Marginal Damage Cost of Nutrient Enrichment: The Case of the Baltic Sea

Abstract

The purpose of this article is to investigate the link between marine pollution and marine renewable resources. An extended bio-economic model of a fishery is developed to include nutrient enrichment and built into a general model of the polluting and fishery sector with nutrient concentration and fish stock as state variables. The marginal damage function for nutrient enrichment is derived. This function can be compared with the marginal abatement cost and hence it provides a basis for policies that balance the use of nutrients in land-based industries (for example agriculture) with the external cost to the marine environment. The model is empirically applied to the case of the Baltic Sea, where Eastern Baltic cod fisheries are affected by nutrient enrichment. The results indicate that nitrogen loading needs to be reduced slightly (around 1 %) to reach optimal levels. The results also show that the optimal fishery policy plays a more important role in producing the net benefits than nitrogen reduction policies do. Further, the impact on the productivity of the fish stock from pollution reduction is higher when an optimal policy is followed.

Appendices

Appendix 1

See Appendix Table 7.

Table 7 Environmental factors which may potentially moderate Baltic cod recruitment

Appendix 2

See Appendix Table 8.

Table 8 The incorporation of environmental factors in the stock-recruitment relationship

Appendix 3

Solving the first order necessary conditions for the problem (4).

All derivatives marked with subscript capital letters are evaluated at time $t$. From Eqs. (6), (7), (8), and (9) we have

$$\begin{aligned} \lambda _{t+1}&= \frac{\pi _H ^{F}}{\rho G_t } \end{aligned}$$

(25)

$$\begin{aligned} \varphi _{t+1}&= \frac{-\pi _L ^{A}}{\rho \omega } \end{aligned}$$

(26)

$$\begin{aligned} \lambda _t&= \pi _S ^{F}+\rho \lambda _{t+1} \left[ {G_t +\left( {S_t -H_t } \right) G_S } \right] +\rho ^{{\upgamma }+1}\lambda _{t+{\upgamma }+1} R_S \end{aligned}$$

(27)

$$\begin{aligned} \varphi _t&= \rho \lambda _{t+1} \left[ {\left( {S_t -H_t } \right) G_N } \right] +\rho ^{{\upgamma }+1}\lambda _{t+{\upgamma }+1} R_N +\rho \varphi _{t+1} (1-\varepsilon ) \end{aligned}$$

(28)

In equilibrium, all variables are stationary over time; therefore the $t$ subscript can be dropped

$$\begin{aligned} \lambda&= \frac{\pi _H ^{F}}{\rho G} \end{aligned}$$

(29)

$$\begin{aligned} \varphi&= \frac{-\pi _L ^{A}}{\rho \omega } \end{aligned}$$

(30)

$$\begin{aligned} \lambda&= \pi _S ^{F}+\rho \lambda \left[ {G+\left( {S-H} \right) G_S } \right] +\rho ^{{\upgamma }+1}\lambda R_S \end{aligned}$$

(31)

$$\begin{aligned} \varphi&= \rho \lambda \left[ {\left( {S-H} \right) G_N } \right] +\rho ^{{\upgamma }+1}\lambda R_N +\rho \varphi (1-\varepsilon ) \end{aligned}$$

(32)

From (30) we observe that the costate variable $\varphi$ is negative because “more nutrient concentration” is “bad”. In equilibrium the growth function (2) and the nutrient Eq. (1) are as follows:

$$\begin{aligned} H&= S-\frac{S-R}{G} \end{aligned}$$

(33)

$$\begin{aligned} N&= \frac{\omega L}{\varepsilon } \end{aligned}$$

(34)

Substituting (29) and (33) into (31) yields

$$\begin{aligned} \frac{1}{\rho }=\left( {\frac{\pi _S ^{F}}{\pi _H ^{F}}+1} \right) G+\frac{(S-R)}{G}G_S +\rho ^{\upgamma } R_S \end{aligned}$$

(35)

Given a discount rate $r$ and the other economic and biological parameters, equation (35) can be solved for the optimal stock level, $S$*, as a function of nutrient concentration $N$. Furthermore, the optimal harvest level, $H$*, can be derived from (33) as a function of N. To find N* we substitute (29), (30) and (33), (34) into (32) which yields

$$\begin{aligned} \frac{\pi _L ^{A}}{\omega }\left[ {\varepsilon +r} \right] =-\frac{\pi _H ^{F}}{G}\left[ {\frac{S-R}{G}G_N +\rho ^{\upgamma } R_N } \right] \end{aligned}$$

(36)