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Efficient ecosystem services and naturalness in an ecological/economic model

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Abstract

In an integrated economic/ecological model, the economy benefits from ecosystem services that include: (1) the consumptive use of a harvested species, (2) the non-consumptive use of popular species, and (3) naturalness, i.e., the divergence of the ecosystem’s biodiversity from its natural steady state. The biological component of the model, which is applied to a nine-species Alaskan marine ecosystem, relies on individual optimizing behaviour by plants and animals to establish population dynamics. The biological component is used to define naturalness. By varying harvesting we arrive at different steady-state populations and humans choose from among these steady states. Welfare maximizing levels of the ecosystem services are derived, then it is shown that in the laissez-faire economy overharvesting occurs when the harvesting industry ignores ecosystem services (2) and (3). Lastly, we introduce efficiency restoring taxes and standards that internalize the ecosystem externalities.

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Notes

  1. See Jin et al. (2003) for an economy linked to a marine ecosystem with fish species, zooplankton and phytoplankton. The authors investigate the linkages between the systems, using an input–output model.

  2. An ecosystem externality occurs when economic activity causes an ecosystem to shift to an alternative state with different biodiversity, and the shifted ecosystem feeds back to impact economic activity (Crocker and Tschirhart 1992).

  3. Although our harvested fish species can become extinct if over harvested, this does not jeopardize the fish’s predator species because the predator will switch to a different fish species in the food web.

  4. The sign of the partial derivative of the utility function (1) with respect to the state of the ecosystem may be positive or negative because there may be natural states that are undesirable such as wetlands with disease vectors, or unnatural states that are desirable, such as non-native wildflower meadows. But for simplicity, in this paper we assume that naturalness is associated with the richest set of ecosystem services and leave other possibilities to future research.

  5. Ecologists are not in agreement on the relationship between biodiversity and ecosystem function from which ecosystem services flow (Mooney et al. 1995; Armsworth et al. 2004). The consensus is that ecosystem function is a strictly concave increasing function over low levels of biodiversity and may or may not level off at higher levels. Moreover, there may be a critical level of biodiversity below which ecosystem function is severely impaired (Grime 1997; Cervigni 2001).

  6. See Magurran (2004) for a synopsis of measures, most of which use numbers of species and their populations.

  7. In its present form (4) is only applicable to ecosystems with unique steady states. However, (4) can be generalized to multiple steady states and to stable limit cycles. In case of multiple steady states denote by \({n_{i}^{k}}\) the stationary population of species i in steady state k, define \({s^k=-\sum\limits_{i=1}^{N}{\left(\frac{n_{i}(h)-n_i^k} {n_i^k}\right)}^2}\) where s k measures the deviation to the steady state k and s = min [s l, . . . ,s k] enters the utility function (1). In case of stable limit cycles divide the cycle into k points. Then, \({n_i^k}\) is the population level of the limit cycle point, \({s_i^{k}}\) is the deviation to that point and \({s=\min[s^l,\ldots, s^{k}]}\) again is the consumers’ preference for naturalness.

  8. Anthropogenic intervention, h, is a scalar here and in the empirics it represents harvesting a species. However, h could be treated as a vector and additional anthropogenic interventions could include impacts on the ecosystem through pollution, habitat loss, introduction of invasive species, global climate change, and so on. These interventions could be included in the ecosystem model of Sect. 3.

  9. According to Wilcove et al. (1998), in the U.S. the leading threats to biodiversity starting with the greatest threat are; habitat loss to development, introduction of non-native species, pollution and overharvesting. Worldwide the major threats are the same although overharvesting and pollution switch places (IUCN Red List).

  10. Species that have stronger interactions with their neighbors than other species are often labeled “keystone” species (Mills et al. 1993). Keystone species play a larger role in determining community structure. The third property of DNB does not imply that all species have equal impacts on the ecosystem and on S(h). Population changes of keystone species relative to non-keystone species will cause greater numbers of other species to deviate from their natural steady-state populations. Therefore, keystone species have a greater impact on S(h).

  11. Data on biomass demands and populations, along with several physiological parameters, are used to calibrate GEEM. But the data are taken from an ecosystem that has been harvested for many decades and not from a natural system. Therefore, the calibration contains two complete sets of net energy, first-order and balance equations, one set representing the harvested system and the other the natural system, and both sets are solved simultaneously. In this way we obtain a set of parameters that apply to both the harvested and, natural systems, and the parameters can be used to find the populations that would have been present prior to harvesting. More detail on the method is available from the authors upon request.

  12. For brevity, the period-by-period populations are not presented. Convergence of the populations to their steady state values tends to be smooth for long-lived species and possibly oscillatory for short-lived species.

  13. Although steady-state populations turn out to be linear in harvests, the plant and animal objective functions and population update equations used in the simulations are non-linear.

  14. That (7) is determined from GEEM and is an argument in the consumer’s utility function implies that only feasible ecosystem states are available to choose among.

  15. We restrict our attention to interior solutions. The question of optimal extinction is beyond the scope of the present paper.

  16. It is worth mentioning that our problem (8) is compatible with the optimal steady state problem (OSSP) of Carlson et al. (1991).

  17. Essentially, a smaller pollock population means sea lions must pay higher energy prices for their prey, sea lion net energy falls and their population falls, Similarly, the killer whales that prey on sea lions experience a population decline after they start paying a higher energy price for sea lions. But when the energy price killer whales pay for sea lions rises, individual whales switch to capturing more of the relatively cheaper otter (Killer whale switching behavior has been documented by Estes et al. 1998.). There follows a short run drop in otter owing to an ecological “functional response” by the killer whales, but then a long run rise in otter owing to fewer killer whales and this is referred to in ecology as a “numerical response.” Interestingly, the functional response has parallels with economic price effects, and the numerical response has parallels with economic income effects. An advantage of the general equilibrium approach over extant ecological approaches is that, in one model, switching behavior, functional responses and numerical responses are all tracked and explained by individual behavior.

  18. In fact, the pollock fishery was a regulated open access fishery until 1999 at which time a system similar to individual quotas was set up.

  19. Observe that in case of σ = 0 the constraint \({h \ge \sigma}\) is weakly binding which implies that γ s  = 0. In addition, since we assume an interior solution of the social planner’s optimization problem, it can be shown that for the prices and the tax rate specified in Proposition 2 the constraint \({h\le \bar{h}}\) is also weakly binding such that γ b = 0.

  20. In case of the standard it can be shown that \({\gamma_s=\frac{U_{n_8}}{U_x}\cdot\hat{b}_8+\frac{U_{n_9}}{U_x}\cdot\hat{b}_9-U_{s}\cdot2\cdot h\cdot \sum\limits_{i=1}^9{\left(\frac{\hat{b}_i}{\hat{a}_i}\right)}^2}\). The proof of Proposition 3 follows along the same lines as the Proof of Proposition 2.

  21. Realistically, in numerous fisheries the target species has not become extinct, but the fisheries have been depleted to the point of near collapse, and 69% of the world’s major fish species are in decline (McGinn 1998).

  22. To eliminate the degree of freedom in prices we choose harvest as numeraire and set p h  = 1.

  23. The tax rate can be negative if the preference parameter for a larger killer whale population dominates all other effects. This seems highly unlikely and is not found to be the case in the empirics.

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Acknowledgments

This research was supported in part by the United States Environmental Protection Agency (Grant RD-83081901-0) and the National Oceanic and Atmospheric Administration, US Department of Commerce (NMFS Service Order No. AB133F03SE1264). The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of either agency.

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Authors and Affiliations

  1. Department of Economics, University of Siegen, Siegen, Germany

    Thomas Eichner

  2. Department of Economics and Finance, University of Wyoming, Laramie, WY, 82071, USA

    John Tschirhart

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Correspondence to Thomas Eichner.

Appendix A

Appendix A

Derivation of the comparative static results of Table 3: The starting point of the comparative static analysis is (9a) which is rearranged to

$$ h^2\cdot\left[\hat{b}_4\cdot\left(\bar{l}\cdot\mu\cdot\hat{b}_4-1\right)\right] +h\cdot\left[\hat{a}_4\cdot\left(2\cdot\bar{l}\cdot\mu\cdot\hat{b}_4-1\right)\right] +\hat{a}_4^2\cdot\bar{l}\cdot\mu-\frac{\hat{a}_4\alpha}{\beta-c}\equiv A=0 $$
(A1)

Implicit differentiation of (A.1) with respect to the parameter \({\theta = \alpha,\beta,\varphi,\nu_8,\nu_9,\mu,\hat{a}_i,\hat{b}_i}\) yields

$$ \frac{\hbox{d}h}{\hbox{d}\theta}=-\frac{A_\theta}{A_h}. $$
(A2)

We restrict our attention to parameter constellations which satisfy the second-order condition A h < 0. Differentiation of A with respect to \({\theta = \alpha,\beta,\varphi,\nu_8,\nu_9,\mu,\hat{a}_i,\hat{b}_i}\) we obtain

$$ \begin{aligned} A_\alpha&=-\frac{\hat{a}_4}{\beta-c},\quad A_\beta=\frac{\hat{a}_4\alpha}{{(\beta-c)}^2} > 0,\quad A_\varphi=-\frac{\hat{a}_4\alpha}{{(\beta-c)}^2}\cdot\sqrt{\sum\limits_{i=1}^9{\left(\hat{b}_i/\hat{a}_i\right)}^2} < 0,\\ A_{\nu_8}&=\frac{\hat{a}_4\alpha}{{(\beta-c)}^2}\cdot\hat{b}_8 > 0, \quad A_{\nu_9}=\frac{\hat{a}_4\alpha}{{(\beta-c)}^2}\cdot\hat{b}_9 < 0, \quad A_\mu=h^2\hat{b}_4\bar{l}+2h\hat{a}_4\hat{b}_4\bar{l}+\hat{a}_4^2\bar{l}=n_4^2\bar{l} > 0,\\ A_{\hat{a}_i}&=\frac{\hat{a}_4\alpha}{{(\beta-c)}^2}\cdot\frac{\varphi}{\sqrt{\sum\limits_{i=1}^9{\left(\hat{b}_i/\hat{a}_i\right)}^2}} \cdot\frac{\hat{b}_i^2}{\hat{a}_i^3} > 0\quad\quad\hbox{for}\;i=1,2,3,5,6,7,8,9,\\ A_{\hat{a}_4}&=2\bar{l}\mu n_4-\frac{\alpha}{\beta-c}+\frac{\alpha}{{(\beta-c)}^2}\cdot \frac{\varphi}{\sqrt{\sum\limits_{i=1}^9{\left(\hat{b}_i/\hat{a}_i\right)}^2}} \cdot\frac{\hat{b}_4^2}{\hat{a}_4^2},\\ A_{\hat{b}_i}&=-\frac{\hat{a}_4\alpha}{{(\beta-c)}^2}\cdot \frac{\varphi}{\sqrt{\sum\limits_{i=1}^9{\left(\hat{b}_i/\hat{a}_i\right)}^2}} \cdot\frac{\hat{b}_i}{\hat{a}_i^2}=-\hbox{sign}\;\hat{b}_i\quad\quad\hbox{for}\;i=1,2,3,5,6,7,\\ A_{\hat{b}_4}&=h\cdot\left(\bar{l}\mu n_4-h\right)-\frac{\alpha}{{(\beta-c)}^2} \cdot\frac{\varphi}{\sqrt{\sum\limits_{i=1}^9{\left(\hat{b}_i/\hat{a}_i\right)}^2}} \cdot\frac{\hat{b}_4}{\hat{a}_4} > 0,\\ A_{\hat{b}_8}&=-\frac{\hat{a}_4\alpha}{{(\beta-c)}^2}\cdot\left[\frac{\varphi}{\sqrt{\sum\limits_{i=1}^9{\left(\hat{b}_i/\hat{a}_i\right)}^2}} \cdot\frac{\hat{b}_8}{\hat{a}_8^2}-\nu_8\right],\\ A_{\hat{b}_9}&=-\frac{\hat{a}_4\alpha}{{(\beta-c)}^2}\cdot\left[\frac{\varphi}{\sqrt{\sum\limits_{i=1}^9{\left(\hat{b}_i/\hat{a}_i\right)}^2}} \cdot\frac{\hat{b}_9}{\hat{a}_9^2}-\nu_9\right] > 0,\\ \end{aligned} $$

which establishes the second column of Table 3, The derivation of the comparative statics with respect to l h , l x and x is sketched in the text.

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Eichner, T., Tschirhart, J. Efficient ecosystem services and naturalness in an ecological/economic model. Environ Resource Econ 37, 733–755 (2007). https://doi.org/10.1007/s10640-006-9065-4

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