Dasgupta P., (1990) The Environment as a commodity.pdf

8/10/2019 Dasgupta P., (1990) The Environment as a commodity.pdf

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OXFO RD REVIEW OF ECO NOMIC POLICY, VOL. 6, NO. 1

THE ENVIRONMENT AS A COMMODITY

PARTHA DASGUPTAStanford University, University of Cam bridge, and World Institute for Developmen t Econom ics Research*

I. THE PRODUCTION OF COMMOD ITIES

BY MEANS OF RESOURCES

All economic activity is based ultimately on re-sources found in nature. Wh ether it is consum ptionor production, or whether it is exchange, the com-mod ities which are involved are ma de of constitu-ents provided by nature. Thu s, the ingredients ofany manufactured good are other produced goods,labour time and skills, and natural resources. Eachof these constituent produced good s is in turn m adeup from the ingredients that went into i ts m anufac-ture, namely labour time and skills, natural re-sources, and further produced goods. It followsthat any manufactured commodity is ultimately acombination of labour and natural resources.

Labou r too is a produced good. Even raw labour isan output, manufactured by those natural resourceswhich sustain life, resources such as the mu ltitude

of nutrients we consume, the air we breathe, and

the water we drink. All commodities are thereforetraceable to natural resources.

The point in exposing the morphology of producedgoods and services is not to construct a resourcetheory of a value. There are any num ber of naturalresources, and this alone precludes such an at-tempted theory from being coherent. My purpose,rather, is to use it to exp ress su rprise at the fact thatdespite the centrality of natural resources in eco-nomic activity, they find little room in economicsdiscourses. Interest in resource econom ics, moreparticularly environmental economics, has onlybeen intermittent, and if we are currently witness-ing a resurgence (and this special issue is an ex-ample of it), we have also just lived through adecade-long neglect, during which much valuableresearch could have been done.2 W e are way behindwhere we should have been, and could have been,

1 This paper was given as part of the Stevenson Lectureship series in the University of Glasgow, and will appear inInformation Strategy and Public Policy edited by Andrew Stevenson and David Vine s, to be published by Basil Blackwell inthe course of 1990.

2

This neglect has been a persistent phenomen on in British universities. Courses on resource econom ics have been regularlyon offer in major econo mics depa rtments in Scandinav ia, the United States, and Canada o ver the past fifteen years or so. Buteven there, interest has been muted in recent years.

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OXFO RD REVIEW OF EC ONO MIC POLICY, VOL. 6, NO. 1

to confront the many environmental problems wehave again becom e conscious of.

In fact, there is another problem with periodicintellectual slum ber. It is that with each reawaken-ing , much of what had bee n developed earlier is notknown or acknowledged: economists are notori-ously ignorant of intellectual capital. (In manyinstances, however, the extent of ignorance is soastonishing that on e can only assume it is feigned.)Much energy is then spent rediscovering ideas.Thu s, there is no credible reason today why econo-mists should have to write on the analytical founda-tions of environmental taxes, or the informationalparsimony afforded by transferable pollution per-mits. Nor is there any reason why politicians,

journ alists, and internation al agencies have n ow tobe told that estimates of net national product oughtto take account of the degrada tion of environmen talstocks; nor indeed, why we need now to try andfathom what 'sustainable developm ent' might plau-sibly mean; or what ethical drive the concept ofsocial discount rates ma y possess. These issueswere the subject of a rather successful research pro-gramm e am ong technical economists a decade anda half ago.3 As subjects for analytical investigation,these topics are now very cold. As research prob-lems they are dead.

There is even today a widespread misconceptionthat 'economic' calculations and environmentalconce rns are in conflict. The view is so pervasivethat thoughtful commentators on the environmentoften find it necessary first to state it and then tocorrect it by talking of the resurgence of 'greeneconomics' (see, for example, The Economist, 2Septem ber 198 9). In fact, this greening began along while ag o, at least as far back as Pigou (1920)in his classic developm ent of the concept of exter-

nalities, and his exposu re of the difference betweenprivate and social costs (and benefits) in the phe-nom eno n of externa lities. P igou , of cours e, did notcomplete the analysis. He could not, because therewere analytical difficulties he was incapable ofhandling, most especially those connected withtime, uncertainty, and the pervasiveness of asym-metric information, and those involving a small

number of econom ic agents.4 During the decade ofthe 1960s, and even m ore the decade of the 1970s,what we today call environmental econom ics, andmore generally resource economics, was developedand codified. (See, e.g., Coa se, 1960; Kn eese,

1964; Brown and McGuire, 1967; Krutilla, 1967;Dales, 1968; Arrow, 197 1; Starrett, 1972; Meade,1973; Arrow and Fisher, 1974; Maler, 1974; Baumoland Oates, 1975; Kneese and Schultze, 1975; Krutillaand Fisher, 1975; Review of Economic Studies(Symposium, 1974); d a rk , 1976; Maler and Wyzga,1976; Dasgupta and Heal, 1979; Dasgupta, 1982;and Lin d(ed .), 1982. Excellent elementary texts onthe subject are Hartwick and Olewiler (1986) andTietenberg (1988). U lph (1989) is a useful re ade rs'guide to existing textbooks and treatises on the sub-

je ct ) Its incorporation into development econom -ics, especially development planning, has beenrather slower. (For an early attempt, see Dasgupta,1982.) B ut the analytical elemen ts are all availablefor use.

In this paper, I will not produc e a litany of e nviron-mental losses. This has been done to great andfruitful effect by others more knowledgeable onthese matters. (See, for exam ple, the documentspublished regularly by the W orldwatch Institute inWashington, D.C., and the several State of theEnvironment reports, e.g. CSE, 1982,198 6; IIED/WRI, 1987.) I shall approach matters instead fromthe analytical corner and borrow from the literaturewhich I have cited to provide an outline of the mainfeatures of the econ omics of the environm ent.

By an environmental problem I do not of coursemean only the classical one of the factory chimneypolluting the atmosp here. I mean a great deal moreand I shall try to present a unified viewp oint whichwill be wide enough to catch within its net a

seemingly disparate class of resource problems.The advantage of a unified formulation is that itenables us to econom ize in our thinking. Given anembracing framework, we can borrow from ourunderstanding of one class of issues when w e con-sider some other class of issues. And it puts theonus on us to prove when we claim, as we rightly doin many cases, that a given environmental p roblem

' See below in the text for references and sources for further references.4 Even HoteUing's great article (Hotelling, 1931) merely scratched the economics of exhaustible resources. The

incorporation of substitutability among resources, of technological change, and, more generally, the placing of the subject inthe context of intertemporal general equilibrium, could be completed only over four decades later.

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has its own special features, reflected not only bythe specific nature of the resource under study, butalso by its location, the time in question, and thesocio-econom ic context in which it occurs.

As it happens, even here there are a number ofroutes along which one can enter a discussion. Ishall, to begin w ith, adopt one which is hallowed bytradition, and is in other respects as good as anyother route. Late r in this paper (section VI), I shalladopt a different route. W e will see that the two willhave the same implications for public policy. Ourstarting gate will therefore not matter. The twoavenues w ill lead u s to the same destination.

II . MISSING MARKETS AND THEBREAKDOWN OF SOCIAL NORMS

I want to begin by thinking of market failure and Ibegin with the observation that in many caseswhere markets malfunction, their malfunctioningcan be ascribed to the fact that for certain comm odi-ties mark ets simply do not exist. Sometimes theyhappen not to exist for accidental or historicalreasons, sometimes there are logical reasons whythey cannot exist, sometimes the nature of the

physical and political situation keeps them fromexisting, or makes them function desperately wronglywhen they do exist. What are usually called envi-ronmental resources are, as it happens, p articularlyvulnerable to this problem.

By ma rkets I do not necessarily mean price-guidedinstitutions, I mean something a good deal moregeneral. By markets I mean institutions whichmake available to affected parties the opportunityto negotiate courses of actions. And by malfunc-tioning markets I mean circumstances where suchoppo rtunities are not present, w here they are at bestpresent only partially, or where they are somew hatone-side d. (This last, the often one-sidedness ofopportunities, means that I am thinking of distribu-tional issues as well, not merely those bearing onefficiency.) The existence of com petitive marke tprices presupposes only one set of institutionalarrangements within which such negotiations can

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take place (as it happens they render unnecessaryany negotiation ). Bilateral bargaining is another,and there are a whole host of intermediate institu-tions, those providing the scope for multilateralbargaining, the agreements arising from which areon occasion codified over the years through theemergence of social norms, and the associatedsocial sanctions imposed up on those in violation ofsuch norms; and upon those who fail to imposesanctions upon those in violation of such norms;and upon those who fail to impose sanctions uponthose who fail to impose sanctions upon those inviolation of such norms, and so on indefinitely.

This is important to recognize, that social normscan be seen as implicit social contrac ts. P ut anotherway , social norm s are strategies of beha viour. Butthey are strategies that are sustained by self-enforcement, and not by the law courts. Providedpeople are not unduly myop ic (see Appe ndix), thecontract could be enforced if each perso n were ablecredibly to threaten a withdrawal of his co-operalionfrom any person who violated the contra ct. Sinceso much of resource management in traditionalsocieties has been sustained by norm s of behaviour,I shall try to make all this a bit mo re precise. It willalso suggest why norms can break down during

periods of change. And if they are not replaced bynew, effective norms, the society begins to sufferfrom 'market failure'.3

At any date, call a person a conformist if he co-operates with a person if and only if that person hasshown himself at the previous date to have beena conformist.6 At the starting date, we define aconformist to be one who co-operates; that is, on ewho keeps his side of the bargain. From thedefinition of a conformist, this society can thenrecursively determine at any future date whether agiven person is a conformist. It is then possible toshow that if people are not unduly myopic, itis in the .^//-interest of each person to be aconform ist if all others conform. But this meansthat universal conformism is self-enforcing.

Notice that the social norm in this example isconformism. A non-conformist is a deviant. And

5 In the A ppen dix I give a formal accoun t of this line of argument for a simple 2-person m odel of negotiation. I should addthat norms can b e inefficient. The Folk Theorem in game theory is an articulation of this fact. But in what follows I shall bethinking of norms which ar e efficient.

6 This assumes that individual actions arc publicly observable.

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OXF ORD REVIEW O F ECON OMIC POLICY, VOL. 6, NO. 1

a conformist pun ishes him by w ithdrawing his co-oper ation. Th us, in particular, a conformist pun-ishes a person who has failed to punish someonewho has violated the social norm. This is becausein failing to punish the violator, the person in

question himself is a violato r of the social norm Inthe Ap pend ix, I will prese nt the simplest version ofthe formal argum ent. It will make clear the roleindividual discount rates play in sustaining socialno rm s, and thus tacit co-operation. But even thisinformal account demonstrates that my startinggate, the phenomenon of market failure, has al-lowed me immediate access to the province ofanthropologists who have so often illuminated ourunderstanding of customs regarding the use ofenvironm ental resources in com munities that are atfirst sight not easy to comprehend. As it happens,such social customs are often instrumental in sup-porting objectives that are not dissimilar to thoseof a 'modem' bent, and they are often undererosion this is the m arket failurethrough shift-ing demographic features, newly emerging eco-nomic opportunities, and changing social moresand lifestyles. Rec ent work on the theory of bar-gaining, particularly in the context of repeatedgam es, has shown how fragile such social customscan be, how depe nden t they are on the ability of af-fected parties to mon itor the actions of others that

is , compliance of implicit contractsand on theability of each p arty to asse ss the value that othersattach to the resource in question. And so on. I shallcom e back to these issues in the following section.

III. RECIPROCAL EXTERNALITIES

Much of this has been studied under the generalrubric of what is today called the Problem of theCommons, a problem which is associated with

resources to which no property rights have beenaw arded. Such resources are therefore free to allwho w ish to avail themselve s of them. Being freeand finitely available they are used excessively.(One nee ds to add some qualifications to make thisinference, but I will ignore theoretical nicetieshere.) W e may conclud e that the social value, oraccounting p rice, of a 'com mo n property' resourceis positive, on occasion large and positive, evenwhile it is free to individual users.

Such resources abound. The earth's atmosphere,which is in a continual state of diffusion, is a

paradigm . It is a global com mo ns, and such prob-lems as are thought to arise from various green-house gases, including carbon dioxide which is no trecycled by vegetation and plankton, are globalproblems and have to be attacked at an internationallevel of discourse. Moreover, all nations will haveto be involved in negotiation. It will not be eno ughif only a few nations agree on a joint co-ordinatedpolicy; those not party to the agreem ent w ill followpolicies that will vitiate the point of the ag ree me ntSo too with other global comm ons, such as interna-tional fisheries, deep-sea nodu les, and the interna-tional waters as a repository of our garbage. TheUnited Nations Law of the Sea Conferences havebeen an instance of this; not an inspiring instance,but it was better to have had them tha n not.

The global commons associated with greenhousegases poses particularly interesting questions be-cause it is twin-edged. Reca ll that the comm onproperty here is the earth's atmosphere, measuredby a quality index, what one might call a general-ized air-quality index. The burnin g of fossil fuelsadds to the emission of greenhou se gases . If thegreen hou se effect is indeed significant and if this infact does lead to overall dam age in crop production,fisheries, habitation, and so forth, we would sayceteris paribus the emission of greenhouse gaseslowers this quality index. As we noted earlie r, fromthe fact that we are all free to emit carbon dioxide,nitrous oxides, methan e, etc. we m ay conclud e thatwe emit too much of it. This is a problem of globalcomm ons w ith a vengeance. Unhappily, it is onlyone side of the matter. The other side is the fact thatcarbon dioxide is recycled by plants and vegetation,and if their stock is allowed to fall, the retention ofcarbon dioxide by the atmosphere will be increased.Brazil is one major repository of such vegetation.Notice that the private cost to Brazil of p ursuing a

depletion policyinsofar as the carbon dioxideissue is concernedwill be far less than the globalcost. Brazil will not take account of the dam agesincurred by the rest of the world. So then, one willexpect Brazil to deplete at a faster pace than isglobally warranted, thus exacerbating the carbondioxide problem. As it happ ens, Brazil is engagedin a murderou s depletion policy. Th e gap betweentheory and applicationin environm ental econom icsis a pleasantly narrow one.

So whatis one to do? I cannot think it w ill do to looksolemn and utter pious sentiments concerning our

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mo ral duty. Morality is a scarce resource, and oneneeds to economize its use when considering im-plementable public policy. Truly multilateral bar-gaining about reductions in carbon dioxide emis-sion is one way. How ever, multilateral bargaining,leading to mutual reduction in po llution emission isa plausible way only when the problem is some-what common, and is perceived to be common,with the stakes being roughly the same for allparties. This is so when the damages which areinflicted are reciprocal; that is, when each of theparties damages all the other parties through itsactions to roughly the same extent. It is a lessfeasible way w hen the damage is somewhat unilat-eral, as with Brazi lian deforestation. The idea ofinternational compensation to the depleter for re-

ducing the rate of depletion should no longer beregarded as far-fetched. Part ial debt-re lief for alower rate of plunder of the Amazonian forestis something that will probably be on the agendain the near future. This is Pigouvian subsidy.It is hard to imagine that there are many otheroptions open to us.

I have begun with global comm ons because they areas good as any on w hich to fix ideas, and in any casethey are the ones that receive the greatest attentionin both the national and internationa l press. But aswe go about our daily lives, it is local commonswhich we encoun ter most often. Their effect ismo re imm ediate and is often shattering, mo st espe-cially for those whose livelihood is based directlyon them . Overg razing, overfishing, the depletionof trees and shrubs from common land for use asfuel are familiar problem s. They are traceable to thecom mon property nature of such resources as graz-ing land, fisheries, and forest cover. So too with thedrawin g of water from aquifers which by the natureof things must usually be common property evenwhen the land covering the aquifer is privatelyowned.7

One reason why the problem of the commons hasbeen studied so intensively by economists is thatthe policy issues they give rise to possess theagreeable feature of our not having to choose be-tween equity and efficiency. If the users of acommon property resource are pretty much sym-

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metrically replaced, a joint policy of restrictingtheir use will be beneficial to all, and to roughly thesam e extent. It ma y even save the resource fromruin and this will benefit future users who are notcurrently a party to the social contract. Nothin gcould be nicer.

IV. COMM ONS CUSTOMS AND NORMS

It may seem that geographically localized com-mo ns have a better chance of being protected fromexcessive use than global commons. It is not somuch the smaller num ber of users that make localcommons easier to manage, it is rather that theusers ' activities are easier to mo nitor. If private

action cannot be monitored publicly, sanctionscannot be imposed on violators, and a social con-tract, even if it were to be reached, would amo unt tonothing. An unenforceable contract is no contract.Then of course, there is the question whether anagreem ent would in practice be reached. Agree-ment is presumably easier to reach if the partieshave long know n on e another, expect to continue toknow one another, and hope to avail themselves ofthe resource for a long w hile. It is not merely aquestion of social niceties, although this can be

imp ortant. It is also that the parties are then likelyto know how the resource is valued by each. (Thisis important, although it is often overlooked indiscussio ns on these matters. You cannot effec-tively bargain with someone if you have no cluewhat his values are. Indeed, you may think that hethinks there is nothing to bargain over, that is, thereis no mutually beneficial set of actions to agreeupon .) And finally, yet another reason why theseconditio ns are a prerequisite is that it is only undersuch circum stances tha t each party will have a long-term interest in the resource. It will then discoun tits future value at a low rate. Th is, as I shall arguein a rather different context, is in practice of greatsignificance.

Social contracts, whether or not they are explicit,have to be simple to be effective. More specifically,contractual obligations need to be pretty muchinvariant across states of nature, or eventualities.This is partly because the mind has limited capacity

7 I am ignoring the pressu re of popu lation grow th on natural resource use in this paper. This raises a som ewhat w ider set

of issues, connected n ot only with com mon p roperty resources and the absence of an adequate set of capital markets. It is alsotied to the fact of the subjugation of women, a phenomenon that is particularly acute in poor countries.

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OXFORD REVIEW OF ECONOMIC POLICY, VOL. 6, NO. 1

forprocessinginformation, for evaluating informa-tion, and for acting upon informa tion. And so it willnot do for such a contract to have too many quali-fications, to allow for too many exceptions to therule. B utit is partly also because agre atma ny statesof nature are only privately observable, and notpublicly confirmable, and one should recall thatobliga tions which are conditiona l only on privatelyobservable states of nature are not enforceable,unless they are com patible with private incentives.8

Fo r these reasons, social contracts need to be sim pleif they are to promote individual or group well-bein g. As we noted earlier, social norms can beregarded as implicit contractual obligations.9

In stationary socio-economic environments they

are enshrined in custom s and rituals, with the resultthat the contractual behaviour is adopted effortlessly.If you are steeped in norms that are socially codified,you do not calculate every five minutes how youshould behave. You simply follow the norm. Thissaves on computation costs all round, not only foryou as an actor, but also for you as 'policem an' and'jud ge'. This will be fine so long as the backgroundenvironm ent remains pretty much the same. But itwill not be fine if the environment changes suddenly.You m ight even be destroyed. It is this heightenedvulnerability, often more real than perceived, whichis the cause of som e of the greatest social tragediesin contemporary society. This additional vulnerabilityis brought in their wake by shifting populations,ageing populations, predatory governments andthieving aristocracies (see sections V and VI), andtechno logical p rogress; but a part of the underlyingcauses is the absence of adequate property rightsand the psychological and learning costs involvedin altering on e's behavioural norms. As notedearlier, a stationary society need not tamper withthe commonality of a common property; it can

arrive at an efficient use through an implicit con tractThe tragedy I am alluding to is the breakdown of thecontract unreplaced by a new and, for the historicaluse rs, beneficial co ntract. The locus of the problemdoe s not usually lie in the place identified by H ardin(196 8) in his famous essa y. It lies where I haveidentified it

V. UNIDIRECTIONAL EXTERNALITIES

A defining characteristic of the problem of thecomm ons is its reciprocal nature. If I bring anadditional cow into the comm on pasture I harm youand all other cattle people: there will be just thatmuch less grass for your cattle and for those ofothers. If you bring an additional cow into thepasture you harm me and all other cattle people.

The commons may, of course, involve many eco-nom ic actors. In this situation, the damage eachactor inflicts on on e is often ne gligib le. But the su mof the damages inflicted by the man y on one can besubstantial.10 Now , all this ma kes for a certainsimplicity of analysis an d, as we have note d, for an

ease in locating mutually beneficial policies. Mattersare greatly more problematic, in need usually ofpublic action, for damages which are unilaterallyinflicted. A m ost significant instance of this isdeforestation in the up lands inflicting damag es onthe lowlands. As alway s, itpa ys to concentrate firston the assignment of property rights before seekingremedies. The com mon law , if one may be permit-ted to use this expression in a universal context,usually recognizes pollu ters' rights, not those of thepollutees. Translated into our present example thismeans that the timber merchan t who has obtained aconcession in the upland forests is under no o bliga-tion to com pensate farmers in the lowlands. If thefarmers want to reduce the risk of heightenedfloods, it is they wh o have to compensate the timbermerchant for reducing the rate of deforestation.Stated this way, the matter does look morallybizarre, but it is how things are. Had property rightsbeen the other way round, one of pollutees rights,the boots would hav e been on the other set of feet,and it would be the timber merchant who wouldhave had to pay compensation to farmers for the

right to inflict the damages that go with deforesta-tion. How ever, when the cause of the damag e islocated hundreds of miles away and when thevictims are thousands of impo verished farmers, theissue of a bargained outcom e do es not really arise.It is difficult to see such farmers grouping effec-tively as a negotiating party. Judged even from the

* As a half-serious illustration, the reader should ask if it is feasible to engage in bets on people's states of mind.9 In a highly original pie ce of work, Gauthier (1986) argues that even morality should be so regarded.

10 Forma l dem onstration of this can be found in many writings. See, e.g., Dasgupta and Heal (1979, ch. 3).

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viewpoint of efficiency, the system of polluters'rights in such an example is disastrous. We wouldexpect excessive deforestation. The timber mer-chant, it will be recalled, does not have to com pen-sate the lowland farmers. Put another way, them erch ant's private cost of logging falls short of itssocial co st The problem is exacerbated if thetimber concession is a short-lived one and if theconcession is not allied to any serious form ofpublic regulation. In such situations the mercha ntwould discount the future value of the forest at ahigh rate, and thereby log at a fast rate, faster thanthe long view would war rant The com bined effectof high rates of discount and the infliction ofdam ages to farmers can be shattering, and we nowsee evidence of this in many parts of the globe.

In each of the examples I have so far alluded to,whether it involves reciprocal damages (as in theproblem of the com mon s) or unidirectional ones (aswith upland deforestation) there is a wedge be-tween the private and social costs associated withthe use of some n atural resource: in extreme casesprivate costs are nil. But the fact that social costs arehigher, sometimes a great deal higher, means thatother things being the same, resource-based goodsare underp riced in the market. Quite obviously, theless roundabout, or less distant, the production ofthe final goo d from its resource-base the greater isthis unde r-pricing, in percentage terms. Put an-other way, the lower is the value-added to theresource , the larger is the extent of this underpricingof the final prod uct. We can conclude therefore thatcountries which export primary products do so bysubsidizing them, possibly at a massive scale.Moreover, the subsidy is paid not by the generalpublic via taxation, but by som e of the most disad-vantaged m em bers of society: the sharecropper, thesmall landholde r or tenant farmer, and so on. The

subsidy is hidden from public scrutiny; that is whynobody talks of it. But it is there. It is real. Suc hsubsidies are both inefficient and inequitab le. Weshould be in a position to estimate them . As of nowwe have no such estimates.

VI. GOVERNMENT FAILURE

All expositions on the econom ics of environm entalresources with which I am familiar begin with

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market failure. There are pedagog ical advantagesin their doing so. This is why I began with it here.But once you start from there, you know what thenext step is . It is to develop a conceptual basis forgovernment interventionin the design of envi-ronmental taxes, regulations, licenses, and so forth.11

But in fact w e could as well have b egun from theopposite end: the failure of centralized modes ofcontrol in the allocation of resources. The recordof East European governments on environmentalmatters is as good a starting point as any. Now , thereason why we wo uld not expect systems of central-ized control and comm and to work w ell are famil-iar. There is , first of all, the enorm ous poten tial forcorruption to becom e engrained in a system w here

bureaucrats and the military have extensive pow ersto control resources. There is also a technicalreason. It has to do with the massive qu antities ofinformation a centralized agency w ould be requiredto possess and process if it were to app ly con trolseffectively. No single agency can ever obtain suchamo unts, let alone use it in a reliable man ner. It is ,of course , the single-mo st telling characteristic ofdecentralized resource allocation mec hanism s thatinformation is decentralized in them . In the field ofenvironmental resources, where matters pertain tosoil erosion, deforestation, air and w ater pollution,fisheries extraction, and so forth, the necessity ofrelying on mecha nisms w hich make essential use ofdispersed information is immediate.

It follows therefore that ideal resource allocationmechanisms are mixed-'market' systems, where'm ark ets' are allied to judiciou s forms of gov ern-men t intervention in the allocation of a wide rangeof resources.12 Current experim ents in the UnitedStates with transferable permits in the field ofpollution are an instance of this. (See Da les, 1968,for the original proposal, and Tieten berg, 1980, foran overview of the experience accumu lated on theuse of such permits.) A fixed num ber of marketableperm its has two virtues at once. It first of all putsa ceiling on total emission in any given period. Ifthis ceiling is chosen judiciously, there is littlechance that serious dam age will occur. Secondly,their marketability means that polluting f inn s' privateinformation concerning their technologies is al-lowed to play an effective role in the allocation ofthese permits among them. The conceptual sim-

11 Kneese and Schultze (1975) is a good early discussion of these issues.12 I qualify the term 'market' because, as we have seen in sections II and HI, markets should be interpreted in a sense which

is wider than the one in which they are commonly understood.

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plicity of tradeable perm its has much to com mendit. But at an analytical level, there are superiorallocation me chanism s. They involve firm-spe-cific, non-linear pollution taxes. (See Dasgupta etai, 1980, and also Da sgu pta, 1982, ch. 4.)

Let us recall that an environmental problem existswhenever there is a gap between the accountingprice of a natural reso urce and its actual, o r marketprice.13 In earlier sections we have seen that such agap can arise because of missing markets. But, ofcours e, it can arise also as a direct consequence offaulty gove rnmen t policy. Wh en the State subsi-dizes the use of pestic ides and fertilizers with an eyesolely to agricu ltural produc tion, it creates a wedg ebetween their accounting and market prices. This

is because it has not simultaneou sly kept an eye onthe environmental damages that in future will betriggered by the chem icals. Mo re generally, whenpublic policy is determ ined under the suppositionthat natural resources are unlimited, a gap appearsbetween accounting and actual prices. Now herehas this been oc casion ed m ore dramatically than inthe process of con version of agricultural and forestland into ranch es and unuse d, denuded land in LatinAm erica. W hat has attracted most attention inrecent years is the deforestation of the AmazonBasin accom pany ing this territorial expan sion. Inan early and neglec ted p air of articles, Feder (1977 ,1979) described h ow m assive private investmen t inthe expansion of beef-cattle production in fragileecological conditions has been supported by do-me stic govern me nts in the form of tax concessionsand prov ision of infrastructure, and by loans frominternational agencies.14 As a case-study in policymism anagem ent mo re accurately, as an exampleof predatory be haviou r on the part of the Statethisone is difficult to imp rove upon. Governm entpolicy , promp ted by the landed and industrial aris-

tocracy , and the military, and aided by international

agencies, was instrumen tal in degrading vast tractsof valuable environmental resources. And it simul-taneously disenfranchised large numbers of smallfarmers and agricultural labourers from the econ-omy, and made at best destitutes of traditional

forest dwellers. There is absolutely nothing tocommend it1 5

As with market failure, government failure of thekind we have just studied results in an excessive useof environmen tal resources. We can conclude thenthat policy reversals designed to rem ove suc h self-inflicted distortion can b e expected to yield at leasttwo kinds of benefits: an increase in aggregateincome and a discouragement of excessive environ-mental destruction. And to top it, such policy

reversals could well improve the w ell-being of thepoo restin society. F eder 's analysis of Latin Am eri-can agri-business suggests this last strongly.

VII. THE ENVIRONMENT ASRENEWABLE NATURALRESOURCES

Thus far we have been thinking of environmentalresources as those naturally occurring co mm oditiesand services whose markets malfunction for a par-ticular set of reasons: those arising from imper-fectly monitorable rights of use and, in extremecases, from an absence of specified rights. As wehave noted, this allows us to draw fairly strongconclusions about appropriate public policy.

But it is only a partial view . It is a view from theinstitutional side of things. The re is another,complementary perspective from which one maylook at environmental reso urces. It is to study theirphysical characteristics. As it happ ens, there is a

simple and useful way of describing them, one

13 Accounting prices are often called shadow prices. I should add that a comm odity, or resource, should be specified not onlyby its physica l ch arac teris tics , date, location, and state of nature, as in Debreu (1959 ), it should also be specified by the agencytrans actin g in it. T his is vital for environmental re source s. It is important to think of them as named goods. (See Hahn, 1971.See also A rrow , 1 97 1, and Starrett, 1972.) Anoth er way of putting this is to say that these goods are agent-relative. Thus, togive an exam ple, a polluting firm's smoke emission, as it is perceived by the neighbourhood laundry, is a different com mod ityfrom that same emiss ion as perceived by the automobile tyTe shop in the same neighbourhood.

14 Ironic ally, the W orld B ank w as much involved in loans to this agri-business. It has in recent years reversed its policies,and it is now m ore se nsitive to environmental matters. As we noted in section I, concern with the environment is an intermittentaffair.

15 For further d iscussio n, see Dasgupta (1982, ch. 2). Mahar (1988) and Binswanger (1989) have recently compiled a more

complete l is t of macroeconom ic polic ies in Brazi l which have encouraged deforestation of the Am azon Basin . Repe tto (1988)is a fine survey of the general issue, the effect of government macroeconom ic policy on the en vironm ent

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which I elaborated upo n in Dasgupta (1982). I willsketch this now.

Environm ental problems are almost always associ-a ted wi th resources tha t a re na tura l lyregenerativew e cou ld call them renew able natu-ral resourcesb ut w hich are in danger of exhaus-tion from excessive use.16 No tice first that this isvery much consonant with common parlance. Re-sources such as m inera ls and fossil fuels do not fallinto this category; they are non-renew able, exceptin geological time. One should also note that weusually do not regard the depletion of a non-renew-able resource as an environm ental issue, except inso far as the act of extraction and use in productionhave 'environm ental effects'. Thus to take two

examples, the burning of fossil fuels increases theglobal mean tempe rature, and the smelting of oresis a comm on source of atmosp heric pollution. Theenvironme ntal issue here, as is usually understood,pertains not to the fact that the world's supply offossil fuels and min erals is being reduc ed, but ratherto that that such activities ha ve a deleterious effecton the earth's atmosphere, which is a renewablenatural resource. In these examples, the atmos-phere is used as a sort of sink, a repository of certainforms of wa ste produ cts. Stated only a bit differ-ently, we are concerned h ere with natural resources

which are capable of regenerating themselves solong as the 'environment* in which they are nur-tured remains favourable.

The earth's atmosphere, as we noted earlier, is aparadigm of such resources. Unde r normal coursesof events the atmosph ere regenerates itself in termsof its com position. But the speed of regenerationdepends upon the rate at which pollutants aredeposited into it and it depends also on the nature ofthe pollutant. (Smoke discharge is clearly different

from the release of radioactive material.17

) Now,whene ver we talk of a resource, we should think ofits stock and of way s of measuring it. In the case athand we ought to think of an atmospheric qualityindex. We ought also to think about its rate ofregeneration. This last will depend upon the natureand extent of the pollutants discharged. It will,however, also depend upon the current index ofquality; that is , the current level of stock. These are

P. Dasgupta

imm ensely com plex, ill-understood matters. Thereis a great deal of synergism associated with theinteraction of different types of pollutants in theatmosphere sink, but the analytical point I ammaking remains a valid one.

Animal, bird, plant, and fish populations are alsotypical exam ples of renewable resources. Andthere are today a num ber of studies connected withthe reproductive behaviour of different speciesunder a wide variety of'environm ental'conditions,including the presence of parasitic and symbioticneighbours. (For the use of such ideas in econo micmo dels, see Barrett, 1989.) Land is also such acommodity, for the quality of arable and grazingland can be maintained by careful use. Overuse

how ever impov erishes the soil and eventually pro-duces a wasteland. (The symbiotic relation be-tween soil quality and vegetation cover is , of course,at the heart of the current anxiety over sub-Saharanerosion.)

Underground basins of water often have a similarcharacteristic, the matterbeing even more problem-atic because w e are concerned bo th about its qualityand quantity. Und er normal circumstanc es anaquifer u ndergoe s a self-cleansing process as pol-lutants are deposited into it. But the effectivenessof the process depend s, as always, on the nature ofthe pollutants and the rate at which they are dis-charged. Furtherm ore, many aquifers are rechargedover the annual cycle . If, how ever, the rate of wate rextraction exceeds the recharge rate, the w ater tabledrops, thereby raising extraction costs. In factaquifers display another characteristic. On occa-sion the issue is not one of depositing pollutantsinto them. If, as a consequence of excessive extrac-tion, the water table is allowed to fall to too low alevel, then in the case of coastal aquifers there can

be salt-water intrusion, resulting in the destructionof the basin.

I conclude from these examples that one unifyingcharacteristic of environmental resources is theirregenerative capability, a capacity which can bedestroyed if they are exploited unw ittingly. In thissense, issues concerning what is usually labelled'pollution' can be studied in the same general sort

16 T here are excep tions of course, such as the ozone layer. It is an exha ustible res ource , pure and simple. But nothing is lostin my ignoring these exceptions here.

17 As noted in the previous footnote, the ozone layer is another example.

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of w ay as those concerning anima l, bird, plant, andfish populations, aquifers, forests, and soil qual-ity.18 And this brings us naturally back to a pointalready m ade, that markets for such resources caneasily fun ction b adly . If we now add to this a further

point we have noted, that their malfunctioning isbiased, that for reasons w e have identified, there isa strong tendency towards excessive use, rather thaninsufficient use, then we begin to obtain a consis-tent picture of what we are up against and whatpolicy debates should be about.

It is worth reiterating the importance of viewingthese com mo dities as renewab le natural resources.The y force us to look at the intertemporal structureof economic policies with all its attendant difficul-ties. Stated this way one may be led to think that weare up against yet another problem in what econo-mists have labelled 'capital theory', of which wehav e a good understan ding. It is certainly such aprob lem , but it is allied to a number of additionalcomplexities, of which one central class was dis-cussed at some length earlier, concerning imper-fectly o perating rights. But there is another class ofproble ms associated with environmental resources,and I w ant to probe it a bit in what follows.

VIM. NET NATIONAL PRODUCT

To beg in w ith, the kinds of resources we are think-ing of are, on occasion , of direct use in consum ption(as with fisheries), in production (as with plankton,which serves as food for fish species), or both (aswith drinking and irrigation water). Their stock ismeasured in different ways, depending on the re-sourc e: in mass units (e.g. biom ass for fisheries), inquality ind ices (e.g. air and water quality), in vol-ume units (e.g. acre-feet for aquifers), and so on.When we express concern about environmentalma tters we in effect point to a decline in their stock.Enviro nme ntal resources are therefore ap art of our

capital assets. And yet, we have little quantitativefeel for the extent of these s tocks and their rates ofchange. There are countries which suffer from analmost total paucity of inform ation on the extent oftheir forest cover, rates of soil erosion, water sup-

ply, and so forth. This ge ts reflected in the biasedmanner in which indices of econom ic performanceare computed. In what follows, we will discuss themost common indicator of aggregate well-being:real net domestic product1 9

Real net domestic product estimates are in badodour today. It is often thou ght that such estimatesare even in principle incapab le of reflecting aggre-gate well-being. This is not correc t. For it ispossible to show that, subject to certain technicalrestrictions, for any conception of aggregate well-being there exists a set of (agen t-relative) acco unt-ing prices which, if used in the estimation of netdomestic product, will ensure that the measurereflects aggregate well-b eing. (See Dasgupta andWeale, 1989.)20

Now , this is a stateme nt of princ iple. In practice,estimates of net dome stic product are biased, in thatthe prices which are used for valuing certain catego-ries of goods are system atically different from theiraccounting prices. This is especia lly so for natural

resources, and for reasons we have already identi-fied: their accounting prices are positive, but theirvalues are set at zero in estimates of net domesticproduct

Real net dom estic product is by definition the sumof the social (or acco unting) v alue of an econom y' sconsumptions and the social value of the changes inits stocks of real capital assets.21 Provided account-ing prices have been estimated accurately, an opti-mizing economy will choose the flow of its con-sumptions and net investmen ts so as to maximizereal net domestic product at each date.22 It wasshown by Samuelson (1961) and W eitzman (1976)

18 For further discussion of the analytical commonality among disparate environmental resource stocks, see Dasgupta(1982).

19 The analysis which follows was presented originally in Dasgupta and Heal (1979, ch. 8) and Dasgupta (1982, ch. 5).20 The technical restrictions amount to the requirement that both the set of feasible allocations and the social ordering

reflecting aggregate well-being are convex.21 Thus, capital gains or losses are not included.22 Read ers who are mat hem atically inclined will recogniz e that the Hamiltonian associated with in intertemporal well-being-

optim izatio n ex ercise is real net domestic product. This is what provides the motivation behind the definition of net nationalprodu ct; that it is a reduced form of aggregate w ell-being. This statement requires a mild modification if aggregate w ell-being

at any given date is strictly conc ave in consumptio ns. But it is so mild that we may ignore it.

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that real net domestic product at any date along anoptim al econ om ic path reflects its long-run con-sumption possibilities.23 But they proved it in thecontext of econom ies that are capable of sustaininga steady economic state; that is, those that can

maintain a balanced composition of all assets.Now , this precludes exhaustible resources. Dasguptaand Heal (1979) and Dasgupta (1982) showed howexhau stible and renewable natural resources shouldbe incorporated into an ideal measure of real netdomestic product. Thus, for example, when netdomestic product of a country is estimated, thedepreciatio n of fixed capital is dedu cted. An idealindex would deduct depreciation of the country'sresource stocks as wellvalued, of course, at ac-counting prices.24 To the best of my knowled ge, nocountry as yet deducts this latter magnitude, evenwh ile it simultaneously expresses concern about itsdeclining resource base. This is schizophren ia witha vengeance. The reason for this dual attitude is no thard to find. It is connected with the characteristicsof market failure we discussed earlier. But it ismore pernicious in the present context because gov-ernments ought to know better than to fail to imp uteany value to an entire set of capital assets. Real netdomestic product is therefore lower than it is cur-rently estimated. This is almost certainly so forall coun tries. It is also almost certainly the case

therefore that the rates of growth of net domesticproduct are lower than they are alleged to be.

The question arises whether these biases are inpractic e quantitative ly significant. Suppo se byway of illustration that environmental losses amountonly to some 1-3 per cent of national income, notmo re. If this is the order of magnitude in econ omieswe know , such corrections as those I have been ad-vocating here would seem hardly worth the bother.In fact they are very mu ch worth the bother. Reca ll

that when correctly estimated, net national productis a measure of long-run consum ption possibilitiesfacing an econom y. Therefore, when we igno reenvironmental depreciation we may well be wayoff the m ark in our estimate of the econ om y's rateof growth of net national product. Ou r assessmentof the econom y's performance could be quite wrong.

To see this, let 7(0 be net national product (asconventionally m easured) in year t, and let D(t) beenvironmental depreciation at t.25 Consider twoadjacent years, say 1 and 2. Supp ose D(l)/Y(l) =0.01. Being only 1 per cent of nationa l product,

environm ental depreciatio n is neglig ible. Nowsuppose [7(2) - 7(1)] /7(1) = 0.02. This is a fairlyhealthy growth rate, and we would be tempted tocomm end the econom y. How ever, this increase innational output may have come about at the ex-pense of environmental stocks: soil erosion, ground-water depletion, deforestation, and so on. Wewould not know this if these losses were not toappear in national income accounts. T hus, supposethat D(2 )/7(l) = 0.03. As a ratio of nationalproduct, environmental losses are still negligible.But the real growth in net national p roduct is not 2per cent, but rather

and this is zero. The economy has not actuallygrown at all. Our assessment of the economyshould be quite different now.

Difficulties associated with the estimation of realnet domestic product are compounded by the factthat unlike computers and tractors, environmentalresources usually affect welfare directly as stocks,not merely as service flows. (An exception is noisepollution.) Fisherie s and aquifers are useful notonly for the harvest they p rovide (this is the flow);as a stock they are directly useful, b ecause harvest-ing and extraction costs are low if stocks are large.Tropical forests are beneficial not only for thetimber they may supply (this is the flow of service);as a stock they prevent soil erosion and, in the caseof large tropical forests, help maintain a variedgenetic pool and contribute substantially to the

recycling of carbon dioxide . Like wis e, air andwater quality have direct w ell-being effects; (it is,let us remember, the concentration of pollutantswhich is relevant here). And finally, the directeffect of the stock of ozone in the ozo ne layer on theflow of well-being is obvious.

23 This is a theorem concerning real net national product: it is not a definition of real net national product24 T his leads to the seemingly paradoxical result that net dom estic product in a country wh ich lives solely off its exhaus tible

resou rces is nil, and it is nil no matter how high the current consum ption is. See Dasgupta and Heal (1979).25 These are in per capita units.

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The direct well-being effects of environmentalresource sto cks are in som e cases relatively easy toestimate, as with fisheries and groundwater, inothers almost imp ossibly difficult. But the pointremains that ignoring what one might refer to as

environmental overhead durable consumption leadsto a further bias in estimates of real net domesticproduct, in the direction of over-estimation.

To make this precise, let us assume that aggregatewell-being in an economy at any given date, t,depen ds not only on the flow of consumption, C{t),but also directly on the stock o f its assets, SO).26 LetU(C(t)(t)) deno te the flow of aggregate well-being at t. Using the all-purpose comm odity as ournum eraire, it is easy to show that real net dom esticproduct, Y(t), in this economy should read as:

Y(t) = C{t) + dS(i)ldt + (UJUc)S{i) 0 )

In equation (1), Us an d Uc are, respectively, themarginal aggregate well-being of the resource stockand cons um ption flow. We have earlier com -me nted on the seco nd term on the right hand side of(1)the depreciation of environmental capital. Itis the final term I am a lluding to now. If the stockis directly beneficial (as with the current stock ofthe ozone layer), U s is positive. If it is damaging (as

with atmospheric pollution), Us is negative.27 In thelatter case the final term in e quation (1) is negative.On ce again, neglec ting environm ental resources innational accounting would lead to an over-estima-tion of aggregate well-being.28

I am of course using the measurement of real netdom estic product merely as a prop on which to hanga number of issues concerning public policy.Ap propriate c riteria for public investment, and the

public screening of private investmen t, are intrinsi-cally related to the correct way of measu ring real netdom estic product. They hang together through anetwork of accounting prices. Optimal investm entcriteria are merely a way of ensuring that real net

domestic product at each instant is maximized.And this in turn is a means of ensuring that theeconomic path which is followed indeed maxi-mizes the present discounted value of the flow ofaggregate well-being.29 While we ignore resourceaccounting in our aggregate reporting of econo-mies, we overlook as well to include them in theevaluation of investmen t projects. At an analyticallevel this amounts to regarding resource stocks asvalueless. They are regarded free. In this article Ihav e tried to trace a chain of implications this has onbiases in resource use and resource accounting.

IX. INADEQUATE INCENTIVES FOROBTAINING INFORMATION

In fact there is another implication of this, equallygrave, and which I hope will finally justify mychoice of starting point in this article: the non-existence of generalized m arkets for environm entalresources. It is the implied absence of privateincentives for obtaining information about resourcestocks and the technology of resource regeneration;or, in other word s, the ecology of the matter. It isremarkable how little we know of things that are ofsuch long-run interest, remarkable not because w ecannot offer an explanation for why we do notknow I have just provided it but because of theextent of ourign oranc e. Often enough , the data onesees, when scrutinized, are merely anecdotal, nomore than pure guesses. As noted earlier, there area number of countries which have no reasonable

26 For simplicity of exp ositio n I shall think of an economy posse ssing a single, all-purpose good. Th e reader can easily

generalize to the case where there arc many kinds of real assets and many consumption goods.77 Notice that a commodity can have direct well-being effects which are deleterious even while being indirectly beneficial

because of the consum ption benefits it provides. Pollutants like pesticides have this property. The model in the text is merelyillustra tive. A prope r mode l of pollution will lead us to the idea of negative accounting prices. S ee Dasgupta (1982, ch. 8).

28 It is unfortu nate that for the most part public debates on environm ental ma tters have concentrated on those resou rces, suchas the atmosphere and tropical forest cover, whose direct well-being effects are unusually difficult to estimate. This usuallyhas the effect of making one think that environmental issues cannot really be analysed in the way we analyse other economicissue s. Wi tness th e fact that the label 'conservatio n move me nt' sets off a chain of images in on e's m ind. As I have tried toelaborate in this essay, a great many environmental problems, of immense importance to human well-being, are onesconcerning resources whose direct effects are not all that difficult to measure.

v Arro w and Kurz (1 970) contin ues to be the most thorough treatme nt of this topic. But they do not include an account ofnatural resources.

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estimates of the extent of their forest cover, soillosses, water evaporation rates, and so on. Publicknowledge of ecological processes is usually neg-ligible. I am thinking here of the functional, or in-strumental value of such knowledge. I am thinkingof knowledge of ecological processes on a par withknowledge of technological transformation possi-bilities. The re is a strong case for the publicacquisition of such knowledge, because privateincentives are particularly dull in this field. If thefarmers in the lowland s can claim no compensationfrom the upland timber m erchant, neither party hasan incentive to disco ver the functional relationshipbetw een deforestation and soil erosion. Thesemassive uncertainties are real, and a great deal inexcess of what they should be.

At a more general level, the direction of techno logi-cal change is biased on accoun t of all this. W henenvironmental resources are free, there is abso-lutely no incentive to econom ize in their use. Tech-nological innovations which are profligate withthem look profitable, certainly more so than theyought to look. Ov er tim e, an entire sequence ofresource-intensive technologies is thus installed.And if we add to all this the fact that there are oftenstrong leaming-by-doing and learning-by-using

effects, even at the stage of research and develop-ment, w e arrive at a depressing conclusion: it mayrequire a big push to move so cieties away from theircurrent profligacy in the use of environmentalresources. We may well have got locked into badhabits, not only as consumers and manufacturers,but also as scientists and techno logists. In themeantime, a move towards a more appropriate setof price signals is clearly the right one.

APPENDIX

In the text (sections II and III), we presented aninformal account of how co-operation may be sus-tained over time by means of norms of conduct. Asocial norm is a behaviour strategy. The criticalpoint in the exe rcise is to show that there is no needfor an outside ag ency to enforce the no rm s, and thusto assure co-opera tion. We have therefore to showthat co-operation can be self-enforcing if appropri-ate norm s are followed. (If the strategy neededoutside enforcement, e.g. the law courts, it wouldnot be a social norm, it would be something else.)

In this Append ix I shall provide a formal accou nt ofthis by means of a very special example, that of atwo-p erson, repeated game. Specifically, I shallstudy the two-person, repeated Prisoners' DilemmaGame, and I shall develop tw o types of norm.(There are othe r norms that can sustain the sam e co-operative outcome.) I begin by describing theirdilemma when the prisoners face each other onlyonce.

There are two agents, 1 and 2. They are genericallylabelled i andy. Thus, ij - 1,2. Agent i has twostrategies to choose from, A C) and B(i). The pay-

off-matrix is given below. Agen t 1 choo ses rowand agent 2 chooses column. The first number ineach box is the pay-off to player 1; the second, toplayer 2. I assume throughout that the game iscomm on knowledge. (See, for exam ple, Binmorcand Dasgupta, 1986; Aumann, 1987, for exposi-tions of this.) Plainly , the game has a uniqu e non-co-operative (Nash) equilibrium outcome (10,10).In fact, (fi(l),B(2)), which supports the equilib-

Figure 1Pr isoners ' Dilemma

XA(l)

B(l)

A(2)

(25,25)

(30,6)

B(2)

(6,30)

(10,10)

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rium , is a pair of dom inant strategies. But theequilibrium is sub-optimal: both parties would bebet ter off w ere th ey to ch oose the pair (^4(1)^4(2)).We n ow assum e that the parties do not have accessto any co-operative infra-structure which wouldenable them to enforce the choice of the strategypair (A(l)^4(2)).30 Thus, (5( 1)^ (2)) will prevail.All this is well know n.

In what follows, we call the Prisoners' Dilemmajust analysed the stage game, and we assume thatthis stage game will be repeated.

It is an easy m atter to confirm that if the stage gam eis to be repeated only afinite num ber of periods, andif this number is common knowledge, the unique

non-co-operative outcome w ill be the repeated p layof (B(1)JB(2)). The players are thus locked in aPriso ners' Dilemm a even in this case.31

Th e interesting ca se is therefore one where the stagegam e is to be repeated ad infinitum and where thisis comm on know ledge. The banal observation, thatpeople are mortal, does not provide an argumentagainst this hypo thesis. The point in studying aninfinitely repeated stage gam e is to avoid having theplaye rs use the final da te of play as an anchor fromwhich to work backwa rds. Discounting future pay-offs is a way of introducing uncertainty about theactual duration of the play: the higher the discountrate, the low ert he w eight players give to future p ay-offs relative to present ones. Discounting is a way

of capturing in an analytical mo del the fact that theactors know that play in all probability will not goon forever, but that neither knows for sure when thegame will terminate.32 We suppose for simplicityof exposition that both players disco unt their future

pay-offs at a constant, positive rate, r.

Individual strategies can be extremely complicatedin the repeated Pris one rs' Dilemm a game . A strat-egy is now a plan of action at each po ssible contin-gency. To be precise, choice of an action by eitherparty at date T can be made to depend on how thegame has been played until the previous periodT-\. We are inicrcsted in checking w hether an in-definite sequence of (25,25) can be realized as anon-co-operative equilibrium outcom e by tacit co-

operation; that is , whe re the policing is done by theplayers themselves and no co-operative infrastruc-ture, such as governm ent, is involved.

Consider the following strategy for player i (i= 1,2)which I shall call strategy Z:

Z: Play A(0 in the first period, and continue to playA(i) so long as the other player,;, plays A(j). Switchto B(f) the period following the first time j playsB(f), and play 5(0 thereafter.33

We want to locate conditions under which it is ineach party's interest to choo se Z, were the other tochoose Z. In other words, we want to locateconditions unde r which Z^Z) is a non -co-operative

50 B y a co-op erative infrastructure I mean a machinery, such as that provided by the law courts, which can enforce agree-me nts. Wh en such an infrastructure is not present, agreements are not binding. Since (fl(l) ,5(2)) is a pair of dominant strate-gies, it will unque stion ably be chosen in the absence of any possibility of binding agree men ts. This is the dilemma. Noticethat if the resourc e costs involved in establishing a co-operative infrastructure w ere small enough, it would be in the mutualinteres t of the part ies to establish it. Th e 'infrastru cture' could then impose a stiff penalty to any party which plays the B strat-egy. By so im posing a penalty, the game is changed into one where A(i) becomes the dom inant strategy for person i. Notice

that in this altered gam e the penalty is never actually paid There is no occasion to, becau se A(i) is now i's dominant strat-egy . He rein lies the advant age of the co-opera tive infrastructure. In recent years it is these ideas from gam e theory which havebee n used in articulatin g social contract theories. See Rawls (1972), Gauthier (1986), Hampton (19 86), and Hardin (1988).The more general idea behind the possibility that one can in many circumstances imp rove one's lot by tying one 's hands wasa central theme in Schelling (1960).

31 T o confirm this, use the backw ard induction arg ume nt, and have the players reason back from the last period. See Luceand Raiffa (1957).

32 A constant discount rate implies, of course, that no matter how long is the horizon, there is a positive (though vanishinglysmall) probability that the stage game will be repeated beyond the horizon.

33 To the best of my knowledge, the efficacy of this strategy was formally studied first by Friedman (1971). It should benoted that Z is not tit-for-tat, a strategy ma de famous by Ax elrod (1984). Z is not at all forgiving. A single deviation fromthe (implicitly) agreed play of A(j) by j is punished forever by i when i plays Z. This me ans of course that after a possibledeviation, renegotiation is not possible. If it is, strategy Z is not credible. Strategies supporting (25,25) indefinitely, whichare invulnerab le to renegotiation, have been much studied recently. See strategy X below. See also Farrell and Maskin (1987),Bernheim and Ray (1987), and Abreu and Pearce (1989).

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S Uni v e r s i t

d e B

or d e a ux on J ul y2 4 ,2 0 1 4


D o wnl o a d e

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(Nash) eq uilibrium of the infinitely repeated Pris-one rs' Dilemm a game. Notice that if both partiesplay Z , the outcome to each is the infinite pay-offsequence (25,25,...).

Tim e is discrete. Play begins at t = 0. If bothparties choose Z, the present discounted value ofthe flow of pay-offs to each is:

25 + 25/(l+r) + 25/(l+r)2 + ... = 25(1+r)/r 041)

We wish to locate conditions under wh ich it doesnot pay either party to deviate from Z, given thatthe other is playing Z.

Towards this, consider an alternative strate gy for,say player 1, which consists, among other things,of playing i4(l) until date T-\, and then switchingto 5(1) at T.34 We are assuming that 1 is playingagainst strategy Z. We can therefore con clude thatit will be in his interest to switch perm anently to5(1 ) once he has played 5(1) . Thus, if it is ever in1 's interest to switch to 5(1 ), it is in his interest toplay 5(1 ) thereafter. Now notice that i f I plans toswitch to 5(1 ) at T , and //t he plan is credible, itwill be in 1 's interest to switch to 5(1) at T whenT arrives. But atT,Tis the present; it is no longerthe future. It follows that, withou t loss of gener-ality w e may as well assume that T - 0. In otherwo rds, we may as well assume that 1 plays thesequence (5(1),5(1),...) against 2's choice of Z.We wish to see if it is in 1 's interest to do so.

Now if 1 were to play an infinite seq uence of 6 ( 1 )sagainst 2's play of Z, his pay-off sequ ence w ill be(30,10,10 ,10,...). And the present discountedvalue of this stream is:

30 + 10/(l+r) + 10/(l+r)2 + ... = 30 + 10/r (AT)

We m ay co nclude that it is in 1 's interest to playZ against 2's choice of Z if expression (AY) is atleast as large as expression (AT). It follows thatfor Z^Z) to be an equilibrium pair of strategies inthe infinitely repeated Prisoners ' Dilemma ga me ,we must have

P. Dasgupla

Stating matters more generally, tacit co-operationcan be self-enforcing in an infinitely repeated Pris-oner's Dilemma game if neither party discountsfuture pay-offs a t too high a rate. In our sp ecificexam ple, if the parties discount at a rate in excess of300 per cent, (Z) is not self-enforcing. It is not anon-co-operative equilibrium pair of strategies.

All this is congenial to intuition. There is a one-period gain to player i in reneging and playing 6 (0forever against Z. T h e g a i n i s 3 0 - 2 5 = 5. Setagainstthis a loss o f 2 5 - 1 0 = 1 5 in each period s ta rt ing theperiod after the first dev iation. If i is my opic he willrenege. If he is not, he will no t

We should note how this analysis provides a

reductionist explanation for such notions as 'cu stom ','codes of condu ct' , 'social norm ', 'social sanctions' ,and so forth. Ho wev er, we should also note that thereare many possible 'no rm s' for sustaining the mutuallybeneficial, co-operative outcom e. The strategy wehave studied in this Append ix is unforgiving, in thateven one deviation (that is, one lapse) on the part ofa person is met with eternal punishm ent. The normlacks com passion. But it has analytical appeal. Itallows us to say that, in the numerical example athand, were the parties to discount future pay-offs ata rate in excess of 300 pe r cent, no social norm couldtake hold.

How do we know this? We know this because Zinflicts the severest possible p unishm ent for a singledeviation. Any other norm w ould therefore inflictless severe punishm ent. It follows that the cost borneby a person for deviating on ce is less under any othernorm. But the benefit remains at 5 for the period atwhich the norm -breaker breaks the norm. We canconclude then that if r exceeds 300 per cent no normcan sustain an indefinite

An alternative social norm, which we called con-formism, was outlined in section II. We formalize itnow, and call it strategy X.

X: At any date, choose A(f) if and only if the otherparty had 'conformed' at the previous date, where'conform ism' at the first date is

Dasgupta P., (1990) The Environment as a commodity.pdf

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