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The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use

Author(s): James A. Brander and M. Scott Taylor

Source: The American Economic Review, Vol. 88, No. 1, (Mar., 1998), pp. 119-138

Published by: American Economic Association

Stable URL: http://www.jstor.org/stable/116821

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The Simple Economics of Easter Island:A Ricardo-MalthusModel of Renewable Resource UseBy JAMESA. BRANDERAND M. ScoTr TAYLOR

This paper presents a general equilibrium model of renewable resource andpopulation dynamics related to the Lotka-Volterrapredator-prey model, withman as thepredator and the resource base as the prey. We apply the model tothe rise and fall of Easter Island, showing thatplausible parameter values gen-erate a 'feast and famine" pattern of cyclical adjustment in population andresource stocks. Near-monotonic adjustmentarises for higher values of a re-source regeneration parameter, as might apply elsewhere in Polynesia. Wealsodescribe other civilizations thatmighthave declined because of population over-shooting and endogenous resource degradation. (JEL Q20, N57, J1O)

The world of the late twentieth century ismuch more heavily populated and has muchhigher average living standardsthan any pre-vious period in human history. However,widely publicized concerns have been ex-pressed over whether per capita real incomecan continueto increaseoreven be maintainedat current evels in the face of rapid populationgrowth and environmentaldegradation.Econ-omists normally tend to be skeptical aboutsuch claims, largely on the basis of the histor-ical record. At various timesin the past, peoplehave worried about overpopulationand envi-ronmentaldegradation,yet the past, at least aswe imagine it, seems to provide a record ofimpressive progress in living standards.The application of modem science to ar-chaeological and anthropologicalevidence is,

however, producing interesting new informa-tion on the role of natural resource degrada-tion. Specifically, a pattern of economic andpopulation growth, resource degradation,andsubsequent economic decline appears morecommon than previously thought. A majorquestion of present-day resource managementis whether the world as a whole, or some por-tion of it, might be on a trajectoryof this type.A first step in addressing such concerns is toconstruct a formal model linking populationdynamics and renewable resource dynamics.The primary objective of this paper is toconstruct such a model. The second objectiveis to apply this model to the very interestingcase of Easter Islandwhich, until recently,hasbeen one of the world's great anthropologicalmysteries. Our model contains three centralcomponents. The first component is Malthu-sian population dynamics, following ThomasR. Malthus (1798). Malthus argued that in-creases in real income arising from productiv-ity improvements (or other sources) wouldtend to cause population growth, leading toerosion and perhaps full dissipation of incomegains. He also suggested that populationgrowth might overshoot productivity gains,causing subsequent painful readjustment.'

* Brander:Facultyof Commerce, Universityof BritishColumbia,2053 MainMall, Vancouver, British Columbia,CanadaV6T 1Z2; Taylor:Departmentof Economics,Uni-versity of British Columbia, 997-1873 East Mall,Vancou-ver, British Columbia, Canada V6T IZI. We thank threeanonymousreferees for very helpful suggestions. We arealso grateful to Bob Allen, Elhanan Helpman, JanisJekabsons,GrantMcCall,Hugh Neary, Phil Neher, TobeyPage, Jim Teller, Guofu Tan, and participants at severalconferences and university seminars. Carol McAuslandprovided valuable research assistance. Financial supportfrom the SSHRC, the Killam Trusts, the Canadian nstitutefor Advanced Research, and the Network Centre of Ex-cellence for Sustainable Forestry Management is grate-fully acknowledged.

'Malthus was not a fatalist. He believed that enlight-ened public policy could reduce populationgrowth, con-templating both contraception and "moral restraint" as119


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120 THE AMERICANECONOMICREVIEW MARCH1998The second component of the model is anopen-access renewable resource. Malthus as-serted (Ch. 10 pp. 82-83) that the negativeeffects of population growth would be worsein the absence of established propertyrights.Property rights are a particularproblem withrenewable resources such as fish, forests, soil,and wildlife. Thus, if we are to observe Mal-thusian effects anywhere,we are perhaps ike-liest to see them where renewable resourcesare an importantpart of the resource base. Theextreme version of incomplete propertyrightsis an open-access resource,where anyone canuse the resource stock freely. Malthus did notprovide a clear formulation of open-access re-newable resources, but we can take this step,drawing on the modem theory of renewableresources.The third component of the model is a Ri-cardian production structure at each momentin time. Thus the model might reasonably bereferred to as a Ricardo-Malthus model ofopen-access renewable resources. The com-ponents of the model are relatively simple.Even so, the model exhibits complex dynamicbehavior. For example, one possible outcomeof the model is a dynamic pattern in which,starting rom some initial state, populationandthe resource stock rise and fall in dampedcy-cles. A change in parameters, however, canshift dynamic behavior toward monotonic ex-tinction of the population or might lead tomonotonic convergence toward an interiorsteady state.The model provides a plausible explanationof the rise and fall of the EasterIsland civili-zation. Applying the model to largerand morecomplex modern resource systems would re-quire an expanded model structure,but the

simple model presented n this paper provides,at the very least, insights that should be con-sidered in evaluating current renewable re-source management practices.

The mainintellectual precursors o our anal-ysis are Malthus (1798), David Ricardo( 1817), and thepioneeringworkon renewableresources of H. Scott Gordon ( 1954) andM. B. Schaefer (1957). Resource dynamicshave been studiedby many scholars, and a par-ticularly valuable overview of this material(with considerableoriginal work) is Colin W.Clark (1990). The particularresource modelused here is due to Brander and Taylor(1997), and is also related to Anthony D.Scott and Clive Southey (1969). Detailedmodeling and estimation of particularrenew-able resource stocks has been carried out bymany scholars including, for example, Jean-Didier Opsomer and Jon M. Conrad (1994).Careful studies of Malthusianpopulation dy-namics include Maw-Lin Lee and David J.Loschky (1987) andGeorgeR. Boyer (1989).The claim that environmental constraints areimpinging negatively on living standards s acentral theme in RichardB. Norgaard(1994)and Lester R. Brown (1995).Applying formal economic analysis to anarchaeological mystery is an unusual activityfor economists, but is not without precedent.In particular,Vernon L. Smith (1975) used aformal model of huntingto explain the extinc-tions of large mammals during the late Pleis-tocene era and more recently (Smith, 1992)suggested using formal economic models toexplain humanprehistorymoregenerally.Thisidea parallels evolution in the field of archae-ology itself, where mathematicalmodels areincreasinglyused as aids to interpretingphys-ical evidence. A valuable overview of thisrap-idly changing field is Kenneth R. Dark(1995).Section I provides a brief description ofEaster Island's past. This past is fascinatinginits own right, as are the methods by which ithas been uncovered, but our main goal is toprovide backgroundto our approach. SectionII presents our general equilibriummodel ofresource use and Malthusian population dy-namics. Section III analyzes population andresource interactions, and states the mainpropositions characterizing the dynamic be-havior of the system. Section IV applies themodel to Easter Island andSection V describesothercases where the model might apply. Sec-tion VI discusses the role of institutional

mitigating factors. He noted that reduced fertility arisingfrom social responses (such as increased age of marriage)was the major check on population in Westem Europe.Otherchecks included reducedfertilityandincreasedmor-tality arising from poor nutrition and increased incidenceof disease. Famine, in his view, was only nature's lastresort, and he noted that in much of Europe "absolutefamine has never been known" (Malthus, 1798 p. 61).


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VOL.88 NO. ] BRANDERAND TAYLOR: IMPLE ECONOMICSOF EASTERISLAND 121change, and Section VII contains concludingremarks.

I. EasterIslandEaster Island (also called Rapa Nui) is asmall Pacific island over 2,000 miles (3,200km) from the coast of Chile, with a population(as of the early 1990's) of about 2,100. Forthe past two centuries, EasterIsland has beenregarded as a major archaeological and an-thropologicalmystery. In particular, he Poly-nesian civilization in place at the time of firstEuropeandiscovery in 1722 is known to havebeen much poorer and much less populousthan it had been a few hundredyears earlier.

Thus the economic record in Easter Island isone of rising wealth and risingpopulation,fol-lowed by decline.The most visible evidence of Easter Island'spast glory consists of enormousstatues(called"moai"), carved from volcanic stone. Manystatuesrested on large platformsat variouslo-cations on the island. The largest "movable"statues weigh more than 80 tons, and the larg-est statue of all lies unfinished in the quarrywhere it was carved, and weighs about 270tons. The puzzling feature of the statues andplatformsis that the late stone age Polynesianculturefound on Easter Islandin 1722 seemedincapable of creatingsuch monumental archi-tecture. First, the culture seemed too poor tosupporta large artisanclass devoted to carvingstatues, and certainlyno such group existed inthe eighteenth century.Also, the statues weremoved substantialdistances from the island'slone quany to their destinations,but the pop-ulation, estimated at about 3,000 in 1722,seemed too small to move the larger statues,2at least without tools such as levers, rollers,rope, and wooden sleds. However, the islandin 1722 had no trees suitable for making suchtools. Local residents had no knowledge ofhow to move the statues,and believed thatthe

statues had walked to the platforms undertheinfluence of a spiritualpower.Various theories have been advancedto ex-plain these statues and other aspects of EasterIsland. The most well-known theory is due toThor Heyerdahl (1950, 1989), who arguedthat native South Americans had inhabitedEaster Island (and other Pacific islands), hadbuilt Easter Island's statues, and had subse-quently been displaced by a less advancedPolynesian culture. To support his thesis,Heyerdahl traveled on a balsa raft, the Kon-Tiki, from off the coast of South America tothe Pacific islands. A more exotic theoryof the"Atlantis" type, proposedby John MacmillanBrown (1924), is that EasterIsland is the tinyremnant of a great continent or archipelago(sometimes called "Mu") that housed an ad-vanced civilization but sunk beneath theocean. A still more exotic theory, proposedbyErich von Daniken (1970), is that the statueswere created by an extraterrestrial civili-zation. Two recent books describing the cur-rent understandingof Easter Island are Bahnand Flenley (1992) and Van Tilburg (1994).This understanding does not support theHeyerdahl, "Atlantis," or extraterrestrialtheories of Easter Island, but fits well withthe Ricardo-Malthus model of open-accessresources.Recently discovered evidence suggests thatEaster Islandwas first settledby a small groupof Polynesians about or shortly after 400 A.D.The pollen recordobtainedfrom core samplesand dated with carbon dating methods showsthat the island supporteda great palm forest atthis time. This discovery was a majorsurprisegiven the treeless nature of the island at thetime of firstEuropeancontact.In the yearsfol-lowing initial settlement,one importantactiv-ity was cutting down trees, making canoes,andcatching fish. Thus the archaeological rec-ord shows a high density of fish bones duringthis early period. Wood was also used to maketools and for firewood, and the forest was anesting place for birds that the islanders alsoate. The population grew rapidly and waswealthy in the sense that meeting subsistencerequirementswould have been relativelyeasy,leaving ample time to devote to otheractivitiesincluding, as time went on, carving and mov-ing statues.

' Thereis a significantliteraturedevoted to methodsofmonumentconstruction and movement. Even 3,000 peo-ple could not have moved the larger statues without thebenefit of wooden sleds and levers. See Paul Bahn andJohn Flenley ( 1992) andJo Anne Van Tilburg ( 1994) fora discussion of statue transportation.


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122 THEAMERICANECONOMICREVIEW MARCH 1998Noticeable forest reductionis evident in thepollen record by about 900 A.D. Most of thestatues were carved between about 1100 and1500.' By about 1400 the palm forest was en-tirely gone. Diet changedfor the worse as for-est depletion became severe, containing lessfish (and thus less protein) than earlier.Lossof forest cover also led to reduced water re-tention in the soil and to soil erosion, causinglower agriculturalyields. Population probablypeaked at about 10,000 sometime around 1400

A.D., then began to decline.4The period 1400to 1500 was a periodof falling food consump-tion and initially active, but subsequently de-clining, carving activity.Carvinghad apparentlyceased by 1500. Atabout this time, a new tool called a "mataa"enters the archaeological record. This tool re-sembles a spearheador dagger and is almostcertainly a weapon. In addition, many island-ers began inhabiting caves and fortifieddwellings. There is also strong evidence ofcannibalism at this time. The natural nferenceis that the island entered a period of violentinternecine conflict. However, at first Euro-pean contact in 1722 no obvious signs of war-fare were noted. This visit (by three Dutchships) lasted only a single day, however, andmuch may have gone unnoticed.The next known contact with the outsideworld was a brief visit from a Spanish ship in1770, followed in 1774 by a visit from JamesCook, who provideda systematicdescription'of EasterIsland. There had been some changebetween 1722 and 1774. Most noticeably, al-most all of the statues had been knocked over,whereas many had been standing in 1722.Statueworship, still in place in 1722, had dis-appearedby 1774. Populationwas apparently

less numerous than it had been in 1722, andwas estimated at about 2,000.6Thus Easter Island suffered a sharpdeclineafter perhaps a thousand years of apparentpeace and prosperity.The populationrose wellabove its long-run sustainable level and sub-sequently fell in tandemwith disintegrationofthe existing social order and a rise in violentconflict. Kirch (1984 p. 264) suggests that"EasterIsland is a story of a society which-temporarily but brilliantly surpassing itslimits-crashed devastatingly."The mystery of Easter Island's fall is re-garded by many as solved. In simple form,the current explanation is that the islandersdegraded their environment to the point thatit could no longer supportthe population andculture it once had. However, Polynesians al-most always dramaticallyaltered the environ-ments of the islands they discovered. Why didenvironmentaldegradationlead to populationovershooting and decline on Easter Island,but not on the other major islands of Poly-nesia? Furthermore, there are 12 so-called4"mystery islands" in Polynesia. These is-lands were once settled by Polynesians butwere unoccupied at the time of Europeandis-covery. All these Polynesian islands representpieces of "data" that should be consistentwith whatever theory is proposed as an ex-planation for Easter Island.II. TheRicardo-MalthusModel

A. Renewable Resource DynamicsThe resource stock at time t is S(t). ForEaster Island it is convenient to think of theresource stock as the ecological complex con-

sisting of the forest andsoil. The change in thestock at time t is the natural growth rate' Radiocarbondates are available in Van Tilburg ( 1994p. 33). These dates are attributed o unpublished work ofW. S. Ayres.4 This population estimate appearsseveral places in theliteratureandis often attributed o W. Mulloy. Othershavesuggested that the reasonable range for the populationmaximum was between 7,000 and 20,000, with most fa-voring about 10,000.'Cook had a Tahitian crew member who could com-municatequite easily with the Easter Islanders,as Tahitianand the Easter Island language were similar. See P. V.Kirch (1984 Chs. 3 and 11).

6 In 1862 the population was reliably estimated at about3,000. In 1862 and 1863, slave traders rom Peruinvadedthe island and took about one-thirdof the population asslaves. Many of these slaves died of smallpox. A few re-tumed to the island, inadvertently causing a smallpox ep-idemic that killed most of the remaining Islanders.In 1877the population reached its low point of 111, from whichit subsequently increased by natural increase and by im-migration rom Tahiti and Chile.


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VOL 88 NO. ] BRANDERAND TAYLOR: IMPLEECONOMICS OF EASTERISLAND 123G(S(t)), minus the harvestrate,H(t). Drop-ping the time argumentfor convenience,(1) dSldt = G(S) -H.We use the logistic functional form7 for G,which is perhapsthe simplest plausible func-tional form for biological growth in a con-strained environment.(2) G(S) = rS(1 - SIK).K, the "carrying capacity," is the maximumpossible size for the resource stock, as S = Kimplies that furthergrowth cannot occur. Vari-able r is the "intrinsic" growth (or regenera-tion) rate.The economy produces and consumes twogoods. H is the harvest of the renewable re-source, and M is some aggregate "othergood." In the case of Easter Island, we thinkof the (broadly defined) harvestas being food(i.e., agriculturaloutput from the soil and fishcaught from wooden vessels made fromtrees), while good M would include tools,housing, artisticoutput (including monumen-tal architecture), household production, etc.Good M is treated as a numerairewhose priceis normalizedto 1. Aside from resourcestockS, the only other factorof productionis labor,L. We make the inessential simplificationthatlabor force L is equal to the population.GoodM is produced with constant returns to scaleusing only labor. By choice of units, one unitof labor produces one unit of good M. Sincethe price of good M is 1, the wage (denotedby w) must equal 1 if manufactures areproduced.We assume that harvesting of the resourceis carried out according to the Schaefer har-vesting production function (proposed bySchaefer [1957]) as follows,(3) HP = aSLHwhereHP is the harvestsupplied by producers.(The superscriptP stands for "production".)LH s the labor used in resourceharvestingand

a is a positive constant. Letting aLH(S) rep-resent the unit labor requirement in the re-source sector, (3) implies that aLH(S) = LHIHP = 1/(aS). Production in both sectors iscarried out underconditions of free entry. Be-cause of open access there is no explicit rentalcost for using S, and the price of the resourcegood must equal its unit cost of production.(4) p = waLH= wl(aS).

A representativeconsumer is endowed withone unit of labor and is assumed to have in-stantaneous utility given by the followingCobb-Douglas utility function(5) u = hm' --8where h and m are individual consunmption fthe resourcegood and of manufactures,and:6is between 0 and 1. Maximizing utility at apoint in time subject to instantaneousbudgetconstraintph + m = w yields h = wf3lp andm = w( 1 - 6). Since total domestic demandis L times individual demand,we have(6) HD = w3Llp; MD = W(l --3)Lwhere superscriptD represents demand.At a moment in time the resource stock isfixed, the population (and labor force) isfixed, and the economy's production possibil-ity frontier is given by the following full-employment condition.(7) HWaLH(S) + M ==L.A linear production structure of this type isreferredto as a Ricardianproductionstructure(after Ricardo, 1817). The Ricardiantempo-rary equilibrium can be determinedalgebrai-cally by substituting (4) into (6) (i.e., thesupply price equals the demand price) to ob-tain temporaryequilibrium resource harvest,H.(8) H-=aOLS.

The equilibrium output of M is M = (1 -/3)L, implying that manufactureswill alwaysbe produced and therefore that wage w = 1.At a Ricardian temporary equilibrium, the7 Our major results can be extended to the case of ageneral compensatory growth function. See Appendix B.


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124 THE AMERICANECONOMICREVIEW MARCH 1998Panel A: Resource Dynamics

ResourceHarvest, /Growth t /| \/ H=4o:LSI / (Harvest unction)

//G G(S)/ ~~~~~(Growthunction)

S* ResourceStock,S K

Panel B: Population Dynamics

(dL/dt)lL - b-d+F=b-d+ (oapSdL/dt)/L ~ ~ ~ ~ "~ (netfertility)0 S* ResourceStock, S

b-dFiGURE1. A RICARDO-MALTHUSTEADYSTATE

harvest will not necessarily equal the under-lying biological growthrateof the resource. If,for example, temporaryequilibriumharvest Hexceeds biological growth G, then the stockdiminishes. Substituting(2) and (8) into (1)yields the following expression for the evolu-tion of the resource stock.(9) dSIdt = rS( - SIK) - a,/LS.If the resource stock falls, then labor produc-tivity in the resource sectorfalls, the Ricardianproduction possibility frontier shifts in, andthis establishes a new temporaryequilibriumwith a lower harvest.Panel A of Figure 1 illustrates a typicalsteady state (i.e., where dSldt = 0) using theharvest function (8) and the resource growthfunction (2). (Ignore the dashed lines fornow.) As shown in the figure,stock S* impliesthat harvest H = ac4LS just matches resourcegrowth G(S) at S = S*. Thus S* is a steadystate if the actualpopulationlevel is L.

B. MalthusianPopulation DynamicsOur discussion of Figure 1 so far implicitlytreats population as fixed at size L, allowing

us to focus purely on resource dynamics. Wenow consider population dynamics. We as-sume an underlying proportionalbirth rate, b,and an underlying proportional death rate, d.Thus the base rate of population increase is(b - d), which we assume to be negative, im-plying that without any forest stock or arablesoil the population would eventually disap-pear. However, consumption of the resourcegood increases fertility and/or decreases mor-tality, and therefore increases the rate of pop-ulation growth.8In particular, the populationgrowth rate is given by(10) dLIdt = L[b - d + F]where F = 4HIL is the fertility function, and4*s a positive constant. Thus higher percapitaconsumption of the resource good leads tohigher population growth. It is in this sensethatpopulation dynamics are "Malthusian."9Noting from (8) that HIL = a/3S, equation(10) can be rewritten as(11) dL/dt = L(b- d + afS).

III. Population nd Resource nteractionsEquations(9) and(11 ) form a two-equationsystem of differentialequationscharacterizingthe evolution of the Ricardo-Malthus model.These equations are a variationof the Lotka-Volterra predator-preymodel.10 Human pop-ulation, L, is the "predator" and the resource

8 One might let net fertility depend on total consump-tion rather than on resource consumption, although thecase could be argued either way and has little effect onthe analysis.9 Among modern high-income societies, populationgrowth is negatively correlated with income at both thecountry and individual level. Most premodern societiesappearto exhibit Malthusianpopulation dynamics, in thathigher consumption causes higher population growth.'0 Predator-prey ystems have sometimes been studiedin renewable resource economics. See, in particular,DavidL. Ragozin and GardnerBrown (1985) and Philip Neher( 1990).


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VOL.88 NO. I BRANDERAND TAYLOR: IMPLEECONOMICSOF EASTER SLAND 125stock, S, is the "prey." We concentrate firston steady-state analysis, then turn to the sys-tem's dynamic behavior.

A. Steady-StateAnalysisThe system given by (9) and ( 1) will havea steady state if dLldt and dSldt are simulta-neously equal to zero. There are three solu-tions, as expressed in Proposition 1.

PROPOSITION 1: The Ricardo-Malthusmodel exhibits threesteadystates. Steadystatel isa corner solution at (L = 0, S = 0). Steadystate 2 is a corner solution at (L = 0, S K).Steady state 3 is an interiorsolution at(12) L= [rl(a/3)]

X [ 1 - (d - b)I(afK)],S (d - b)l(4oa/).

PROOF:The proof follows immediatelyfrom simul-taneously setting equations (9) and (11) tozero and can be seen by inspection. To obtainsteady state 3, one can solve for S from ex-pression ( 11), then substitutethis value in (9)to obtain L. Note that steady state 3 impliespositive values for L and S as d > b, and r,a, /, and qfare all positive. The steady-statestock, S, must be less than carrying capacityK. In steady state 3, S = (d - b)l(4a/3) sothis consistency requirementcan be written as(13) (d - b)I(4a/3) < K.If ( 13 ) comes to equalityorreverses direction,then steady state 3 collapses to steady state 2.

We focus on the interior steady state. Asshown in Proposition 4, when (13) holds, theinterior steady state is stable whereas steadystates 1 and 2 are saddlepoints. The interiorsteady state can be illustratedgraphically byusing the two panels of Figure 1. Panel A rep-resents the resource dynamics conditional onpopulationL. Panel B capturesthe populationdynamics given in ( 11) by graphing the per-centage rate of change of the population (dLI

dt)IL on the vertical axis, and the resourcestock on the horizontal. The upward-slopingline is net fertility (b - d - F), which is linearin S as F = Oa,/S [substituting (8) into thedefinitionof F].At any stock S < S*, there is an excess ofdeaths over births and the population shrinks;at any stock greater than S* the populationgrows. At stock S* population growth is zeroand the populationlevel is stationary.We de-note this level as L*. Therefore, at resourcestock S*, the population s stabilized at L* andthe harvest of the resource is just equal to itsunderlying growth rate, implying that S is alsostationary.The two panels together thereforeillustrate an interior steady state. Using ex-pression (12), or Figure 1, we can determinehow changes in exogenous parameters affectinteriorsteady-state resource stocks and pop-ulation. Proposition 2 follows by inspection,and Proposition 3 is obtained by differentiat-ing L as given in (12).PROPOSITION 2: The steady-state resourcestock(i) rises if the mortalityrate rises, the birthrate falls, or fertility responsiveness

falls;(ii) falls if there is technological progress inharvesting; and(iii) is unaffectedby changes in the intrinsicresource regeneration rate, r, or carry-ing capacity, K.PROPOSITION 3: The steady-state popula-tion level(i) rises equiproportionately with an in-crease in the intrinsic rate of resourcegrowth, r;(ii) falls when harvesting technology im-proves if S < K12 and rises if S > K12;(iii) fails when the taste for the resourcegood rises if S < K12 and rises if S >K12; and(iv) rises if the carrying capacity of the en-vironmentrises.It follows from (8) and (12) thatper capitasteady-stateresource consumption, h, is (d -b)I4. Per capita consumption of the other


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126 THE AMERICANECONOMICREVIEW MARCH 1998good is (1 -- /3). Thus steady-state resourceconsumption is determinedby demographics,and rises if the birth rate falls or if fertilityresponsiveness falls." It is instructive to seehow population growth dissipates gains fromresource productivity improvements.Supposethe economy is at the steady state in Figure 1and r rises. The growth curve will shift up asshown by the dashed line in Panel A. At stockS *, the harvest is then less than resourcegrowth and the resource rebuilds. Per capitaconsumptionof the resource good rises, caus-ing population growth, and the harvest func-tion in Panel A rotates upwards (as L rises).Since nothing has altered the demographicsteady statein Panel B, the resource stock mustreturnto S*, but with a higher population andunchanged per capita real income.

B. DynamicsWe now characterize the dynamic behav-iour of the system. We assume thatparameterrestriction(13) is met, implying that an inte-rior steady state exists.

PROPOSITION 4: When an interior steadystate exists, the local behavior of the systemisas follows.(i) Steadystate I (L=O, S=O) isan unstablesaddlepoint allowing an approach alongthe S = 0 axis.(ii) Steady state 2 (L = O,S = K) is an un-stable saddlepoint allowing an approachalong the L = 0 axis.(iii) Steadystate 3 (L > 0, S > 0) is a stablesteady state and a "spiral node" withcyclical convergence if

(14) r(d - b)l(Koafl)+ 4((d - b) - Kpa/) < 0.

ResourceStock, S

K A

(d-b)/+act'p dLUdt=O

/dt=O

r/cef Population, L

FIGURE 2. TRANSITION DYNAMICS

(iv) Steady state 3 is a stable steady state andan 'improper node" allowing mono-tonic convergence if the inequality in( 14) runs in the other direction.PROOF:See Appendix A.

Proposition 4 is based on the fact that thedynamic system is locally linear in the neigh-borhoodof a steady state. Since Proposition4shows that the interior steady state is locallystable, our earliercomparative steady-stateex-ercises (Propositions 2 and 3) are meaningfulin that small perturbations n parameterswilllead to small changes in steady-state valuesand allow convergence to a new steady state.Condition (14) is central in understandingthe model's local dynamics. It can be rewrittenas r < 4K0a04(K4a3 - (d - b))/(d - b).Noting from (13) that the right-handside ofthis inequality must be positive, one interpre-tation of (14) is that a slow enough rate ofintrinsicresourcegrowth insures a locally cy-clical trajectory.Conversely, given r, ( 14) in-dicates that cyclical dynamics will occur iffertility is very responsive to per capita con-sumption (represented by 4) or if the har-vesting technology is very efficient (i.e., if ais high).To examine the global properties of themodel, consider the phase diagram in Figure2. Population L is on the horizontal axis andresource stock S is on the vertical axis. Thehorizontal ine labeled dLIdt = 0 derives from

" Another easily derived point of interest is that a de-cline in the birth rate causes steady-state resource outputto rise if S < K/2. This possibility is unusual for Malthu-sian models, but arises here because of the resourcedynamics.


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VOL. 88 NO. I BRANDERAND TAYLOR: IMPLE ECONOMICSOF EASTERISLAND 127expression ( 11), which implies that dL/dt =0 if S = (d - b)/4oa/. If the system is abovethis line, then dL/dt > 0, and if the system isbelow it, then dL/dt < 0. The other line, la-beled dS/dt = 0, is obtained from expression(9), which implies thatdS/dt = 0 if S = K -(Kaf6/r)L. Above this line, dS/dt < 0 andbelow it, dS/dt > 0. The intersection of theselines is the interior steady state. The directionsof motion for each of the four regions in thediagram are shown by the right-angle arrows.Consider, for example, point A, whichmight represent "first arrival" (i.e., a smallpopulation andthe resource atcarryingcapac-ity). Point A is above the dS/dt = 0 line, im-plying that the resource stock must be falling,and is also above the dLldt = 0 line, implyinga rising population.The figureshows one pos-sible adjustmentpath towardthe steady state,but other types of adjustmentare also consis-tent with the arrows of motion, includingmonotonic adjustment oward the steady state.Proposition 5 characterizes the global ap-proachto steady state conditional on differentstarting points.PROPOSITION 5: When an interior steadystate exists, the global behavior of the systemis as follows.(i) If L > 0 and S = 0, the system ap-proaches steady state 1 with L = 0 and

S = 0.(ii) If L = 0 and S > 0, the system ap-proaches steady state 2 with S = K andL =0.(i) If S > 0 and L > 0, then the system con-verges to the interior solution in steadystate 3.PROOF:See Appendix A.

It is strikingthat the system converges to aninteriorsteady state from any interiorstartingpoint. There are two important parameterre-strictionsunderlyingthis property.The first isinequality (13). If this inequality is not satis-fied, the system crashes toward zero popula-tion. In this case, steady state 2 becomes aglobally stable impropernode. Thus, if (13) isnot satisfied, our model implies extinction of

the humanpopulation and a restorationof theresource base to carrying capacity.The second parametercondition is given by(14) which, as shown in Appendix A, deter-mines whether the linearized system in theneighborhood of the interior steady state hascomplex or real roots. If the linearized systemhas complex roots, then all trajectoriesexhibitcyclical adjustment sufficiently close to thesteady state. If the linearized system has realroots, then all trajectoriesapproach he interiorsteady state along a path increasingly close tothe dominanteigenvector of the system. Sucha trajectory may be globally monotonic andmust be locally monotonic.If we start far away froin the steady state,then it is more difficult to describe the pathsof the system completely, butmany qualitativefeatures of the global system follow from anunderstandingof the local analysis. For ex-ample, suppose the system is perturbedfroman initial steady stateby the instantaneousdis-appearanceof some fraction of the predatorpopulation. Cyclical behavior arises if thepredator grows quickly in response to thisshock while the resourcegrows slowly. In thiscase, the quick growth of the predatorcausesit to overshoot its new long-runlevel. The nowoverabundantpredatorthen reduces the preybelow its steady-state level, and this in turncauses a decline of thepredatorpopulationbe-low its steady-state level. But when the pred-atordeclines, theprey rebuilds andovershootsthe steady state, leading to a resurgenceof thepredator,which againovershoots, etc., tracingout a damped cycle with anovershooting pred-ator population chasing a slowly adjustingprey toward the steady state. This interpreta-tion is consistent with condition (14), whichshows that adjustment must be cyclical if r(the intrinsic growth rate of the prey) is suf-ficiently low or if ca,6 (the growth responseof the predator to a change in the resourcestock S) is sufficiently high.This description describes the forces af-fecting the local behavior of the system neara steady state, but it also applies to globalbehavior. A complete analytical characteri-zation of all possible trajectories as a func-tion of parametersis difficult to develop, butthe limiting case in which the resource stockadjusts instantaneously to its steady-state


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128 THEAMERICANECONOMICREVIEW MARCH 1998value is instructive. In this case the economywould always operate on the dSIdt = 0 lo-cus. As the founding population is (by as-sumption) smaller than its steady-statevalue, the economy would move down thedSldt = 0 locus until it reached the steadystate. In this case, when the predator adjustsslowly and the prey adjusts infinitelyquickly, both the resource stock and the pop-ulation level adjust monotonically towardtheir steady-state values.Technically, we can use the conditiondS/dt = 0 to solve for S as a function of L[from (9)] then substitute this in (11) to geta one-variable differential equation in L. Thesolution is logistic: population grows fast atfirst then levels off, as in the standarddescrip-tion of Polynesian islands.

IV. Applying heRicardo-MalthusModel oEasterIslandIn this section we use simulations of theRicardo-Malthusmodel to make two points.First, by choosing parametersthat are consis-tent with our knowledge of Easter Island,Polynesian civilizations generally, and otherNeolithic populations,we are able to generate

a time series for population size and resourcestocks that appears to (approximately) repli-cate EasterIsland's past. We take this as ten-tative support or ourtheoryof the rise and fallof the Easter Island civilization. Second, pa-rameterchanges can change the time patternof population and resource stock evolutionfrom extreme cyclical overshooting to mono-tonic adjustment owardthe steady state.12Wetake this feature of the model as a possibleexplanationas to why Easter Islandappears obe different from otherPolynesian islands.A. Parameter Choice

Some parametervalues are simply a matterof scaling, such as the carrying capacityof the

forest/soil resource complex. It is convenientfor the stock to be similar in magnitude to thepopulation, so we let the carryingcapacity ofthe resource stock be 12,000 units. This is thestarting value of the stock when Polynesiancolonization first occurred. (The forest hadbeen in place for approximately37,000 yearsbefore first colonization, so carryingcapacityhad certainlybeen reached.)The next parameter to consider is a, laborharvestingproductivity. The productivity of aunit of labor is aS. One unit of labor corre-sponds to the amount of labor one person canprovide in one period. It is convenient to letten-year intervals be periods. If we let a =0.00001, this means thatif S = K, a householdcould provide its subsistence consumption(the amount ust necessary to reproduce tself)in about 20 percentof its available labortime.Accordingly, there is considerable surplus onthe island when the resource stock is large.This seems roughly consistent with knowninformation.ParameterP reflects the "taste" for the out-put of the harvestgood. One way of trying toget some idea of /3 s to recall that / is equalto the share of the labor force devoted to har-vesting the resource. The other sectorincludesmanufacturingand service activities. Variouspieces of evidence suggest that the resourcesector probably absorbed somewhat less thanhalf the available labor supply. A value of 0.4for ,B s probablyin the reasonablerange.Another importantparameteris r, the in-trinsic growth (or regeneration)rate of the re-source.We initially assume an intrinsicgrowthrate of 0.04, implying that, left to itself, theforest/soil complex would increase by 4 per-cent per decade in the absence of congestioneffects (i.e., if the stock were small comparedto the carryingcapacity). The remaining keyparameters are the demographic parameters.Let (b - d) = -0.1 and let 4 = 4. The valuefor (b - d) means that the populationwoulddecrease by 10 percent per decade in the ab-sence of the resourcestock. Letting4 = 4 im-plies that there would be positive populationgrowth if the stock were approximately50 per-cent of its carryingcapacity, andnegativepop-ulation growth otherwise. Throughout thesimulation period annual population growthnever exceeds 1 percent per year, which is

2The key parameterdifference that we considerin ex-plaining the difference between Easter Island and otherPolynesian islands is substantial.The model also impliesbifurcations (in parameterspace) around which majorchanges in predictions arise.


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VOL.88 NO. I BRANDERAND TAYLOR: IMPLE ECONOMICSOF EASTER SLAND 1291 000 . .........

' , $~iPopulatio10000 ~~~~~~~~~~~~~~ResourcetockI

4 000

11 200(

O J

Year (A.D.)

FIGURE3. EASTER SLANDBASE CASE

consistent with the demographicliteratureonNeolithic populations. The range of estimatesfor the founding populationranges from 20 to100 or more, with 40 being commonly usedas a plausible estimate. We take the startingvalue to be 40, butvaryingthis estimate makeslittle difference to the results. These parame-ters yield the time-series pattern shown inFigure 3.Figure 3 shows an interesting dynamicpat-tern.For the first 300 years,humanshave littleimpacton the resource. Populationthen beginsto increaserapidlyandthe resource stock fallsprecipitously for the next 800 years. About900 years afterdiscovery the initialpopulationof 40 has grown to about 10,000. The periodof high population (and high labor supply) inthe simulation correspondsto the period of in-tense carvingin the archaeologicalrecord.Thesimulated resource stock reaches its troughabout 250 years later, close to 1500 A.D., asdoes per capita resource consumption.Recallthat a new weapon (the "mataa") appearsinthe archaeological record at about this time,evidence of cannibalism also appears, andthere is movement to fortified structuresandcaves as dwellings. The simulated resourcestock begins its recovery but populationcon-tinues to fall, implying a 1722 population ofapproximately3,800 to meet the Dutch ships,not far from the 3,000 actuallyestimated.Thesimulated 1774 population is about 3,400,again somewhat more than the 2,000 Cook es-timated. In the 1800's there is substantialout-side intervention so our model would nolonger hold.

B. WhyIs Easter Island Unusual?Our model allows both cyclical and mono-tonic behavior so it offers the potential to ex-

plain both the cyclical overshooting thatoccurred on Easter Island and the monotonicbehavior apparently observed on the majorPolynesian islands. There is no reason to be-lieve that Easter Island was an outlier in itsunderlying demographics, its tastes, or itstechnology. However, it was an outlier in onevery important respect. The palm tree thatgrew on Easter Island happened to be a veryslow-growing palm.This palm (which was thesingle most significant component of the for-est/soil complex on Easter Island) is nowknown (due to J. Dransfield et al., 1984) tohave been a species of Jubea Chilensis (theChilean Wine palm). This palmtreegrows no-where else in Polynesia, and it is perhapstheonly palm that can live in Easter Island's rel-atively cool climate. An authoritative text(Alexander M. Blombery and Tony Rodd,1982 p. 110) reports that "Cultivation pre-sents few problemsin a suitable temperatecli-mate, but growth of these massive palms isslow and it is generally later generationswhoget the benefit from their planting." Underideal conditions,theJubeapalm requiresabout40 to 60 years before it reaches the fruit-growing stage, and can take longer.13In contrast, the two most common largepalms in Polynesia are the Cocos (coconutpalm) and the Pritchardia Fiji fanpalm). Nei-ther of these palms can grow on EasterIsland,and both are fast-growing trees that reachfruit-growing age in approximately seven toten years.For a resourcebased on thesepalms,it would be more reasonable that the intrinsicgrowthrate would be about 0.35 or 35 percentper decade. 4 Figure4 shows a simulation that

13This infortmation is based on private communicationwith palm growers. Easter Island was also an outlier inrainfall and temperature,contributing to slow growth ofthe resource.'4 Translating "time-to-fruit" into intrinsicgrowthrater is difficult,as trees continueto grow well afterfirstyield-ing fruit and we are interested in the entire forest/soilcomplex in any case. Associating a 40-year time-to-fruitwith r = 0.04 and a seven-ten-year time-to-fruit with r =0.35 is plausible but very rough. Also, the trees were not


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130 THEAMERICANECONOMICREVIEW MARCH 1998600X0 -_ _, 2000X

60 1800050000 6

Population 16000v | - -Resource Stock 14000

40000 00

/ 10000 100000. 8000 0

- ~~~~~~TimeFIGURE 4. POPULATION AND RESOURCE DYNAMICS WITH

FAST REGENERATION

is identical to Figure 3 except that the growthrate is raised from 0.04 to 0.35.The higher intrinsic resource growth ratecauses the population to adjustmoresmoothly.In fact, this simulation is technically cyclical,but the cycle is so muted that the adjustmentpath is virtually monotonic, as the populationpeaks at 42,245 before leveling out at itssteady-state value of 41,927. The populationtrajectory would not become strictly mono-tonic unless the intrinsic growth rateexceeded0.71, but even at moderategrowth rates of 0.15or 0.2, the population "crash" would be toosmall to be evident to archeologists. Lowgrowth rates, on the other hand, produce dra-matic cyclical fluctuations.Thus an island with a slow-growingresourcebase will exhibit overshootingand collapse.Anotherwise identical island with a more rapidlygrowingresource will exhibit anear-monotomicadjustment of population and resource stockstoward steady-state values. Even if everythingelse were similar across islands, this one factwould allow the Ricardo-Malthusmodel to beconsistent with both the spectacularovershoot-ing and collapse on Easter Island and the farless dramaticdevelopment exhibited on othermajorPolynesian islands.The model is also consistent with the 12 so-called "mystery islands" that were once set-

tled by Polynesians but were unoccupied atEuropean contact. All but one of these islandshave relatively small carryingcapacities. Ap-plying our model, we observe that if K is suf-ficiently small then condition ( 13 ) will not besatisfied and there will be no "interior"steadystate. A colonizing population could arrive,but would eventually drive the resource stockdown to a level that would cause extinction ofthe humanpopulation.Another noteworthy Polynesian settlementis New Zealand's South Island.The South Is-land had a high concentration of large flight-less birds (up to 10 feet tall and 500 poundsin weight) called "Moas." First Polynesiansettlement is thoughtto have occurred around1000 A.D. (although it may have been later).Following settlement the South IslandMaoris(or "Moa-hunters") lived "high on the bird"by hunting Moa, along with fishing and agri-culture.Over this period there was substantialdeforestation and the Moa were drivento ex-tinction. It is not clear exactly when the Moabecame extinct, but the larger species disap-peared first, possibly lasting as little as 200years following settlement. There is some dis-agreement over whether population overshotthen declined, or whether it merely stagnatedas the Moa disappeared.15 However, the SouthIsland was more densely settled than theNorthduring the Moa-hunting period, but at Euro-pean contact (about 1700) settlement wasdenser in the more temperate and warmerNorth. Thus it is possible thatthe South Islandexhibited population overshooting, as wouldbe consistent with the slow-growing resourcebase (consisting of Moa and slow-growingforests).While Easter Island and Polynesia moregenerally offer interesting applicationsof ourmodel, the significance of our analysis wouldbe greatlyexpandedif thebasic approachwerealso relevant for other cases. In the followingsection we ask whetherpopulationgrowthand

the only element in the forest/soil complex, which furthercomplicates the problem of estimatingthe intrinsicgrowthrate for different hypothetical situations.

'5 Peter Bellwood (1987 p. 157) contends that a pop-ulation overshoot did occur, stating that "the picture isone of ultimatepopulationdecline,with agradualdecreasein cultural energy owing to an insurmountabledecrease nresources." A good reference on the Moa is AthollAnderson(1989).


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VOL. 88 NO. I BRANDERAND TAYLOR:SIMPLEECONOMICS OF EASTERISLAND 131endogenous resource degradationhave playedan important role in the decline of othercivilizations.

V. OtherApplicationsOurmodel mightbe consistent with the Ma-yancollapse which, like EasterIsland,was longregardedas a mystery.The Mayan empire oc-cupied what is now the YucatanPeninsula ofMexico; and parts of Guatemala,El Salvador,and Honduras.The empirereachedits peak inthe period600-830 A.D., then suffered a rapiddecline in both population andculturalsophis-tication over the following 100 years.The civ-ilization was partiallyrebuilt n anoutlyingareabut this laterMayan civilization went into de-cline about 1200 A.D. Only fragmentsof theMayan people and civilization still existed atthe time of Spanishconquestin 1521.Recent evidence (including T. PatrickCulbert [1988] and Sarah L. O'Hara et al.[1993]) shows the key role of environmentaldecline in the Mayan collapse. As on EasterIsland, much of the evidence is from carbon-dated core samples showing deforestation,drying,soil erosion andcontamination,and re-duced crop yields in major agriculturalareas.By the early ninthcentury, agriculturaloutputcould no longer supportthe dense populationin the region, leading to out-migration,a sharpdecline in population, and a collapse of thesophisticated civilization that had developed.The main unresolved question concerns theextent to which drying and erosion were theendogenous result of human activity ratherthanarising from exogenous climate changes.The evidence suggests that both factors wereimportant.The following quotes from Culbert(1988 pp. 99-101) provide a now widely ac-cepted interpretation.All available datashow thatpopulationsin the Southernlowlands rose rapidlytoa Late Classic peak. Not only was thepopulation unusuallydense (200 per sq.km.), but it covered an area too large toallow adjustmentthrough relocation oremigration....Maya agriculture becameincreasingly intensive as populationrose.... Overextension-overshoot insystems terminology-often afflictscomplex systems duringa period of ex-

pansion... . In the Maya case, the over-extension was ecological and consistedof a population system dependentuponmaximal results from a subsistence sys-tem that made no allowance for long-termhazards.

Culbert's description of Maya seems similarto the operation of our model. Maya achievedhigh population density throughintensive ag-riculturethat, at best, left no margin of safetywhen climatic conditions changed marginallyfor the worse and, at worst, createdan endog-enously determinedagriculturalshortfallaris-ing from deforestationand soil erosion.Resourcedegradationalso played an impor-tantrole in the decline of the ancientMesopo-tamian states (in what is now Iraq). Variouscivilizations and empiresrose and fell in partsof thisregion betweentheperiod2350 B.C. and600 A.D. The first true empire was the Akka-dian Empire (2350-2150 13.c.). Soil samplesfrom the Akkadianregion indicate ncreasinglyintensive agriculturalanduse untilabout 2200B.C., when the soil in the northernpartof theempire became too dry to support the popula-tion(H. Weiss et al., 1993). The entirenorthernportion of the empire was abandoned,causinga majormigration nto the South,which in turnstrained food and water supplies in the Southto thepoint of civic collapse andbreakdownofcentral authority (Ann Gibbons, 1993). By2150 B.C. the empire had degeneratedinto agroupof independentcity states.Latercivilizations made extensive use of ir-rigation.JosephTainter(1988) writes "In thisarea, agricultural ntensification and excessiveirrigation ead to short-termabove-normalhar-vests, with increasing prosperity ... [but] therise of saline groundwatererodes or destroysagriculturalproductivity." By the end of thethirddynastyof Ur (about 2000 B.C.), agricul-turalyields perunit of landhadfallen by about50 percent since the first dynasty (about 300years earlier), and about twice as much seedper unit of land was required even to achievethis lower yield. (See Robert McCormickAdams, 1981 p. 151.) Declining agriculturalproductivitywas an important ontributing ac-tor to the decline of Ur.Other major Mesopotamian civilizations,including the Assyrians, the Babylonians, and


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132 THE AMERICANECONOMICREVIEW MARCH 1998the Sumerians suffered the same salinizationproblem suffered by the Ur. Gradually,through successive empires based in differentparts of the region, nearly the entire area be-came infertile. According to Tainter (1988),by about 1200 A.D. the total occupied area inthe region had fallen to perhaps 5 or 6 percentof its earlierpeak, and most previously fertileland was uninhabitable. Furthermore, whileclimate has fluctuated in the region over thepast few thousand years, there is no discern-able trend in precipitation (as described byAdams, 1981 pp. 12-13). Therefore, whilethe relative contribution of natural climatechange and human activity to the destructionof a major agriculturalregion cannot be pre-cisely determined, human agricultural prac-tices seem to have been the dominantfactor.A less well-known example concems theChaco Anasazi in the southwestern UnitedStates. Between about 1000 A.D. and 1150A.D. the Chaco Anasazi built an impressivesystem of roads, settlements, and "greathouses." As described in Stephen H. LeksonandCatherineM. Cameron(1995), the largestgreat houses had about 700 rooms and arethoughtto have been administrative enters fora complex trading system. In this period,pop-ulation grew rapidly, probablythroughimmi-grationas well as natural ncrease.This regionis prone to significant rainfall variations, anda dry period began in 134, lasting until 1181.After 1134 no new great houses were built,much of the land was abandoned,andthe eliteculture of the ChacoAnasazi disappeared.Thepuzzle here is that this droughtwas no moresevere than droughts of the previous centurythat had been weathered without strain.Tainter ( 1988) suggests thatChacoanAnasazieconomic organization had already beenpushed beyond its limits by populationgrowthand thatthe moderatedroughtof 1134 pushedan alreadyoverloaded system into collapse.The Maya, the Anasazi, andthe ancientMe-sopotamian civilizations all show a similarpattern.In each case, decline of the resourcebase, particularly soil degradation, was themain factor precipitating a population crashand the decline of a complex civilization.While exogenous climate fluctuations mayhave played a significant role in these cases,population growth and endogenous resource

degradationwere also important,making themsimilar to Easter Island."6Overall, evidence on soil change and cropinformation recently obtained from core sam-ples has significantlychanged the way modemarchaeologists interpret the past. Resourcedegradation s now understood to be commonin major civilizations. The role of warfare andviolent conflict is also being reinterpreted.Ratherthan being the cause of decline, violentconflict is commonly the result of resourcedegradation and occurs after the civilizationhas startedto decline, as on Easter Island.VI. InstitutionalAdaptation

A critic might object that our analysis un-derestimates institutional adaptation.We as-sume an open-access resource, butperhapsweshould expect more efficient resource manage-ment institutions to evolve. This is primarilyan empirical question."7Elinor Ostrom ( 1990)has studied the historical record on commonproperty problems and argues persuasivelythat efficient institutional reforms sometimesoccur in primitive (and advanced) societies,but sometimes do not. (See also Ostromet al.,1994.) In Ostrom (1990 p. 21) she writes6"some individuals have brokenout of the trapinherent in the commons dilemma, whereasothers continue remorsefully trappedinto de-stroying their own resources." She also ob-serves (1990 p. 210) that 6 6we cannot [adopt]... a presumptionthat appropriatorswill adoptnew rules whenever the net benefits of a rulechange will exceed net costs."The main objective of Ostrom (1990) isto determine the factors that favor efficientinstitutions and those that impede efficient in-

6 It is also possible thatexogenous climate change mayhave affected EasterIsland,as emphasizedto us in privatecommunicationby GrantMcCall. See also J. Flenley et al.(1991).1 Various theoretical argumentscan also be advancedto explain why a society may not undertakean efficiency-enhancing policy change. Raquel Fernandez and DaniRodrik (1991) model a status quo bias against such re-forms thatarises when individualgainers and losers fromreform cannot be readily identified ex ante. Similarly,Alberto Alesina and Allan Drazen ( 1991 ) providea modelin which reforms are delayed if different groups can at-

tempt to shift the burdenof adjustment o othergroups.


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VOL. 88 NO. I BRANDERAND TAYLOR: IMPLE ECONOMICSOF EASTER SLAND 133stitutional response. The most importantfa-vorable factor is an agreed-upon and correctunderstandingof the problem. If a soil ex-haustion problem is falsely attributedto lowrainfall, then the response might be more raindances rather hanrestructured ropertyrights.To use a modem example, it was not possibleto settle on an effective response to ozone de-pletion until there was substantial agreementthat a problem existed and on the mechanismcausing the problem. Even then, obtainingconsensus was difficult, and several majorcountrieshave refused to participate n the re-sulting internationalagreement.It is also helpfulif proposedrulechangesaf-fect relevantparties n a similarway rather hangeneratingwinners and losers. Otherfavorablefactorsinclude low discountrates and low en-forcementcosts. It is also helpfulif the affectedgroupis small andif the grouphas a high levelof initial trustand sense of community. Thus,forexample, f thereare existingethnicorsocialdivisionsthatdominate he way peopleperceiveissues, this makes appropriate institutionalchangedifficult o achieve.Theseconditions ol-low from the generalprinciplethat nstitutionalchangeis morelikelyto occurwhenthe individ-uals who must make the change are confidentthat they will be among the beneficiaries.EasterIsland did not presenta favorable en-vironmentfor efficient institutionalchange. Itis unlikely that the Islanders understood thebiology of the forest-soil complex or the likelyincentive effects of alternative nstitutionalar-rangements.It is even possible that individualislanders did not recognize that depletion wastaking place. Although the forest disappearedrapidly by archaeological standards, changewas slow over the course of an individual lifespan. Typical life spansfor those who survivedinfancy would have been on the order of 30years, and even during most rapid depletion,the forest stock would have declined by nomore than 5 percent over a typical lifetime.Even if the problemhad been recognized, the40 to 60 yearstaken for a tree to maturewouldexceed the working life of virtuallyall island-ers.18Thus a programof replantingandcaring

for seedlings would almost never have been ofdirect benefit to the cultivators.The Easter Islanders did make some institu-tional changes in responseto resourcescarcity.One majorchange was that at some point theEasterIslandersabandoned he system of statueworshipand apparentlypushedover almost allof the statues (usually facedown). Institutionalchanges of this type, amounting to religiousrevolution, are clearly very costly and, whilethey are understandable esponses to decliningcircumstances, hey areunlikely to have helpedthe underlyingresource-useproblem.The other kind of institutionalreform sug-gested by our miodels population ontrol.Thereis a large and fascinating iterature n social in-stitutions affecting fertility. Perhaps the mainpointis simplythatthe rangeof suchinstitutionsis very large. Some societies adoptedpracticesthat directlylimitedpopulationgrowth,includ-ing infanticideand genitalmutilation.Moresub-tle and benign approaches nvolving mariagecustoms and crude contraceptivemethods werealso used. Such populationcontrolstend to bedensitydependent.Forexample,as crowding n-creasesand resourcesbecome morescarce,it ismore difficultfor young men to acquiresuffi-cient wealth to marry,and both infanticideandcontraception would be practiced more fre-quently.Thiswas thepattern lsewhere n Poly-nesia and was probablytrue of EasterIsland aswell. This is consistent with our model, as itmeansthat net fertilityfalls when percapitare-sourceconsumption alls.However, in societies that lack a clear sci-entific understandingof their world, institu-tional adaptation involving fertility, propertyrights, and other matters s likely to be a "trialand error" process. Efficient institutionswould probablybe achieved only after a longperiod of time and many trials. It would bedifficult for a society like Easter Island toadapt efficiently in a single boom and bustcycle.

8 These longevity estimates are derived from the fourmajor skeletal series available for prehistoricPolynesia.

We have used the life tables in Kirch (1984 pp. 112-14)to calculate that life expectancy at age 5 is slightly lessthan 30 years, andthatthe percentagesurviving untiltheirmid-forties would be approximately5 percent.


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134 THE AMERICANECONOMICREVIEW MARCH 1998The other declining civilizations also seemto be poor candidates for efficient institutionalreform.We do not have space to discuss eachcase in detail,but anticipationandunderstand-

ing of the ecological problemwould have beenlimited, and conflict between competinggroups would have delayed reform. Even insophisticated societies like Maya and Meso-potamia, where property ights may have beenrelatively secure, the complex arrayof exter-nalities involved in soil erosion, salinity anddeclining water tables would have been hardto addresssuccessfully.We recognize,however, thatmodem knowl-edge of institutions n preliterate ivilizations svery lmited. InconsideringPolynesia,we knowthere was substantial ariationacrossthe differ-ent islands.Therefore,one alternative ypothesisto ours is that institutionalvariationacross so-cieties withinPolynesiamightbe theexplanationfor contrastinggrowthexperiences.VII. ConcludingRemarks

This paper presents a simple model of re-newable resource growth and population dy-namics and employs this model to provide aplausible account of the rise and fall of theEaster Island civilization. For reasonable pa-rametervalues, the model generates a boomand bust cycle in which populationgrows, theresourcebase is degraded,and population ul-timatelyfalls. This cycle arisesbecause there-source base has a slow regenerationrate. Afaster-growing resource would allow mono-tonic convergence toward the steady-statepopulation. Thus the model can explain thedifference between Easter Island and otherPolynesian islands based on known differ-ences in resourcegrowth rates.Our analysis has several lessons for themodem world. First, the model implies thatchanges in technology, the environment, orhuman behavior can create feast and faminecycles thatmay be a recipe for violent conflictover apparentlydiminishing resources. EasterIsland may be only one case of many whereunregulated resource use and Malthusianforces led to depletionof the resource base andsocial conflict. Identifying countries at risk inthe modem world may be difficult, but ourmodel provides some guidance as it identifies

the key prameters that make cyclical down-tums more likely.A modern case thatmight be consistentwithour model is Rwanda,which entered the newsduring 1994 because of a violent civil war.This war was normallyattributed o ethnicten-sions between Hutus and Tutsis, but morecareful analysis suggests the possibility thatMalthusian population growth, resource deg-radation, and resulting competition for re-sources was atthe rootof theconflict. Between1950 and 1994, population in Rwanda quad-rupled. The boom began in the 1950's whenadvainces n health care and agriculturalprac-tice led to increasing real incomes and risingnet fertility. By the 1980's what had been anopen frontierwas "filled up," and real livingstandardsstartedto fall. Conflict over land be-tween Hutus and Tutsis became increasinglysevere, culminating in a civil war in which asignificant fraction of the population waskilled and a very large fraction (perhaps 25percent) became refugees. Thomas Homer-Dixon (1994) describes several othermoderncases where resource degradation driven bypopulation growth has caused violent conflictand local decline of living standards.Modelsof the Easter Islandtype, withexplicit resourceand demographicdynamics, mght be helpfulin understandingsuch situations.A second lesson of our analysis is that itprovides one of the first formal empirical ex-amples in which the cycles that arise in non-linear models appear relevant in analyzinglong-run economic development. In short, itsuggests thatnonlineardynamics are likely tobe relevant in studying economic growth, es-pecially in situations where renewable re-sources arremportant.Third,our analysis of Easter Island and theother cases suggests that economic declinebased on natural resource degradation is notuncommon. Institutionalchange could poten-tially have averted collapse in many of thesesocieties but it was not undertaken or at leastwas not undertaken ast enough). Institutionalfailure in renewableresourceuse does happen,and it has been fatal for several societies. Re-cent events in the world's majorfisheries sug-gest that institutionalchange remains difficult.An extremecase is the (Canadian) Newfound-land cod fisherywhich was closed in 1992, as


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VOL 88 NO. I BRANDERAND TAYLOR: IMPLE ECONOMICSOF EASTER SLAND 135cod stocks were down to less than 5 percentof their 1960 levels. Our work offers supportfor the position that it is both importantanddifficultto reach efficient institutionalarrange-ments in renewable resource use.Finally, despite our model's rather gloomyimplications, we do not wish to embrace thepessimism of modern neo-Malthusians.First, in considering the modern world, onewould introduce nonlinearity in the responseof fertility to consumption so as to allow fora demographic transition of the type ob-served in modern high-income societies.Specifically, net fertility declines with in-come at sufficiently high-income levels. Inour model, cyclical dynamics arise onlywhen fertility has a strong enough positiveresponse to per capita consumption, so in-corporating a demographic transition wouldprobably allow the possibility of escapefrom cyclical dynamics if a high enough in-come could be reached.In addition, our model abstractsfrom tech-nological progress, which is the main forceemphasized by growth optimists. Abstractingfrom technological progress is reasonable forour discussion of Easter Island, and perhapsfor most of the other examples we have dis-cussed, but it would clearly be a serious omis-sion in considering the modem world. Themodel can, however, be readily augmentedinthis direction. Both the r parameter(resourcegrowth) and the a parameter(harvesting ef-ficiency) could be viewed as susceptible toeither exogenous or endogenous technicalprogress. Furthermore, progress in the formof further scientific understanding may alsofacilitate institutional adaption in resourceuse. This would requirea largermodificationin the model as it implies a different charac-terization of temporary equilibrium in theresource sector. On the other hand, the pos-sibility of demographic transition notwith-standing, net fertility (particularly decliningmortality) is affected by technical progress,and increases in net fertility driven by im-provements in medical technology may welllead to population overshooting.Finally,while technicalprogresshasbeen thedominantforce in the growthprocess since thebeginning of the industrialrevolution,this last300 years is a small fraction of the time that

humanshave harvested romthe earthand builtcomplex, but ultimately fragile, societies. It is,for that matter,shorterthan what might be re-gardedas the "golden age" of EasterIsland.APPENDIX A

PROOF OF PROPOSITION4:Let (L *, S *) representa steady state. Definethe vector u = ( UL, US) = (L - L*, S - S*).Thus u is the vector of deviations in L and Sfrom a particujlarteady state. It follows thatdULIdt= dLldt and du5ldt = dSldt, wheredLldt and dSldt are given by (11) and (9).Using a Taylor series expansion for duldtaroundu = 0 [i.e., around (L*, S*)], it canbe shown (as in WilliamE. Boyce and RichardC. DiPrima, 1992 pp. 450--51) that duldt canbe expressed as follows.(Al) duldt - J(L*, S*)u + R(L, S)where J is the Jacobian matrix of first-orderpartial derivativesof dLldt anddSldt with re-spect to L and S, and R(L, S) is a remainderof higher-order ermsthat can be ignorednearu = 0. J is evaluated at (L*, S*). Denotingthe components of J as J11, J12, etc., in theobvious way, we can write this linear systemas(A2) duldt_ JI I J12][ULJ21 -122 usA two-equation system of linear differentialequations [as in (A2)] has a general solutionof the form(A3) u(t) = c,Ejezlt + c2E2ez2twhere cl and c2 are constants, zI and z2 arethe eigenvalues of coefficient matrixJ, and Eland E2 are the corresponding eigenvectors.The dynamic behavior of the system dependson whether zl and z2 are real, complex, orimaginary, and on whether any real part ofthese eigenvalues is positive or negative. Thesystem is explosive if zi and z2 are positivereal numbers,andconverges rnonotonicallytothe steady state if zI andz2 arenegative. If zIand z2 are complex numbers then cyclical be-havior emerges. The coefficients of J can be


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136 THE AMERICANECONOMICREVIEW MARCH 1998determinedby taking partialderivatives of (9)and (11).(A4) J11 (b - d) + 4Pa,S; J12= 4PaL;

J21= - a3S; J22 -r - 2rS/K - a13L.(i) For steady state 1 (L = 0, S - 0), coef-ficient matrix J becomes(A5) J(O,O) 0]The eigenvalues are the diagonal elementsb - d < 0 and r > 0. This combination of onenegative real eigenvalue and one positive realeigenvalue implies that steady state (0, 0) isan unstable saddlepoint.(ii) and (iii) For steady state 2 (L - 0, S -K) and steady state 3 (L = (r/caf)(1 - S/K),S = (d - b)/4af6)) we proceed in the sameway, making the appropriatesubstitutionsinmatrix J using (A4) and calculating the as-sociated eigenvalues of J. For steady state 2the eigenvalues are -r and (b - d) + 4a,wK[which is positive by (13)]. As with steadystate 1, the combination of positive and neg-ative real eigenvalues implies thatsteady state2 is an unstable saddlepoint. For steady state3, matrix J has nonzero off-diagonal elements,so the eigenvalues cannot be seen by inspec-tion but must be obtained as the roots of thecharacteristicequation. Letting S* denote thesteady-statevalue of S, thecharacteristic qua-tion is z(rS*IK + z) - (d - b)r(l S- 1K) = 0, which is quadratic n z and has roots(A6) z=[-rS*/K? ((rS*/K)2

-4(d-b)r( l-S*/K) )l21/2.If the discriminant of (A6) is positive (orzero), then both solutions for z must be neg-ative real numbers and the steady state is astable node with monotonic convergence. Anegative discriminant mplies complex eigen-values with a negative realpart,andthe steadystate is a stable spiral point. The system thenexhibits damped cycles that converge on thesteady state. Noting that equation (14) givenin the proposition is simply the discriminant

of characteristicequation (A6), the proof iscomplete.PROOF OF PROPOSITION 5:

(i) Proposition 4 establishes thatsteady state1 (L - 0, S = 0) is a saddlepointallow-ing a local approach along the horizontalaxis, and we can tell from inspection ofthe full nonlinear system thatsteady state1 is reached from any point along thehorizontal axis. If S = 0, and L > 0, thenL must fall to zero. Thus one trajectoryof our full nonlinear system is given bythe horizontalaxis in Figure 2.(ii) We know from Proposition4 that steadystate2 (L = 0 and S = K) is a saddlepointallowing a local approach along the ver-tical axis, andwe can tell frominspectionthat steady state 2 is reached from anypoint along the vertical axis. That is, ifL = 0, and S > 0, then S must raise to-ward level K, hence anothertrajectoryofour full nonlinearsystem is given by thevertical axis in Figure 2.(iii) As the differential equation system is au-tonomous and continuously differentia-ble, no two trajectoriesof the system canintersect. Any trajectorythat startsfroma point strictly interior in Figure 2 mustremain strictly interior. (Otherwise itwould touch one of the axes, which weknow is impossible, as the axes them-selves are trajectories.)We can then di-vide equation (9) by ( 11) to obtain theslope of any system trajectory as dSIdL = [rS(l - S/K) - aI3LS]/I[L(b -d + 4a/3S)]. Inspection of this slope ineach region of the phase diagram n Fig-ure 2 implies that the direction of anytrajectorymust eventually be inwardto-wards the interiorsteady state.Limit cy-cles can be ruled out by applying atheorem due to Kolmogorov as providedby Robert M. May (1973 pp. 85-89).Therefore, the trajectorymust approachthe steady state.

APPENDIX BThe paper uses the logistic growth func-tion, but the analysis is readily generalized


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VOL.88 NO. I BRANDERAND TAYLOR: IMPLEECONOMICSOF EASTER SLAND 137to a general compensatory (bent over)growthfunctionprovidedthatG(O) = G(K) =0 and that G(S)IS is strictly decreasingin S.In this case we let r = lims,o G(S)IS. Equa-tion (9) becomes dS/dt = G(S) - a3LS.Equation ( 11) is unchanged.Proposition1 fol-lows immediately, except that in steady state3, the steady-state value of L is expressed asL* = G(S*)I(S*acf), where S* = (d -b)l(a/p4) as before. Proposition 2 follows im-mediately. To obtain an analog of Proposition3, we need to replace the experiment of in-creasing r by an overall increase in G(S)ISand, instead of focussing on whetherS < K12or S > K12, we focus on whether G(S) is in-creasing or decreasing. Figures 1 and 2 havethe same general form as before. In Proposi-tion 4, parts (i) and (ii) are unchanged, and(iii) follows as before except that condition(14) becomes H(S* )2 - 4(d - b)G(S*)IS*< 0, where H(S*) = G'(S*) - G(S*)IS*.Proposition 5 is unchanged. To carry out theEaster Island simulationwe, of course, requiresome specific functional form. The logisticform works well, but it is clear from this briefdiscussion that other forms would also work.More general analysis of general functionalstructures s difficult, althoughmethods alongthe lines of those used in Peter Howitt and R.Preston McAfee (1988) could perhaps beapplied.

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