\theta {z}_C^{\theta -1}\frac{\partial {z}_C^{\ast }}{\partial p} $$

$$ \frac{\partial {q}^{\ast }}{\partial p}=-\theta {z}_C^{\theta -1}\frac{\alpha \left(\alpha -\beta \right) wT}{{\left(\alpha \left(p-w\right)\right)}^2}<0 $$

$$ \frac{\partial {c}^{\ast }}{\partial p}=\frac{T\beta}{\alpha }>0 $$

1.3 Effects of Payment for Ecosystem Services

$$ \frac{\partial {z}_C^{\ast }}{\partial w}=\frac{\alpha \left(\alpha -\beta \right) pT}{{\left(\alpha \left(p-w\right)\right)}^2}>0 $$

$$ \frac{\partial {z}_F^{\ast }}{\partial w}=\frac{-\alpha T\alpha \left(p-w\right)+\alpha \left( T\beta p-\alpha wT\right)}{{\left(\alpha \left(p-w\right)\right)}^2} $$

$$ \frac{\partial {z}_F^{\ast }}{\partial w}=-\frac{\alpha \left(\alpha -\beta \right) pT}{{\left(\alpha \left(p-w\right)\right)}^2}<0 $$

$$ \frac{\partial {q}^{\ast }}{\partial w}=\theta {z}_C^{\theta -1}\frac{\partial {z}_C^{\ast }}{\partial w} $$

$$ \frac{\partial {q}^{\ast }}{\partial w}=\theta {z}_C^{\theta -1}\frac{\alpha \left(\alpha -\beta \right) pT}{{\left(\alpha \left(p-w\right)\right)}^2}>0 $$

$$ {c}^{\ast }=\frac{T\beta p}{\alpha } $$

$$ \frac{\partial {c}^{\ast }}{\partial w}=0 $$

(A.9)

Result in Eq. (A.9) is intriguing. It shows that the return provided by the ecosystem does not have any negative impact on the households’ income but does have a positive effect on the environment. At first sight it seems to indicate that it is possible to conserve the environment without any opportunity cost in terms of consumption only by increasing w, leading in the end to a total conservation of land. However, this is not the case. Our restrictions show that if total land is devoted only to conservation, it is not possible to achieve minimum levels of consumption only through the captured revenues from ecosystem services. Some level of extraction activity is necessary to sustain life.

Another way to see the null impact of w on aggregate income is trough total differentiation of the budget constraint

$$ {c}^{\ast }=p{z}_F^{\ast }+w{z}_C^{\ast } $$

$$ \frac{d{c}^{\ast }}{dw}=p\frac{d{z}_F^{\ast }}{dw}+{z}_C^{\ast }+w\frac{d{z}_C^{\ast }}{dw} $$

(A.10)

According to the land constraint

$$ -\frac{d{z}_F^{\ast }}{dw}=\frac{d{z}_C^{\ast }}{dw}, $$

rewritten Eq. (A.10)

$$ \frac{d{c}^{\ast }}{dw}={z}_C^{\ast }-\left(p-w\right)\frac{d{z}_C^{\ast }}{dw}. $$

It is possible to show that ${z}_C^{\ast }=\left(p-w\right)\left({dz}_C^{\ast}\right)/ dw$, and thus (dc ^∗)/dw = 0

$$ {z}_C^{\ast }=\frac{\left(\alpha -\beta \right) pT}{\alpha \left(p-w\right)} $$

$$ \left(p-w\right)\frac{d{z}_C^{\ast }}{dw}=\left(p-w\right)\frac{\alpha \left(\alpha -\beta \right) pT}{{\left(\alpha \left(p-w\right)\right)}^2}=\frac{\left(\alpha -\beta \right) pT}{\alpha \left(p-w\right)} $$

Hence, the additional income obtained by the higher price of conservation ${z}_C^{\ast }$ is totally compensated by increasing ${z}_C^{\ast }$ and reduced ${z}_F^{\ast }$ while the former is less productive by the latter.

1.4 Welfare Effects

According to Eqs. (4.1), (4.9) and (4.10), the indirect utility function is given by

$$ u={\left(\frac{T\beta p}{\alpha}\right)}^{\beta }{\left(\frac{\left(\alpha -\beta \right) pT}{\alpha \left(p-w\right)}\right)}^{\theta \left(1-\beta \right)}. $$

This expression in logarithms becomes:

$$ \ln u=\lambda +\beta \ln p+\theta \left(1-\beta \right)\ln p-\theta \left(1-\beta \right)\ln \left(p-w\right) $$

with λ, a constant, given by

$$ \lambda =\beta \ln \left(\frac{T\beta}{\alpha}\right)+\theta \left(1-\beta \right)\ln \left(\frac{\left(\alpha -\beta \right)T}{\alpha}\right) $$

$$ \frac{\partial \ln u}{\partial p}=\frac{\beta }{p}+\frac{\theta \left(1-\beta \right)}{p}-\frac{\theta \left(1-\beta \right)}{\left(p-w\right)} $$

(A.11)

According to Eq. (A.11), it is possible to show that an increase in the return of forest p is welfare enhancing if the condition $p>\frac{\alpha w}{\beta }$, holds, or equivalently, if the income from ecosystem services is not enough to satisfy minimum standard of consumption, i.e. it is required that c > wT. However, in a more general setting an increase in price and in this higher returns in the extraction sector can be welfare reducing if

$$ \frac{p}{w}<\left(1+\theta \frac{1-\beta }{\beta}\right) $$

(A.12)

If Eq. (A.12) holds, higher returns in the extractive sector (e.g. a subsidy) is welfare reducing if the left side of Eq. (A.12) is low or the right side is high. Thus, if the relation between the return to conservation to the return of the extractive sector w/p is high; if the relative valuation of the environment to the valuation of consumption (1 − β)/β is high or if the richness of the ecosystems in terms of provision of ecosystem services θ is high.