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Marino Gatto Politecnico di Milano

Discounting and multicriteria optimization in ecology, evolution and the management of renewable resources. Marino Gatto Politecnico di Milano. Outline. Discounting and the management of renewable resources Critical issues: time uncertainty, extinction, substitutability

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Marino Gatto Politecnico di Milano

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  1. Discounting and multicriteria optimization in ecology, evolution and the management of renewable resources Marino Gatto Politecnico di Milano

  2. IVSLA-Gatto

  3. Outline • Discounting and the management of renewable resources • Critical issues: time uncertainty, extinction, substitutability • Sustainability concept: discussion • Benefit-Cost Analysis and pricing techniques Contingent Valuation and related problems • Multi-objective analysis and the Pareto boundary • The spandrels of San Marco IVSLA-Gatto

  4. The dynamics of exploited populations Colin W. Clark x = resource biomass F(x) = resource growth rate R(x) = growth rate per unit biomass h = harvesting rate Fin whale (Balaenoptera physalus) IVSLA-Gatto

  5. Harvesting rate h and effort E • Effort E is some suitably defined measure of the harvesting stress on the resource being exploited • No. of operating vessels • No. of hunters • Tonnage • Labour force employed • Fuel consumption • Capital invested in the harvesting activity • A combination of all these Obviously harvest h = g(E, x) with g increasing function of both E and x Very often we can assume h = qEx with q being the catchability coefficient (depends on technology) IVSLA-Gatto

  6. Introducing economics (H.S. Gordon 1954) Open access – no regulation BIONOMICEQUILIBRIUM dx/dt = F(x) -qEx dE/dt = k(pqEx - cE) p= price of unit biomass c = opportunity cost of unit effort pqEx – cE = total profit k = sensitivity to profit Effort E Unexploited resource dx/dt=0 dE/dt=0 c/pq Biomass x • Lotka-Volterra-type model (assume constancy of p and c) • Periods of overcapitalization and strong overexploitation • At bionomic equilibrium net benefit is zero IVSLA-Gatto

  7. No. of vessels Population size The Northern fur seal (Callorhinus ursinus) The exploitation of fur seal in North Pacific between 1882-1900 IVSLA-Gatto

  8. Open access: Gordon’s static analysis At biological equilibrium F(xeq) = natural growth rate = qExeq = harvest rate = sustainable yield Y Total sustainable profit TP = pY – cE = pqExeq – cE. Therefore TP(x) = pF(x) - cF(x)/qx = (p – c/qx)F(x) c/qx = C(x) is the cost of harvesting one unit biomass when the standing biomass is x. Thus TP(x) = (p – C(x))F(x). € F(x) TP(x) (p – C(x))F(x) p p – C(x) x x xB = c/pq K xB xopt K IVSLA-Gatto

  9. Open access: moral At xB (bionomic equilibrium) the net benefit is dissipated by overexploitation Regulatory methods should be introduced to decrease effort thus generating positive economic benefits to the society and reducing the risk of extinction. At xopt the sustainable net benefit is maximum (fine!) Two problems: (1) transient, (2) discounting IVSLA-Gatto

  10. Interest - discount rates • Present value • TP(t) = flow of revenues minus costs • δ = discount rate • It conveys two concepts • uncertainty about future revenues • alternative investments Stern vs. Nordhaus IVSLA-Gatto

  11. Optimal regulation Determine the fishing effort policy E(.) that maximizes the discounted net monetary benefit (= instantaneous rate of discount). It’s a problem of optimal control (E = control variable). Can be solved via Pontryagin’s Maximum Principle. with the constraints IVSLA-Gatto

  12. The optimal solution (the modified golden rule of capital accumulation) Bang-bang approach to singular arc x* x x0 E = Emax Biomass E = E* x* E = 0 x0 t (time) Paul A. Samuelson IVSLA-Gatto

  13. Understanding the golden rule Remember that total sustainable profit is TP(x) = (p – C(x))F(x) Let z(x) is the monetary value of resource x, namely the cash that would be obtained if x were harvested down to xB where the profit vanishes. So x* is the biomass that maximizes TP(x) – δz(x) sustainable rent minus the cost of “capital” IVSLA-Gatto

  14. The opportunity cost of capital € If the discount rate is 0, x* coincides with xopt , the biomass that maximizes the sustainable rent. If the discount rate tends to infinity x* tends to the bionomic equilibrium δz(x) TP(x) xB x xopt x* K The discount rate δ is the opportunity cost of one unit of capital and δz(x) is the cost of not disposing of the capital represented by the renewable resource IVSLA-Gatto

  15. The fin whale (Balaenoptera physalus) Logistic model with K = 400,000 r = 0.08 yr-1 Current population estimate = 84,000 IVSLA-Gatto

  16. Coping with uncertainty • What should we optimize? • Mean vs. variance • Several strategies (constant effort, quotas, constant escapement, etc.) • Pareto frontier C. J. Walters, 1975. JFRBC 32: 1777-1784 IVSLA-Gatto

  17. Most commonly caught whales IVSLA-Gatto

  18. The decline of whaling IVSLA-Gatto

  19. Whaling, catch quotas and substitutability The Blue Whale Unit was used by the International Whaling Commission. The catch limit was expressed in BWUs, equal to 1 blue whale, 2 fin whales, 2½ humpback whales, or 6 sei whales. These ratios were based on the relative oil yields of the individual species. IVSLA-Gatto

  20. Can extinction be economically optimal? Suppose that technology is so devastating that we can harvest the resource down to extinction (or quasi-extinction) without worrying about skyrocketing costs, e.g., C(x) = constant. Then the golden rule becomes simply F’(x) = δ If δ > F’(0) EXTINCTION is “optimal” Populations with small growth rates such as marine mammals are at risk slope δ F(x) x* IVSLA-Gatto

  21. The issue of sustainability • sustainable development: a development that meets the needs of the present without compromising the ability of future generations to meet their own needs(WCED, 1987) Gro Harlem Brundtland

  22. Weak vs. strong sustainability Development is sustainable if it does not consume the capital assets of a nation, which are its resource base : • Km manufactured capital (goods, buildings, infrastructures) • Kn natural capital (natural resources and services) • Kh human capital (labour) • Kc cultural capital (life expectancy, education) weak sustainability: Km + Kn + Kh + Kc = constant • perfect substitution between capital types (e.g. Km vs. Kn) strong sustainability: Km + Kn + Kh + Kc = constant, Kn Kn min • a certain amount of natural capital cannot be replaced and must therefore be kept constant over time Robert M. Solow 1987 Nobel Prize for Economics

  23. IVSLA-Gatto

  24. Weak vs. strong sustainability human-made capital + = perfect substitution between capital types natural capital

  25. The debate between two schools The idea that ecosystem valuation is something that we just should not do keeps coming up. While we can certainly appreciate the many sides of this argument, ultimately, we agree with Herendeen (1998) that: "the argument that we lose our souls by economically pricing environment is silly" and ultimately counterproductive. Costanza et al., 1998 Unfortunately, for all its theoretical attractiveness, ascribing money values to nature's services is only a partial solution to the present dilemma and, if relied on exclusively, may actually be counterproductive. Rees, 1998 IVSLA-Gatto

  26. Decision making: the pricing approach • Instrument • Benefit – Cost Analysis (BCA) • One measurement unit • Money • One goal • Discounted social benefit > 0 • Choosing among alternatives • Max Σi[Benefitsi - Costsi](1+DF)-i DF = Discount factor IVSLA-Gatto

  27. Morbidity Ground concentration Dose-response function Damage in measurable units Concentration $ Monetary damage Work-days lost How to price goods without a market Emissions • Example: air pollution IVSLA-Gatto

  28. Valuing nature TEEB (2010) The Economics of Ecosystems and Biodiversity: Mainstreaming the Economics of Nature: A synthesis of the approach, conclusions and recommendations of TEEB http://www.teebweb.org/ IVSLA-Gatto

  29. Contingent Valuation Methods • They simulate a hypothetical market for an environmental good • Questionnaires • How much one is willing to pay for a hypothetical welfare increase due to environmental amelioration • How much one is willing to accept in compensation for a hypothetical welfare decrease IVSLA-Gatto

  30. WTP & WTA IVSLA-Gatto

  31. The demand curve for a public good Price = WTP or WTA per unit of good Total demand curve p=pA+pB Consumer B demand pB Consumer A demand pA q Public good quantity IVSLA-Gatto

  32. Limits of CVM’s • The very definition of existence value • Aesthetic appeal, incomplete information • Reference group • How many “consumers”? • Significance of simulated market • Can the invisible hand of market work in a market for biodiversity units or dissolved oxygen concentration? • Part of the natural capital is simply nonsubstitutable • The precise contribution of many species is unknown • Ecological processes should be valued as a whole, not individually • Free riding IVSLA-Gatto

  33. Decision making: multi-attribute and multi-objective analysis • Gives up monetary evaluation of all environmental effects • Accounts for the existence of noncomparable welfare indicators • Accounts for the existence of conflicting objectives • EIA and SEA IVSLA-Gatto

  34. Example... • To build a freeway we want: • to minimize the cost • to minimize landscape alteration 1…7: Alternatives IVSLA-Gatto

  35. Pareto efficiency  Pareto optimal solutions • Each point is the result of a multidisciplinary study • The Pareto boundary is a measure of the trade-off between the two incommensurable objectives IVSLA-Gatto

  36. Hybrid Power System Options in northern Kenya IVSLA-Gatto

  37. Implicit pricing a posteriori vs. a priori IVSLA-Gatto

  38. Personal conclusion • Use pricing techniques and BCA whenever this is reasonable • In addition to BCA perform a multiobjective analysis for all those aspects that are intangible, typically biodiversity and ecosystem functions and services • Make a decision choosing among nondominated alternatives IVSLA-Gatto

  39. Optimization in evolution IVSLA-Gatto

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