The Economics of Non-Convex Ecosystems PDF
Preview The Economics of Non-Convex Ecosystems
THE ECONOMICS OF NON-CONVEX ECOSYSTEMS THE ECONOMICS OF NON-MARKET GOODS AND RESOURCES VOLUME 4 Series Editor: Dr. Ian J. Bateman Dr. Ian J. Bateman is Professor of Environmental Economics at the School of Environmental Sciences, University of East Anglia (UEA) and directs the research theme Innovation in Decision Support (Tools and Methods) within the Programme on Environmental Decision Making (PEDM) at the Centre for Social and Economic Research on the Global Environment (CSERGE), UEA. The PEDM is funded by the UK Economic and Social Research Council. Professor Bateman is also a member of the Centre for the Economic and Behavioural Analysis of Risk and Decision (CEBARD) at UEA and Executive Editor of Environmental and Resource Economics, an international journal published in cooperation with the European Association of Environmental and Resource Economists (EAERE). Aims and Scope The volumes which comprise The Economics of Non-Market Goods and Resources series have been specially commissioned to bring a new perspective to the greatest st economic challenge facing society in the 21 Century; the successful incorporation of non-market goods within economic decision making. Only by addressing the complexity of the underlying issues raised by such a task can society hope to redirect global economies onto paths of sustainable development. To this end the series combines and contrasts perspectives from environmental, ecological and resource economics and contains a variety of volumes which will appeal to students, researchers, and decision makers at a range of expertise levels. The series will initially address two themes, the first examining the ways in which economists assess the value of non- market goods, the second looking at approaches to the sustainable use and management of such goods. These will be supplemented with further texts examining the fundamental theoretical and applied problems raised by public good decision making. For further information about the series and how to order, please visit our Website http:/www.wkap.nl/series.htm/ENGO The Economics of Non-Convex Ecosystems Editedby Partha Dasgupta CambridgeUniversity,FacultyofEconomics,Cambridge,UK and Karl-GöranMäler BeijerInternationalInstituteofEcologicalEconomics, RoyalSwedishAcademyofSciences,Stockholm,Sweden KLUWER ACADEMIC PUBLISHERS NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW eBookISBN: 1-4020-2515-7 Print ISBN: 1-4020-1864-9 ©2004 Kluwer Academic Publishers NewYork, Boston, Dordrecht, London, Moscow Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook maybe reproducedor transmitted inanyform or byanymeans,electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstoreat: http://ebooks.kluweronline.com Contents TheEconomicsofNon-ConvexEcosystems:Introduction P.Dasgupta,K.-G. Mäler 1 Scale andScaling in EcologicalandEconomicSystems J. Chave, S. Levin 29 ConvexRelationshipsinEcosystemsContainingMixtures ofTrees andGrass R.J.Scholes 61 ManagingSystemswithNon-convexPositiveFeedback W.A.Brock, D.Starrett 77 TheEconomicsofShallowLakes K.-G. Mäler, A.Xepapadeas,A. deZeeuw 105 _ Multiple Species Boreal Forests W hat Faustmann Missed A.-S. Crépin 127 Evaluating Projects and Assessing Sustainable Develop- mentin Imperfect Economies K.J. Arrow,P.Dasgupta,K.-G. Mäler 149 The Economics of Non-Convex Ecosystems: Introduction PARTHADASGUPTA1andKARL-GÖRANMÄLER2 1CambridgeUniversity,FacultyofEconomics,SidgwickAvenue,CambridgeCB39DD,UK (E-mail:[email protected]);2BeijerInternationalInstituteofEcological Economics,Stockholm,Sweden Abstract. The word “convexity” is ubiquitous in economics, but absent from economics. In this paper we explain why, and show what difference it makes to economic analysis if ecosystem non-convexities are taken seriously. A simple proof is provided of the connection between “self- similarity” and “power laws”. We also provide an introduction to each of the papers in the Symposiumanddrawoutthewayinwhichtheyformalinkedsetofcontributions. Key words: bifurcation points, environmental Kuznets curve, hysteresis, irreversibility, non- convexity, Pontryagin Principle, power laws, property rights, separatrix, structural stability, thresholds 1. Economists’Convexities andNature’sNon-Convexities Theword“convexity” isubiquitous ineconomics, butabsent fromecology. There isareasonforeach.Aspricesareprominentinmoderntransactions,itisbutnatural that we would wish to uncover the ways in which the price system is capable of functioning as a resource allocation mechanism. In recent years economists have identi ed notonlythewayinwhichpricesaggregate dispersed pieces ofinforma- tion, but also the sense in which they re ect the relative scarcities of goods and services. Wenowknowthatthepricesystemcanbeanef cientallocation mecha- nismiftransformation possibilities amonggoodsandservices–inandovertime– constitute aconvexset.1 However, except in the case ofpartial economic systems, as in models of industrial organization (Tirole 1993), or of systems harbouring very speci c forms of non-convexities, as in modern growth models (Jones 1998) or in models of poverty traps based on the connection between nutritional status and human productivity (Dasgupta and Ray 1986, 1987; Dasgupta 1997) or in models of spatial economies (Fugita, Krugman and Venables 1999), we still do nothaveaclearunderstandingofthemechanismsbywhichresourcesareallocated in non-convex environments. So we economists continue to rely on the convexity assumption, alwayshopingthatitisnotanembarrassing simpli cation. Ecologists have no comparable need to explore the structure of convex sets. They are interested in identifying pathways by which the constituents of 1 P. Dasgupta& K.-G.Mäler (eds.), The Economics of Non-Convex Ecosystems,1 _ 27. ©2004 Kluwer Academic Publishers. Printed in the Netherlands. 2 PARTHADASGUPTAANDKARL-GÖRANMÄLER an ecosystem interact with one another and with the external environment. A large body of empirical work has revealed that those pathways in many cases involve transformation possibilities amongenvironmental goods andservices that, together, constitute non-convex sets. Often the non-convexities re ect positive feedbacks in Human-Nature interactions. Mathematical ecologists therefore study the structural stability of ecosystems and the sizes and shapes of their basins of attraction for given sets of environmental parameters.2 Such notions as the “resilience” ofecosystems areexpressions ofthisresearchinterest.3 The price mechanism is especially problematic in economic systems charac- terised by positive feedback processes. We now know that in such environments it may prove impossible to decentralise an ef cient allocation of resources by means exclusively of prices. Ef cient mechanisms would typically involve addi- tional social contrivances, such as (Pigouvian) taxes and subsidies, quantity controls, social norms of behaviour, and so forth. This was proved formally in a justly famous article by Starrett (1972), who showed that for certain types of non-convexities associated with environmental pollution, a competitive price equilibriumsimplydoesnotexist:marketsforpollutionwouldbeunabletoequate demandstosupplies.Starrett’snon-convexitiesarepresentwhenlossestraceableto environmentalpollutionarebounded.Ifthemarketpriceforpollutioninsuchsitua- tions were negative (i.e., the pollutor has to pay the pollutee), pollutees’ demand would be unbounded, while supply would be bounded. On the other hand, if the pricewerenon-negative, demandwouldbezero,whilesupply, presumably, would bepositive.4 Starrett’s ndingimpliedthatprivatepropertyrightstoenvironmentalpollution would not be capable of sustaining an ef cient allocation of resources by means of the price system. In a subsequent note, Starrett (1973) demonstrated by means of an example that if property rights are awarded to polluters, even such a non- price resource allocation mechanism as the core may not exist. But he showed (Starrett1972)thatasuitablychosen setofpollution taxes,together withasystem ofcompetitivemarketsforothergoodsandservices(assumingthatthelatterconsti- tute a convex sector), would be capable of supporting an ef cient allocation of resources. Asthere are no markets forpollution insuch anallocation mechanism, the problem of equating supply to demand in pollution activities is bypassed. The moral would appear to be that social dif culties arising from the non-convexities can be overcome if the State were to assign property rights in a suitable way – permitting private rights to the convex sector, but reserving for itself the right to controlemissions anddischarges.5 2. EcologicalThresholdsandtheEnvironmentalKuznetsCurve Despitetheecologist’sstrictures,weeconomistshaveremainedambivalenttoward Nature’snon-convexities. Oftenenough,thatambivalencerevealsitselfonlyindir- ectly. For example, it is even today commonly thought that, to quote an editorial THE ECONOMICS OF NON-CONVEX ECOSYSTEMS: INTRODUCTION 3 intheUK’sTheIndependent (4December 1999), “... (economic) growthisgood fortheenvironment because countries needtoputpovertybehind theminorderto care”; or, to quote The Economist (4 December 1999, p. 17), “... trade improves the environment, because it raises incomes, and the richer people are, the more willingtheyaretodevoteresources tocleaning uptheirlivingspace”. The view’s origin can be traced to World Bank (1992), which observed an empirical relationship between GNP per head and atmospheric concentrations of industrial pollutants. Based on the historical experience of OECD countries, the authors of the document suggested that, when GNP per head is low, concentra- tions ofsuch pollutants asthesulphur oxides increase asGNPperhead increases, but that when GNP per head is high, concentrations decrease as GNP per head increases further.6 Among economists this relationship has been christened the “environmental Kuznetscurve”.7 Themoralthatwouldappeartohavebeendrawn from the nding is that resource degradation is reversible: degrade all you want now,Earthcanbereliedupontorejuvenate itlaterifyourequire it. The presumption is false. Nature’s non-convexities are frequently a manifes- tation of positive feedback processes, which in turn often means the presence of ecological thresholds. But if a large damage were to be in icted on an ecosystem whose ability to function is conditional on it being above some threshold level (in size, composition, or whatever), the consequence would be irreversible.8 The environmental Kuznets curve was detected for mobile pollutants. Mobility means that, so long as emissions decline, the stock at the site of the emissions declines. However,reversalisthelastthingthatwouldspringtomindshouldagrassland ip to become covered by shrubs, or should the Atlantic gulf stream shift direction or come to a halt, or should a source of water disappear, or should an ocean shery become a dead zone owing to over shing. As a metaphor for the possibilities of substituting manufactured and human capital for natural capital, the relationship embodiedintheenvironmental Kuznetscurvehastoberejected.9 Althoughnon-convexities areprevalentinglobalecosystems(e.g.,oceancircu- lation, global climate), it is as well to emphasise the spatial character of many positive feedback processes. The latter have a direct bearing on the rural poor in the world’s poorest regions. Eutrophication of ponds, or salinization of soil, or biodiversity loss in a forest patch involve crossing ecological thresholds at a spatially localised level. Similarly, the metabolic pathways between an indi- vidual’s nutritional status and his or her capacity to work, and those between a person’s nutritional and disease status involve positive feedback.10 Studies of extremepovertybasedonaggregationattheregionalornationallevelcantherefore mislead greatly. The spatial con nement of many of the non-convexities inherent inHuman-Natureinteractions needsalwaystobekeptinmind. The connection between rural poverty in the world’s poorest regions and the state of the local ecosystems should be self-evident. When wetlands, inland and coastal sheries, woodlands, forests, ponds and lakes, and grazing elds are damaged (owing, say, to agricultural encroachment, or urban extensions, or the 4 PARTHA DASGUPTA AND KARL-GÖRAN MÄLER constructionoflargedams,ororganizationalfailureatthevillagelevel),traditional dwellers suffer. For them – and they are among the poorest in society – there are frequently no alternative source oflivelihood. In contrast, for rich eco-tourists or importers of primary products, there is something else, often somewhere else, which means that there are alternatives. Whether or not there are substitutes for a particular resource is therefore not only a technological matter, nor a mere matter of consumer taste: among poor people location can matter too. Thepoorest of the poorexperience non-convexities inawaytherichdonot. Eventherange between a need and a luxury is context-ridden. Macroeconomic reasoning glosses over the heterogeneity ofEarth’s resources and the diverse uses to which they areput – by peopleresiding atthesiteandbythoseelsewhere.11 3. Motivation BehindthisSymposium Despitetheirprevalence,weeconomistscontinuetoshowlittleinterestinNature’s non-convexities. Forexample, thenowenormous literature on“greenaccounting” has been built largely on the backs of economic models in which non-convexities aresafelyoutofsight.12 Inviewofthis,theBeijerInternational InstituteofEcolo- gical Economics in Stockholm invited a group of ecologists and economists to studytheeconomicsofnon-convex ecosystems. Beginningin1998,thegroupmet regularly.13 Weknewthatmuchfundamentalworkhadalreadybeenaccomplished on non-linear dynamical systems. Some of it had already been used to study the economics of non-convex social environments.14 Our idea therefore was to use these techniques so as to study proto-typical Human-Nature interactions. Speci c applications wereverymuchinourmind. Asourunderstandingoftheissuesimproved,wefeltitwouldbedesirabletooif thearticleswepreparedwerewrittenexpansively.Soweencouragedourselvesalso toreviewwhathasalreadybeenachievedinthesubject. Wefeltthatthecollection could then serve as a self-contained body of work, useable in graduate courses in environmental andresource economics, perhaps useful aswelltoresearchers who wish to work in this eld. In order to increase accessibility to the collection, we feltitwouldbeappropriate topublishitinajournal, ratherthanasabook. Weare thereforemostgratefultothemembersoftheEditorialBoardofEnvironmental and ResourceEconomics,especiallyIanBatemanandKerryTurner,fortheenthusiasm theyhaveshowntowardourenterprisefromthetimeweapproached them,andfor theencouragement they havegiven ustoproduce thecollection intheform that it nowappears. THE ECONOMICS OF NON-CONVEX ECOSYSTEMS: INTRODUCTION 5 4. MacroRegeneration FunctionsofEcosystems 4.1. PRODUCTION FUNCTIONS AND COMMODITY POSSIBILITY SETS Incontrasttotheproductionscale-economiesstudiedintraditionalpricetheory,the non-convexities associated with ecological thresholds manifest themselves across time. Nevertheless, there is a formal connection between the two types of non- convexities. To see this, consider the economist’s old stand-by, a one-commodity, constant population economy, where the commodity in question is durable and non- deteriorating. Timeiscontinuous andtheeconomyisdeterministic.15 LetK (≥0) t and C (≥ 0) be the “capital” stock and the flow of consumption, respectively, at t t (≥ 0). Output is assumed to be given by the production function F(K), where F is differentiable everywhere, F(0) = 0 and F(K) > 0 for some K > 0. An extreme assumption,muchusedingeneralequilibriumtheory,isthatoutputisfreelydispos- able.Subsequentlywewillseewhattheassumptioninvolvesandwhyitsviolation issignificant forthesubject ofthisSymposium.16 LetI denoteinvestment att.Sinceoutput isfreely disposable, wemayexpress t thebalanceofflowsateachdateintheeconomybytheinequality, I ≤ F(K)−C, fort ≥ 0,andK (> 0)isgiven, (1a) t t t 0 which,withoutrigorous justification, wewriteas, dK/dt ≤F(K)−C, fort≥ 0,andK (> 0)isgiven. (1b) t t t 0 A programme is a complete forecast of the economy, from the present (t = 0) toinfinity.Aprogrammecanbeexpressedas{K,C,dK/dt} ∞.Forsimplicityof t t t 0 exposition, wesuppose thatanyprogrammesatisfying (1b)isfeasible; whichisto saythattheeconomyisnotsubjecttoanyotherconstraint. Thequestion iswhetherthesetoffeasibleprogrammes isconvex. TheanswerdependsonwhetherFisconcaveeverywhere(henceforth,concave). Toconfirmthis,assumethatFisconcave. Consideranytwofeasible programmes, which we write as {K∗, C∗, dK∗/dt} ∞ and {K(cid:5), C(cid:5), dK(cid:5)/dt} ∞. By definition, t t t 0 t t t 0 bothsatisfy(1b).Hence, dK∗/dt≤ F(K∗)−C∗, fort≥ 0,andK ∗ = K , (2) t t t 0 0 and dK(cid:5)/dt≤ F(K(cid:5))−C(cid:5), fort≥ 0,andK (cid:5) = K . (3) t t t 0 0 Nowchooseanumberγ,where0 ≤ γ ≤ 1.Define C¯ = γC∗ +(1−γ)C(cid:5) andK¯ = γK∗+(1−γ)K(cid:5). (4) t t t t t t Wewishtoconfirmthat{K¯ ,C¯ ,dK¯ /dt} ∞ alsosatisfies(1b). t t t 0 From(2)and(3),wehave, γdK∗/dt ≤ γF(K∗)−γC∗, fort≥ 0,andK ∗ = K ,(5) t t t 0 0 and (1−γ)dK(cid:5)/dt ≤ (1−γ)F(K(cid:5))−(1−γ)C(cid:5), fort ≥ 0,andK (cid:5) = K . (6) t t t 0 0
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