ON THE COLLAPSE OF HISTORICAL CIVILIZATIONS DAVID H. GOOD AND RAFAEL REUVENY To explain the collapse of historical civilizations, scholars typically point to suboptimal behaviors including misunderstanding the natural environment, shortsightedness, or a lack of institutions. We examine the collapse of four historical societies with a model of endogenous population growth and renewable resources employing components of optimal resource management, economic growth theory, and the moral philosophy of social welfare function choice. We find that these collapses may have been socially optimal. Further, we show that the transient behavior of the system is more sensitive to assumptions than the equilibrium behavior and that focusing solely on equilibria may miss key insights. Key words: infinite horizon, optimal control, steady state, transient behavior. Scholars in many disciplines have described the increase and rapid decrease of population size associated with collapsed societies such as the Maya, Anasazi, Rapanui, and Sumerians. Malthus (1798) connected population fluctuations of this type to natural resource depletion, yet the issue remains current because of its connections to the sustainability debate (Brander 2007; Pezzey and Anderies 2003). Diamond (2005) summarizes the extensive literature on the collapse of historical civilizations and identifies four broad reasons for societal collapse: (a) damage to the environment due to inadvertent, shortsighted, or uninformed human activities such as deforestation, land erosion, or overhunting; (b) unpredictable natural disasters such as increased cooling or droughts; (c) a deterioration in the relations with neighbors; and (d) cultural responses preventing society from recognizing the problem or considering potential solutions. Arguing that the stories of these societies tell us something relevant today, Diamond (2005, p. 10) concludes: The societies that ended up collapsing were among the most creative and (for a time) advanced and successful of their times, rather than stupid and primitive. Past people were neither ignorant bad managers who deserved David H. Good is associate professor and Rafael Reuveny is professor at School of Public and Environmental Affairs, Indiana University. The authors thank participants in the Workshop in Political Theory and Policy Analysis, participants at the 2007 meeting of the European Association of Environmental and Resource Economists, as well as the reviewers and editor of the journal for helpful comments on earlier versions of this manuscript. Melanie Arnold provided invaluable editorial assistance. Any remaining errors belong to the authors alone. to be exterminated or dispossessed, nor all-knowing conscientious environmentalists who solved problems that we can’t solve today. They were people like us. While popularly received, Diamond’s thesis has been criticized by Dasgupta (2005) and others for not more explicitly incorporating the role of institutions in alleviating and resolving environmental problems. This article has little to contribute regarding issues (b) and (c). Stochastic disasters happen. Strategic interactions between societies are complex and can mitigate (e.g., trade) or hasten (e.g., war) collapse. However, we notice that many of these social collapses occurred in isolation or near isolation. Consequently, we focus on issues (a) and (d) for these particular cases. An evaluation of these historical collapses naturally suggests two counterfactual questions: What would these historical people do in our circumstances? What would we do in theirs? Assuming that we are not shortsighted, ignorant, or act inadvertently, we take Dasgupta’s criticism seriously and examine the role that social institutions and social preferences might have had on altering the history of these societies. Our framework, based on Good and Reuveny (2006), weds an ecological-economic model of human-resource interaction with endogenous population growth (Clark 1990; Brander and Taylor 1998) to economic growth theory (Barro and Sala-i-Martin 2004), considering future consequences of current decisions. We examine the role of endogenous population growth in social welfare from the perspective of moral philosophy (Parfit 1984; Kavka 1982; Cowen 1996; Dasgupta 2000a, 2001a) by Amer. J. Agr. Econ. xx(x) (xxx 2009): 1–17 Copyright 2009 Agricultural and Applied Economics Association DOI: 10.1111/j.1467-8276.2009.01312.x 2 xxx 2009 constructing a family of social welfare functions (SWFs), nesting the utility of the representative individual and aggregate utility as special cases. Given our attention on historical societies, our use of economic growth theory focuses on renewable resources and their socially optimal management (Heal 1998; Mäler 2000; Arrow et al. 2000) rather than capital accumulation or technological change. We represent institutions with either a decentralized system of enforceable property rights or a centralized system of social planning. Real-world social institutions are not perfect, so we assess their impacts as bounded by a best-case scenario (planners possess infinite foresight and have perfect institutions with costless enforcement) and a worst-case scenario (planners have neither foresight nor institutions to implement social plans). Finally, unlike the bulk of economic growth theory, our problem demands that we determine population and resource global transition paths in addition to their steady-state solutions. While it is tempting to conclude that historical civilizations failed because they were shortsighted, had no resource management institutions, or did not understand their problem, our results suggest that, even if they somehow had optimal resource management with costless enforcement and infinite horizons, their societies still would have collapsed, regardless of which SWF we consider. We also find that the principle from moral philosophy called the Repugnant Conclusion (Parfit 1984), a conjecture that societies that seek to optimize the aggregate SWF are doomed to large populations living in misery, does not occur unless the discount rate is extremely small. These results are obtained for historical societies, but, in the spirit of Brander and Taylor (1998), Brander (2007), Arrow et al. (2000), and Mäler (2000), they may offer an allegory with which to draw some cautious lessons about the way we think about the world today. In the next section we describe four historical civilizations that collapsed, followed by our modeling approach and mathematical model. The remaining sections summarize our results and provide discussion and conclusions. The Collapse of Four Societies Diamond (2005), Ponting (1991), Tainter (1990), and Yoffee and Cowgill (1988) describe the collapse of several civilizations. Building on these sources and others cited below, we Amer. J. Agr. Econ. provide some detail on the collapses of the Sumerians, the Maya, the Anasazi, and the Rapanui. Jacobsen and Adams (1958), Gelburd (1963), Adams (1981), and Kirch (2005) chronicle the history of the Sumerians, located in what is now Iraq. The Sumerian civilization increased agricultural production through irrigation, developed a detailed accounting system that monitored and recorded outputs, and is generally considered the first literate society. As their wealth grew, the Sumerians’ prosperous cities became the envy of their neighbors. To defend against invaders, they maintained large armies. Faced with the need to feed these armies, they abandoned their practices of crop shifting and letting land lie fallow in favor of intensified irrigation. In the arid climate, this led to salinization and a sharp decline in output. Sumerian accounting records imply that crop yield fell 42% in 2400–2100 BC and 65% in 2100–1700 BC (Ponting 1991). As a result, health declined, fertility fell, the death rate rose, and civic order deteriorated. The urban population peaked at about 200,000 some time around 2100 BC and fell to about 25,000 by 1500 B.C. (Thompson 2004). The Maya have been studied by Binford et al. (1987), Culbert (1988), Abrams and Rue (1988), and O’Hara, Street-Perrott, and Burt (1993). Centered in the lowland jungle of the Yucatan Peninsula, the Mayan population reached its peak sometime between AD 500 and 800 with 3–14 million in the Peten region, the society’s social core. The Maya were both literate and technically sophisticated, creating the long count calendar. In AD 600 they began building the dazzling pyramids and monuments that they are known for today, but just 200 years later, their society began to deteriorate. The Mayan society had a hierarchy consisting of nobles, priests, warriors, peasants, and slaves. Societal elites demanded pyramids and ornaments, while the warriors, peasants, and slaves demanded sustenance. These demands, together with the reliance on agriculture, required a large workforce. As with the Sumerians, the Mayan economy could not keep up with the demands it faced, so deforestation was intensified to make way for crops and provide the fuel to make lime for adorning buildings. The resulting soil erosion often ended up as silt in the rivers and canals, damaging the irrigation-based agricultural system. As crop yields fell, health and social order deteriorated, and the population declined. When the Good and Reuveny Spanish arrived in the 1500s, they were essentially gone. Bahn and Flenley (1992), Van Tilberg (1994), Kirch (1997), and Flenley and Bahn (2002) study the society on Easter Island. The inhabitants, the Rapanui, arrived sometime during the first millennium finding a lush palm forest. The population of this agrarian civilization grew for several hundred years, peaking between 7,000 and 20,000, and then declined rapidly. The Rapanui cleared the forest for arable land, timber for fishing boats, and logs to serve as rollers to help move large stone statues (moai) from their quarries. It required as many as 500 people to move the moai. As the forest vanished, the topsoil eroded and with no wood for boats, the Rapanui lost the ability to fish. When Europeans arrived on Easter Sunday in 1722 the island was nearly barren. The remaining 2,000 or so people lived in poverty, fighting over the few remaining resources (Reuveny and Maxwell 2001). Finally, Betancourt and Van Devender (1981), Samuels and Betancourt (1982), Betancourt, Dean, and Hull (1986), and Stuart (2000) consider the Anasazi. In one major site in the Chaco Canyon, the Anasazi population peaked between 4,000 and 10,000 (Tainter 1990). In another site located in Montezuma Valley, the population peaked at about 20,000 (Bureau of Land Management 2006). Beginning around AD 600, they erected some of the most dazzling and tallest buildings in preColumbian America. As their number grew, they built outlying settlements where peasants grew food for the civilization’s core. Seeking land for food and timber for kivas, the Anasazi intensified deforestation. By AD 1000, the trees were gone and soil erosion set in. Facing the dry climate, depleted lands, and low plant growth, the Anasazi developed gravitypropelled irrigation, but over time the system cut arroyos into the ground. When the water levels in the arroyos fell below the field levels, agriculture ceased. As food production fell, the population fell. While the Anasazi had withstood droughts before, when a long drought began in AD 1130, they were already weakened by years of decline. By AD 1200, their society was gone. Several factors are shared by these societies. They lived in predominantly isolated spaces and had at most limited trade (such as the Anasazi’s small ornamental items). Each depended on the resources in the environment for their livelihood, facing a finite carrying capacity. Human actions in the form Social Collapse 3 of deforestation (Maya, Rapanui, Anasazi) and unsustainable irrigation (Sumerian, Maya, Anasazi) ultimately led to falling food production and social collapse. Innovations intended to alleviate these problems were either negligible (Easter Island), allowed society to muddle through for a while before facing the problem again (Maya, Anasazi), or created new environmental problems that made things worse (Sumerian, Anasazi). Finally, exacerbating the problem, they allocated some of their productive capacities to non-life-sustaining purposes such as building monuments (Rapanui, Maya, Anasazi) or maintaining large standing armies (Sumerians, Maya). Why would people threaten their existence by degrading their environments? There are several common rationales. They did not either perceive or understand their problem because of its complexity; they understood but they did not care about the future, or they understood and cared but lacked institutions to enforce corrective policies. Our analysis differs from the empirical approach taken by Diamond (2005) and others. They describe differences among a small number of societies, assessing the connection between these differences and societal collapse. Their sample is arguably nonrepresentative since many collapsing societies left almost no evidence of their existence and are consequently excluded from the analysis; the only included societies left monuments to their existence. Our approach avoids this potential selectivity bias by not making a cross-society comparison. Indeed, our lack of discussion of successful societies emphasizes this point. Instead, we focus on the decisions made by individual societies and examine how those decisions might have been made differently. We ask, what would we do if we were in their shoes? Given our goal, we hold the society fixed and remove their shortcomings, giving them an understanding of the future consequences of current actions and the institutions to implement socially optimal policies. Modeling Approach We begin at the beginning and consider the nature of the social contract from the perspective of moral philosophy. If we suddenly found ourselves in charge of planning at the initiation of our society, what would the order of business be? We would first need to know what 4 xxx 2009 parts of our situation cannot be changed. We assume that technology is static, and the preferences, biological features of resources, and procreation behavior are not changed. We use both institutions and the analytical methods of economic growth theory as tools that form the mainstay of a modern approach (Smith 1975; Ostrom 1990; World Bank 2003). Using these tools, we focus on the essence of society’s situation: a lack of understanding, foresight, and institutions for optimal policy making. Our agenda is to identify social goals and policy instruments and to develop a formal model. In considering society’s goals, we follow economic norms by measuring social welfare with either an aggregate (sum of utilities of all individuals) or an individual SWF (utility of a representative individual). As is common, we use a representative individual to build these social welfare measures and ignore distributional issues. While potentially at odds with the social structures of our four societies, we adopt this simplification because it allows us to focus on the dynamic aspects of collapse. When population is static (Aghion and Howitt 1998), individual and aggregate SWFs yield the same results. When population growth is exogenous, both aggregate utility (Cass 1965; Lucas 2002) and individual utility (Blanchard and Fischer 1989; Levy 1992; Turnovsky 2000; Romer 2001) studies ignore the other function or note the two functions are similar except for the discount rate. When the actor is conceptualized as a family whose size grows exogenously, the individual planner and the social planner maximize the family’s aggregate utility (Obstfeld and Rogoff 1998; Barro and Sala-i-Martin 2004). Since the assumptions of a static population or exogenous population growth eliminate the possibilities of population collapse by definition, we reject them. When population growth is endogenous, the controversial issue for the SWF is the relative importance of population size and individual utility. Parfit’s (1984) approach uses the perspective of moral philosophy. He considers a world with limited resources, assumes that social welfare is transitive, and argues that an aggregate SWF implies optimal societies with a huge number of miserable individuals (the Repugnant Conclusion). In contrast, using an individual SWF implies very small populations with high individual utility. He rejects both outcomes as morally unacceptable. He then searches for something else, a “Theory X,” Amer. J. Agr. Econ. which values both life and individual happiness between these two extremes, but he cannot specify it. Taking an axiomatic approach, Cowen (1996) argues that the importance of Parfit’s Repugnant Conclusion lies in its implication for comparing outcomes, not in its establishing a priori objectives. SWFs dealing with paradoxes more successfully and implying fewer unpalatable conclusions should be preferred over others. Finally, Dasgupta (2000a, p. 385) rejects the relevance of the Repugnant Conclusion by writing about an individual with living standards at or below subsistence levels: She is one of the wretches of the earth, and there are hundreds of millions of such people alive today, disfranchised, malnourished, prone to illness–but surviving, and tenaciously displaying that their lives are worth living by the persistence with which they continue to wish to live. . .. There is nothing repugnant about a very large imaginable population, all enjoying positive well-being. Given our task of managing a historical society, this debate is relevant, but difficult to apply precisely. However, it is useful to understand the implications the choice of an SWF has for our society. In the Rawlsian sense, we seek to know a little more about what is on the other side of the veil before making a choice. In deference to Parfit’s Theory X, we employ a family of SWFs nesting both the individual and total aggregate SWFs in addition to intermediate cases. We next identify acceptable policy instruments for our problem. One question is whether or not to directly alter the population growth process, and if so how. The assignment of fertility and resource harvesting decisions to individuals or to the State stands at the heart of this matter. We can see three potential policy types: direct control (a communitarian approach assigning decisions to the State), laissez-faire (a libertarian approach assigning decisions to the individual), and a partial or indirect control that is somewhere in the middle. Under direct control of the resource, harvesting is determined by a central planner recognizing the effects on the future. A policy of direct control of human fertility, such as China’s one-child policy (Tomlinson 1975; Gigliotti 1983; Decter 1997; Dasgupta 1998), is more controversial. Other than China, countries do not currently engage in this policy, and even China is reconsidering it (Attané 2002; Good and Reuveny Hemminki et al. 2005). Alternatively, Hardin (1968, 1998), Ehrlich (1968), and King and Elliott (1997) support direct population control in order to save the environment. With no institutions, a laissez-faire resource policy leads to an overdepletion of common pool resources. A laissez-faire population policy gives people a right to procreate as they wish. In this libertarian vein, Nozick (1974) argues that people should be able to do as they wish so long as they violate no one else’s rights. Kavka (1982) argues that procreation is a basic human right that supercedes other policy objectives. Nagel (1981) and Dasgupta (2001a) reject Nozick’s lack of trade-off between rights, other benefits, and violation of other rights. For example, rights to current resource consumption are clearly in conflict with the rights of future individuals, unless they are taken into account. Unfettered procreation autonomy may exaggerate this conflict by creating even more individuals for the future. Procreative rights are not so clearly in conflict with one another though they may affect the quality of life that progeny face. Dworkin (1978), Sen (1983), Gewirth (1981), and Parfit (1984) also reject their claim to absolute rights. For them, rights are context dependent, reflecting the prevailing social norms. At any rate, since a laissez-faire approach for population growth and resource use is consistent with the rationales that most scholars use to explain social collapse, they form a natural baseline for comparison. To the extent that any human rights exist, most would agree that procreation autonomy is a more basic right than access to a common pool resource. As a consequence, communitarian management of the resource and a laissez-faire approach to procreation form a third possibility where resource management affects population growth indirectly through the effect of consumption on fertility. This appears to be consistent with current social norms claiming that procreation autonomy is a basic human right, as stated in the United Nations Universal Declaration of Human Rights (United Nations 1948) and the Report of the UN World Population Conference (United Nations 1975). The latter report also emphasizes that exercise of this right should take into account the needs of the current and future generations. We use this moral guidance in our decision to focus on resource management institutions that affect population size indirectly by altering consumption, rather than controlling procreation directly. Social Collapse 5 A Mathematical Model In light of the previous discussion, we extend the myopic, no-institutions model of Brander and Taylor (1998), seeking to overcome limitations that scholars have alleged for historical societies. Others have extended this model by adding a resource subsistence requirement (Pezzey and Anderies 2003) or innovation (Reuveny and Decker 2000; Dalton, Coats, and Asrabadi 2005; Decker and Reuveny 2005). While these extensions are interesting, they assume that decision makers are myopic, eliminating any role for resource management institutions. Since the way that institutions interact with the intrinsic social value of population is our primary research question, we exclude these extensions for parsimony sake. Our model gives a social planner the understanding of the effects that current actions have on the future, institutions with costless enforcement, and the foresight to implement socially optimal plans. For our historical societies we assume the environment has a finite carrying capacity, technology is static, individuals are identical with the same preferences and no subsistence requirement, and population growth is described by an augmented Malthusian model with the growth rate a function of consumption. The assumption of a finite carrying capacity may not apply for modern societies but is appropriate here because our societies depended on closed environments for their livelihoods and did not trade much with others. The assumptions of no physical capital and static technology are also appropriate since our societies did not experience any rapid economic growth such as our industrial revolution. In fact, throughout the last 5,000 years, economic growth rates typically hovered around zero (Boyden 1987; Johnson 2000; Dasgupta 2000b, 2001b). The assumption of Malthusian population growth is also suitable, since the relationship between consumption and fertility persisted well into the 19th century (Heerink 1994; Perman et al. 2003). The model incorporates implications of resource management institutions for future populations but does not attempt to directly control their sizes. Mathematically, we solve an optimal control problem to find the level of resources harvesting each period that maximizes social welfare. We assume that all the individuals possess the same endowments and preferences, form a production-consumption unit, and can be characterized by a representative 6 xxx 2009 agent whose utility, u(t), which is a function of the consumption in time t of a harvested good, hc (t), and a manufactured good, mc (t). The harvested good represents a broadly defined composite of renewable resources such as trees, soil, edible plants, and fisheries. The manufactured good represents a composite of everything else. The production functions of our goods, hp (t) and mp (t), are defined as linear in labor. The per capita level of harvest is also linearly related to the resource stock, S(t), representing the increased ease in harvesting with resource abundance. The time spent in production is limited by a constraint: whatever is not spent in harvesting is spent in producing the manufactured good. The fraction of the individual’s endowment of one unit of labor spent in harvesting is f (t), the harvesting effort. Assuming a Cobb-Douglas utility function for the representative agent, we get the following expressions: (1) u(t) = h c (t) m c (t)1− h p (t) = S(t) f (t) m p (t) = (1 − f (t)) where the units of mp (t) are defined from the units of f (t). The per capita harvesting rate is related to f (t) and S(t), with representing harvesting efficiency (Clark 1990). Thus, in per capita terms our model is neutral to the production level obtained with the same effort when people harvest the resource under a centralized direction or a decentralized harvesting from privately owned resource allotments. We assume that goods are consumed when produced and markets clear each period. Thus, hp (t) = hc (t) and mp (t) = mc (t), which gives the following expression: (2) u(t) = (S(t) f (t)) (1 − f (t))1− . Following Lotka (1925) and Volterra (1926), the dynamics of the system arise when population (the predator), L(t), is related to harvesting, and the resource stock (the prey), S(t), is related to population. Total harvesting is determined by the harvesting of the representative agent times population size. The resource growth is logistic, with an intrinsic growth rate r and a carrying capacity K. The change in the resource stock is determined by the difference between total harvesting and the natural resource growth. We assume that fertility increases linearly with consumption ( > 0), and Amer. J. Agr. Econ. the intrinsic population growth rate, , is negative. Thus, the laws of motion for our system are as follows: (3) d S(t) = r S(t)[1 − S(t)/K ] − L(t)[f (t)S(t)] dt d L(t) = L(t)[ + f (t)S(t)]. dt Economic growth studies generally assume that maximizing either an individual or an aggregate SWF is the appropriate societal objective. Parfit’s Theory X lies in between with flexible value for both the quantity and the quality of life. Like Parfit and Cowen, we have no a priori moral grounds to identify the “correct” weight for population in social welfare. However, we can study this issue by considering a family of SWFs with the utility of a representative individual ( = 0) at one extreme and aggregate utility ( = 1) at the other, as well as candidates for Theory X with 0 < < 1. Assuming the social planner faces a discount rate, , these functions can be nested parametrically by ∞ SWF = L(t) [f (t)S(t)] (4) 0 × [1 − f (t)]1− e− t dt. The decision makers choose an optimal harvesting plan, f (t), that solves the following problem: (5) max f (t) ∞ L(t) [f (t)S(t)] [1 − f (t)]1− e− t 0 subject to d S(t) = r S(t)[1 − S(t)/K ] − L(t)[f (t)S(t)] dt and d L(t) = L(t)[ + f (t)S(t)]. dt This model represents a best-case scenario and relies heavily on costless institutions that implement, monitor, and enforce socially optimal harvesting plans. When the social discount rate is infinite, this model coincides with the Brander and Taylor (1998) model, which assumes a laissez-faire market solution and harvesting under open access in the absence of resource management institutions. Good and Reuveny Using Pontryagin’s maximum principle, shadow prices L (t) and S (t) of population and resource stocks, respectively, we write for equation (5) the current value Hamiltonian: Hcv ( f (t), S(t), L(t), L (t), S (t)) (6) = L(t) [f (t)S(t)] [1 − f (t)]1− + S (t)(r S(t)[1 − S(t)/K ] Social Collapse 7 dS (t)/dt S (t) S (t)[r − 2r S(t)/K − L(t) f (t)] + S (t) ⇒ = L(t) f (t) S(t)−1 (1 − f (t))1− S (t) L (t) (t)L(t) + . S (t) + − L(t)[f (t)S(t)]) + L (t)(L(t)[ + f (t)S(t)]). The implied first-order conditions for this problem are the following: (7) max Hcv ( f (t), S(t), L(t), L (t), S (t)) The boundary conditions include the initial state of the system S(0) = S0 and L(0) = L0 , and the transversality conditions and limt→∞ e− t L (t)L(t) = 0 and limt→∞ e− t S (t)S(t) = 0. As usual, the maximization of Hcv with respect to f (t) equates the marginal social value of harvesting with its marginal costs, and the L (t) and S (t) equations relate social value of population and resource changes to the discount rate. f (t) at each point in time ⇒ L(t) S(t) f (t)−1 [1 − f (t)]1− = S(t) f (t) (1 − )[1 − f (t)]− − L L(t)S(t) + S S(t)L(t) d S(t) ∂Hcv = r S(t)[1 − S(t)/K ] = dt ∂S − L(t)[f (t)S(t)] d L(t) ∂Hcv = = L(t)[ + f (t)S(t)] dt ∂L dL (t) ∂Hcv = L (t) − dt ∂L = −L(t)−1 S(t) f (t) × (1 − f (t))1− + L (t)[ − ] − [L (t) − S (t)]S(t) f (t) dL (t)/dt L (t)( + S(t) f (t)) + L (t) L (t) (S (t)S f ) − L (t) ⇒ = L(t)−1 S(t) f (t) (1 − f (t))1− L (t) dS (t) ∂Hcv = S (t) − dt ∂S = S (t)[ − r + 2r S(t)/K ] − L(t) + × f (t) S(t)−1 (1 − f (t))1− − [L (t) − S (t)]L(t) f (t) Results We consider three scenarios. The first serves as a reference case where people have no resource management institutions and ignore the future. In the second, institutions take the form of a social planner maximizing an aggregate SWF with an infinite time horizon. The third scenario differs by maximizing an individual SWF. In this case, decisions either are centralized through a social planner or could be decentralized through the assignment of property rights transferable to the extended family, where agents consider the utilities of future generations as they consider their own. In each case, we study the interior steady state and the transition paths leading to it. The monotonicity of the derivative of the Hamiltonian with respect to f (t) implies a unique interior steady state. The system also has two corner steady states, both involving L(t) = 0 with either S(t) = 0 or S(t) = K. The L(t) = 0 and S(t) = 0 steady state describes a barren environment that cannot support any people and is not reachable from any initial conditions with L(t) > 0. The solution with S(t) = K is only reachable when = 0 (individual utility) and = 0 (no discounting). When → ∞, one gets L (t) = 0 and S (t) = 0, and the problem reduces to maximizing utility with respect to f (t) each period, taking L(t) as given. This leads to a solution of f (t) = . 8 xxx 2009 Amer. J. Agr. Econ. When 0 < < ∞, the steady-state attributes are described by (8) ⎧ ⎨ ( − r )K + r 4r ( + (1 − − )) ( − r )K + r − + − 4( − ) 4r 2 ( + (1 − − )) − 4( − ) 1/2 ⎫ ⎬ K (r ( − 1) + (r − ) − r + 2 ) − ⎭ 2r ( − ) f = − ⎩ − − f r r + L = f 2 K f 2 S= u = − (1 − f )1− . An interior steady state (with a positive population size) exists when − < Kf. As figure 1 shows, the situation occurs except when = 0 and = 0, leading to the corner steady state L(t) = 0 and S(t) = K. The comparative static analysis of equation (8) yields unambiguous results only in extreme cases and the transient behavior cannot be solved analytically. We are thus forced to study the behavior numerically. We use parameters and initial values for population and the resource calibrated by Brander and Taylor (1998) for Easter Island, and present effects of altering the two key parameters of and .1 Figure 1 presents the steady-state solutions for the resource, population, harvesting effort, and the contemporary individual utility. In the no-institutions scenario ( → ∞), the steady state occurs at S(t) = 6,250 and L(t) = 4,972 and is the same regardless of the value of . This case is represented by the horizontal lines in figure 1 and serves as a baseline for solutions that incorporate foresight. To improve visibility, the vertical scale for population in figure 1 is expanded compared to subsequent figures. For the individual SWF, when = 0, the equilibrium is at L(t) = 0 and S(t) = K. This outcome is consistent with one of Parfit’s 1 The carrying capacity, K = 12,000; resource annual intrinsic growth rate, r = 0.004; fertility parameter, = 4; intrinsic annual net birth rate, = −0.01; annual harvesting efficiency rate, = 0.000001; and utility taste parameter, = 0.4. The initial conditions are given by L(0) = 40 and S(0) = K. conjectures: a world of bliss with no one to enjoy it. Intuitively, to maximize individual utility when = 0, it is optimal to maximize S since harvesting is an increasing function of S. Sustaining S(t) at its maximum value of K requires that people do not harvest anything since the resource growth rate is zero when S(t) = K. These conditions hold only when L(t) = 0. Compared with the no-institution case, the harvesting effort for = 0 is lower, the resource stock is larger, population is lower, and individual utility is higher (as the resource stock is higher and time not spent on harvesting is used elsewhere). Unless is less than about 1%, these differences are small, and for a moderate discount rate of 3%, the perfect institutions steady-state harvesting effort is similar to the no-institution case. Diamond’s contention that the resource effects occurred so slowly that they went unnoticed, then, has a counterpart: even if noticed and understood, future resource effects are too small to matter much when = 0, unless is extremely low. This suggests that, in order for policy to have any effect on steady-state outcomes, planners need to have a very low discount rate and a long time horizon. For the aggregate SWF, when = 0 there are more people in steady state than for the individual utility social welfare, and their utilities are lower, consistent with Parfit’s conjecture. As rises, the steady state converges to the no-institution case, though the differences from laissez-faire remain large even for high . Compared with the = 0 case, valuing population explicitly in social welfare also increases pressure on the resource and raises harvesting efforts. The equilibrium population reflects tension between a desire to keep population high, which strains the resource, and a desire to keep the resource high because this increases harvesting for a given effort. Since the future consequences of actions have different dynamics, these forces respond differently to . When = 0, the tension is resolved optimally at L = 4,697 and S = 6,878, and the harvesting effort is lower than the no-institutions effort. As rises above some small value (about 1%), the steady-state population for the aggregate SWF becomes smaller than it is for the individual SWF. This result contrasts Parfit’s Repugnant Conclusion, which takes place in a static environment where resources do not react to population change. It occurs because of short-term gains due to a rise in population resulting from harvesting (higher with an aggregate than an individual SWF) that are more Good and Reuveny Social Collapse 9 Figure 1. Equilibrium values of resources stock, population, harvesting effort, and utility for different and values than offset by the longer term losses due to resource depletion. Figure 1 shows that increasing for any increases the steady-state harvesting effort, decreases the resource stock, and lowers individual utility. A similar pattern occurs for these outcomes as rises. Initially, the differences between the steady states obtained for the alternative values are small. As increases, the differences increase, but as continues to increase above some small level (about 1%), the differences disappear. The pattern for the equilibrium population is different. For = 0, population rises from 0 when = 0 to 4,697 when = 1. If = 0 and held constant, the equilibrium population increases with , reaches a peak, and then decreases with increasing . Consequently, for a society that places a positive value on population in social welfare, increasing that value above some critical level leads to the unintended consequence of decreasing the steadystate population. Values that we hold in a static sense, ceteris paribus, and that we use to formulate the Hamiltonian do not necessarily follow through to outcomes that occur in equilibrium, which consider the dynamics of what keeps the system there. Attempts to maintain a larger population than the no-institutions population level can be futile. Next, consider Parfit’s Theory X. Figure 1 does not specify Parfit’s Theory X, but it says what Theory X is not. Figure 1 suggests that society should prefer low , ceteris paribus, as this raises individual utility. However, the relationship between and L suggests that society should reject values of where population falls with , because for these values both population and the individual utility decline, and consequently also the aggregate welfare declines. In our application, these values of depend on . For 0.2% < < 7%, we reject values of larger than about 0.25, as these values imply equilibria with both smaller population sizes and individual utilities. In practical terms, however, it seems that Theory X is unnecessary. An individual SWF allows society to enjoy the highest equilibrium individual utility, for a given . When is larger than 1% or so, a society maximizing an individual SWF also ends up with nearly the same population size as with any of the other SWFs examined here. The individual SWF also has the added institutional benefit that can be supported by private property rights and the presence of markets. Figures 2 and 3 present transient solutions for the resource (upper left), population (lower left), share of labor spent in harvesting (upper right), and the contemporary individual 10 xxx 2009 Amer. J. Agr. Econ. Figure 2. Trajectories for resource stock, population, harvesting effort, and utility for different values Figure 3. Trajectories for resource stock, population, harvesting effort, and utility for different values Good and Reuveny utility (lower right). Figure 2 presents trajectories with = 0 and = 1 for several discount rates. The trajectories are presented as a function of years since arrival, because the actual date when the colonization of Easter Island began is uncertain. The no-institution case ( → ∞) is shown by the solid black line. Serving as a baseline, it presents a rapid population increase followed by a rapid decline that is roughly consistent with the archeological data on Easter Island (Brander and Taylor 1998). For the aggregate utility social welfare, we show trajectories for of 1, 4, and 8%. For the individual utility social welfare, we show trajectories for = 1 and 4% (the trajectories for > 4% closely resemble the no-institution solution). The aggregate SWF population trajectories differ from the individual SWF trajectories for all values, exhibiting more volatility, and higher booms that climax sooner. For = 0, harvesting rises with , the resource stock falls with , and the maximum population rises with . In this case, foresight moderates the collapse. For = 1, harvesting is higher than for = 0, and it falls for higher values of . The resource is lower than for = 0 and rises with , and the maximum population is higher than for = 0 and falls with . Intuitively, with an individual SWF, the planner can raise welfare only by raising individual utility. In contrast, with an aggregate SWF, the planner can raise welfare by increasing either individual utility or population. Since aggregate SWF rises quickly with population, the harvesting effort is higher for = 1 than for = 0, increasing the maximum population. This, in turn, lowers the resource stock, which eventually reduces population; in an effort to get population high quickly, it rises to an unsustainable level, leading to resource depletion and population collapse. For = 1, reducing exaggerates the collapse, as measured by the difference between the first peak and first trough of the population trajectory. A planner attributing greater importance for future aggregate utility can increase the objective by promoting fertility. This, however, leads to a relatively larger fall in resource stock and eventually population. As rises, the planner discounts aggregate utility more, and the drive to raise population moderates. Figure 2 also shows the effect these dynamics have on individual utility under the two SWFs. In the case of the individual SWF, as the discount rate declines, the trajectory of utility Social Collapse 11 fluctuates less, and the values obtained at each point in time are higher. In the case of the aggregate SWF, the individual utility also fluctuates less over time, but the values obtained at each point in time are lower. Our bounding analyses of the best and worst cases have different implications depending on which SWF is used. With individual SWF our optimal trajectories present a best case in the sense that they lessen the magnitude of collapse compared to the no-institutions case regardless of the value of . For aggregate SWF the most stable solution is presented by the laissez-faire case and the optimal control trajectory aggravates social collapse for any value of shown in figure 2. Figure 3 presents trajectories for of 1% and of 0, 0.1, 0.25, 0.5, and 1. As rises from 0 to 1, the harvesting effort rises and the trajectory is more volatile. The harvesting trajectories for alternative values of appear similar, where the effort first falls and then climbs up, but they do not converge in the long run. Intermediate values of have intermediate trajectories. The resource stock also falls as rises from 0 to 1, more so in the first part of the trajectory, climbing up to steady-state levels that differ for the alternative . Clearly, the best value of at averting social collapse is = 0. The intuition is similar to the one explaining the differences observed between the cases of = 0 and = 1 in figure 2, hinging on the ability of the planner to increase aggregate social welfare by increasing the number of people in the system. The larger is, the larger is the incentive for the social planner to do so. How do figures 2 and 3 compare to the historical record? The estimated date when Polynesians arrived at Easter Island varies from AD 400 to 1000, and the peak population and its date vary between 7,000–20,000 and AD 1100–1500, respectively (Ponting 1991; Bahn and Flenley 1992; Stephens 1969). The island was deforested by AD 1400–1600. When discovered in the 18th century, there were about 2,000–3,000 Rapanui (Hunt and Lipo 2001; Flenley et al. 1991; Flenley 1996; Brander and Taylor 1998). Thus, our population trajectories are consistent with both an assumption of no institutions and a broad range of alternative assumptions about optimal resource management institutions. Figure 1 shows that the relationship between steady-state population and for an aggregate SWF is highly nonlinear, particularly for low discount rates. Population rises with until a 12 xxx 2009 Amer. J. Agr. Econ. Figure 4. Trajectories for resource stock, population, harvesting effort, and utility for very low values value of about 0.1%, falls until 1%, and then rises with . Figure 4 presents a detailed examination of trajectories for of 0.5, 0.2, and 0.1%. For the individual SWF, the decline in continuously dampens the boom-bust cycle. For of 0.1%, the approach to steady state does not exhibit a boom-bust cycle. For the aggregate SWF, a decline of from 0.5 to 0.1% also dampens the boom-bust cycle, reversing the tendency described in figure 2. Yet even a of 0.1% does little to mitigate the boom-bust cycle in this case. Intuitively, with an aggregate SWF the planner can raise welfare by increasing individual utility or population. Procedures for implementing population increases (which depend on harvesting) can be implemented more quickly than those leading to increases in utility (which rely on the slower process of resource recovery). When is large, only these population-increasing efforts show up with importance in the SWF. For a low enough , these dynamic changes and the efforts to increase SWF by increasing individual utility through the effect on future values of S(t) become more meaningful, providing society the incentive to reduce harvesting now, lower population size, and increase the resource stock. Discussion and Implications Our results show that perfect resource management institutions with an infinite time horizon and a reasonable discount rate by today’s standards would have done little to avert social collapse. Our focus on these institutions to avert collapse, rather than on direct population control, may seem controversial. We have no doubt that direct population control could have averted collapse. For example, the Polynesian society on the island of Tikopia averted collapse by controlling population through abstinence, abortion, contraception, one-way ocean voyages with no real chance of success, and infanticide (Kirch 1997). We could avoid collapse in our model by including a population-cap constraint or by seeking optimal population size in order to maximize utility through controlling consumption and population growth, as in Dasgupta (1969). Cowen (1989), however, argues optimal population need not maximize some utility, but is what people living sequential lives would opt for if they would choose how to live out each life, and some, including Dasgupta (2001a) himself, view this as the wrong problem to solve. At any rate, both approaches Good and Reuveny eliminate the linkage between population and the environment and imply restricting procreation autonomy, a potential violation of human rights. Our work, then, has a second interpretation. Finding that any resource management institution fails to avert social collapse, we must conclude that some alteration of the population dynamic is necessary if the collapse is to be averted. One might argue that our model may not accurately describe the world today since it ignores physical capital, innovation, demographic transition, and subsistence-level harvesting and assumes a finite carrying capacity. In addition, the transient phenomenon of a social crash depends on the starting values being far from equilibrium. Yet these issues are not straightforward. While replacing resources with capital can alleviate pressures, critical resources may not have good substitutes. Societies can alleviate pressures by innovation, but progress, particularly in harvesting productivity, can also increase degradation and intensify boombust trajectories. Whether innovation can ultimately alleviate all pressures is unknowable. The overall effect of demographic transition in the model is unclear, depending on the strengths of the Malthusian and nonMalthusian phases and the discount rate. Additionally, many poor countries still exhibit Malthusian fertility. Subsistence requirements are prevalent in developing countries and were likely prevalent in historical societies, but their addition to the model will increase the volatility of trajectories, further deviating from our focus on the best-case scenario. The assumption of a carrying capacity is appropriate at least in the context of historical societies. While notable scholars such as Arrow et al. (1995) argue that our planet has a carrying capacity, the issue is controversial. If this assumption is not relevant for our planet, our analysis has little applicability today. However, if it is relevant, perpetual economic growth may eventually face problems of the type faced by historical societies. Countries may raise their effective carrying capacity through innovation or trade. However, trade cannot raise planetary carrying capacity, and innovation may be too infrequent to do it. In the past, humans went through two major carrying capacity altering events: the switch from hunter gatherers to an agrarian society and the industrial/green revolution. With a recent major carrying capacity altering event and with a population of over 6 billion, doubling every Social Collapse 13 fifty years or so, our society may be on a trajectory at least qualitatively similar to that of these historical societies. While our model may not accurately describe the world today due to its relative simplicity, it may offer insights on the way to think about population and environment interactions. Beginning with moral philosophy, what is at issue in Parfit’s view is how production varies with population. If, as some may argue, production grows proportionately to, or faster than, population, the Repugnant Conclusion does not obtain. Yet we bring a new argument to this debate: it is not only a matter of how production varies with population, but also how population varies with production. Parfit’s view is static: increasing population gives individuals a smaller share of the resources, leading to a decline in individual utility. However, Parfit creates a world in which population increases in a vacuum and additional people exist from nothing. When population growth depends on production, a Repugnant Conclusion motivated by Kavka’s (1982) “obligation to procreate” cannot occur. The impetus to increase population driven by an aggregate social welfare is limited by the environment’s ability to support it. Parfit’s expectation that an individual social welfare would lead to a few people with high utilities is also prevented in this case, as long as > 0. Consider next Parfit’s quest to determine the weight of population in social welfare. We find that for greater than 0.5%, the maximum equilibrium population is achieved for of about 0.25. So, while we cannot say what Theory X is, we can say what Theory X is not. Since individual utility falls with , increasing beyond this level is counterproductive. However, on a practical level, Theory X seems unnecessary. An individual SWF produces roughly the same equilibrium population as any other function for alternative levels of is associated with the highest individual utility, and has the advantage that it is the only optimal solution that is supportable by a market mechanism. Our analysis also has implications for the economic growth literature. Growth studies typically assume that population growth is exogenous, eliminating collapses by assumption. Making population growth endogenous introduces potential for cycles in population and economic variables. Second, the tendency of growth studies to focus on the steady state may miss key insights. We find that for even modest discount rates that equilibrium population levels are roughly similar across welfare 14 xxx 2009 functions, but the transition paths differ dramatically. An equilibrium analysis would mistakenly lead one to conclude that the choice of SWF did not have much impact on population. Third, the growth literature seems to treat the choice among the aggregate or individual SWFs casually, as though the issue is unimportant. We show that the two functions yield different dynamics; the similarity between them cannot be taken for granted. Finally, our results underscore the importance of discounting. There has been resurgence of debate on this topic in light of its relevance to addressing climate change (Stern 2007; Nordhaus 2007; Weitzman 2007). Typically, researchers rule out a zero rate as a matter of mathematical convenience in dynamic optimizations (Barro and Sala-i-Martin 2004; Chiang 1992). Others argue that it is fair to use a zero rate since future generations do not take part in our decisions, but are affected by them (Dasgupta, Mäler, and Barrett 1999). Parfit’s (1984) static logic implies a zero rate. Yet Arrow (1999) notes that a small rate leads to large current savings and if future people do not save much, their profit is at our expense. Still others argue that future generations would likely be more advanced and, therefore, we need not necessarily sacrifice for them (Nordhaus 2007). Taking a middle ground view, Weitzman (1999) suggests using the lowest plausible future rate as a response to uncertainty about this rate in the far future. Which discount rate do people use? Estimates vary widely, including hundreds of percent per year (Frederick, Loewenstein, and O’Donoghue 2002). Nordhaus and Boyer (2000) use 5%. Stern’s (2007) report, which calls for immediate sharp decline in greenhouse emissions, assumes = 0.1%. Nordhaus (2007) argues this rate is inconsistent with today’s real interest rate and uses 1.5%, as also does Cline (1992). Weitzman (2007) argues the driving factor should be how much insurance is needed to offset the chance of a calamity due to climate change and suggests a range of 0.7 to 2.7%. The above-mentioned debate centers on whether intergenerational equity drives us to a moral position for using a very low , or for basing our decision of on the empirical values that people seem to use for private decisions. In the end, the decision is a purely normative one and we cannot resolve the issue anymore than those other writers can. We note that our conclusions have the same flavor as theirs: sacrifices that have long-term benefits are unlikely Amer. J. Agr. Econ. to be undertaken unless the social discount rate is much lower than any rate we can currently motivate empirically. Conclusion An emerging theme in studies on the collapse of historical civilizations attributes the breakdown to anthropogenic environmental degradation. We have described this linkage for the Sumerians, Maya, Rapanui, and Anasazi. These societies are atypical because of the levels of greatness they achieved, and since their collapse was abrupt and spectacular. Rather than empirically comparing these societies to others that may have had better institutions (as Diamond and others do), we construct a counterfactual case by hypothetically endowing them with perfect resource management institutions with complete foresight and infinite time horizons. We find that, with a reasonable discount rate by today’s standards, these best-case institutions would have done little to avert social collapse. When society maximizes an individual SWF, a discount rate of below 0.5% is necessary to prevent a collapse in population. Otherwise, like our no-institutions scenario, it too collapses. When the society maximizes an aggregate SWF, it collapses abruptly even for tiny discount rates near 1%. Having begun our article with a historical slant, one may wonder which SWF guided the leaders of our four societies. One might conjecture they chose an aggregate SWF because it implied the ability to amass armies and build monuments. An equally plausible conjecture is that societies that ended up building monuments or amassing armies did so as a consequence of the large workforces they had. Given the weak archeological evidence, we cannot draw any conclusions about the direction of this causality in a Granger sense. However, in the context of our model, both causal behaviors imply monument building and army amassing outcomes that are more likely to occur with the larger populations generated by an aggregate SWF compared with the individual SWF or no-institutions cases. We are more likely to notice these societies because of it. We speculate that historical societies that placed a prime importance on the welfare of the individual may have still collapsed, though less spectacularly and without our notice. At any rate, it is tempting to argue that our societies collapsed because they were myopic, Good and Reuveny had no resource management institutions, did not grasp their problem, did not pass information over time, or did not notice slow environmental changes. These assertions are essentially circular because the evidence one typically uses in supporting them is the collapse itself. We find that, even if our civilizations had the institutions, understanding, information records, foresight, and SWFs commonly used today, they would still have collapsed. It seems reasonable to assert that these collapses were socially optimal. One of the unique features of our approach is that social collapse is evaluated by the ability of the political, economic, and environmental system to avoid drastic fluctuations in the transient solution to the control problem rather than its effect on the steady state and its neighborhood. Indeed, the choice of SWF, discounting, and the use of institutions have little effect on the equilibrium population at all but the lowest discount rates, yet the effects on population dynamics along the transition path are stark. [Received January 2008; accepted February 2009.] References Abrams, E.M., and D.J. Rue. 1988. “The Causes and Consequences of Deforestation Among the Prehistoric Maya.” Human Ecology 16(4):377– 95. Adams, R.M. 1981. Heartland of Cities: Surveys of Ancient Settlement and Land Use on the Central Floodplain of the Euphrates. Chicago: University of Chicago Press. Aghion, P., and P. Howitt. 1998. Endogenous Growth Theory. Cambridge, MA: The MIT Press. Arrow, K. 1999. “Discounting, Morality, and Gaming.” In P.R. Portney and J.P. Weyant, eds. Discounting and Intergenerational Equity. Washington, DC: Resources for the Future, pp. 13– 22. Arrow, K., B. Bolin, R. Costanza, P. Dasgupta, C. Folke, C.S. Holling, B.O. Jansson, S. Levin, K.G. Mäler, C. Perrings, and D. Pimentel. 1995. “Economic Growth, Carrying Capacity, and the Environment.” Science 268(5210):520– 21. Arrow, K., G. Daily, P. Dasgupta, S. Levin, K.G. Mäler, E. Maskin, D. Starrett, T. Sterner, and T. Tietenberg. 2000. “Managing Ecosystem Resources.” Environmental Science and Technology 34(8):1401–06. Social Collapse 15 Attané, I. 2002. “China’s Family Planning Policy: An Overview of Its Past and Future.” Studies in Family Planning 33(1):103–13. Bahn, P.G., and J. Flenley. 1992. Easter Island, Earth Island. London: Thames and Hudson. Barro, R.J., and X. Sala-i-Martin. 2004. Economic Growth. Cambridge, MA: The MIT Press. Betancourt, J.L., and T.R. Van Devender. 1981. “Holocene Vegetation in Chaco Canyon, New Mexico.” Science 214(4521):656–58. Betancourt, J.L., J.S. Dean, and H.M. Hull. 1986. “Prehistoric Long-Distance Transport of Construction Beams, Chaco Canyon, New Mexico.” American Antiquity 51(2):370–75. Binford, M.W., M. Brenner, T.J. Whitmore, A. Higuera-Gundy, E.S. Deevey, and B. Leyden. 1987. “Ecosystems, Paleoecology and Human Disturbance in Subtropical and Tropical America.” Quaternary Science Review 6(2):115–28. Blanchard, O.J., and S. Fischer. 1989. Lectures on Macroeconomics. Cambridge, MA: The MIT Press. Boyden, S. 1987. Western Civilization in Biological Perspective: Patterns in Biohistory. New York: Oxford University Press. Brander, J.A. 2007. “Sustainability: Malthus Revisited?” Canadian Journal of Economics 40(1):1– 38. Brander, J.A., and M.S. Taylor. 1998. “The Simple Economics of Easter Island: A RicardoMalthus Model of Renewable Resource Use.” The American Economic Review 88(1):119– 38. Bureau of Land Management (BLM). 2006. “Who Were the Anasazi,” U.S. Department of the Interior, Colorado. Available at: http://www. blm.gov/co/st/en/fo/ahc/who were the anasazi. html. Cass, D. 1965. “Optimum Growth in an Aggregate Model of Capital Accumulation.” The Review of Economic Studies 32(July):233–40. Chiang, A.C. 1992. Elements of Dynamic Optimization. New York: McGraw-Hill. Clark, C.W. 1990. Mathematical Bioeconomics. New York: Wiley-Interscience. Cline, W.R. 1992. The Economics of Global Warming. Washington, DC: Institute for International Economics. Cowen, T. 1989. “Normative Population Theory.” Social Choice and Welfare 6(1):33–43. ——. 1996. “What Do We Learn from the Repugnant Conclusion?” Ethics 106(4):754–75. Culbert, T.P. 1988. “The Collapse of Classic Maya Civilization.” In N. Yoffee and G.L. Cowgill, eds. The Collapse of Ancient States and Civilizations. Tucson: The University of Arizona Press, pp. 69–101. 16 xxx 2009 Dalton, T.R., R.M. Coats, and B.R. Asrabadi. 2005. “Renewable Resources, Property-Rights Regimes and Endogenous Growth.” Ecological Economics 52(1):31–41. Dasgupta, P. 1969. “On the Concept of Optimum Population.” Review of Economic Studies 36(July):294–318. ——. 1998. “Population, Consumption and Resources: Ethical Issues.” Ecological Economics 24(2):139–52. ——. 2000a. An Inquiry into Well-being and Destitution. Oxford, UK: Clarendon Press. ——. 2000b. “Population and Resources: An Exploration of Reproductive and Environmental Externalities.” Population and Development Review 26(4):643–89. ——. 2001a. Human Well-being and the Natural Environment. Oxford: Oxford University Press. ——. 2001b. “Population, Resources, and Welfare: An Exploration into Reproductive and Environmental Externalities.” In K.G. Mäler and J. Vincent, eds. Handbook of Environmental and Resource Economics. Amsterdam: North Holland, pp. 191–247. ——. 2005. “Bottlenecks.” London Review of Books, 19 May. Dasgupta, P., K.G. Mäler, and S. Barrett. 1999. “Intergenerational Equity, Social Discount Rates, and Global Warming.” In P.R. Portney and J.P. Weyant, eds. Discounting and Intergenerational Equity. Washington, DC: Resources for the Future, pp. 51–77. Decker, C.S., and R. Reuveny. 2005. “Endogenous Technological Progress and the Malthusian Trap: Could Simon and Boserup Have Saved Easter Island?” Human Ecology 33(1):119– 40. Decter, M. 1997. “The Nine Lives of Population Control.” First Things 38(December):17–23. Diamond, J. 2005. Collapse: How Societies Choose to Fail or Succeed. New York: Viking Books. Dworkin, R. 1978. Taking Rights Seriously. London: Duckworth. Ehrlich, P.R. 1968. The Population Bomb. Cutchogue, NY: Buccaneer Books. Flenley, J. 1996. “Further Evidence of Vegetational Change on Easter Island.” South Pacific Study 16(2):135–41. Flenley, J.R., A.S.M. King, J. Jackson, C. Chew, J.T. Teller, and M.E. Prentice. 1991. “The Late Quaternary Vegetational and Climatic History of Easter Island.” Journal of Quaternary Science 6(2):85–115. Flenley, J., and P. Bahn. 2002. The Enigmas of Easter Island. New York: Oxford University Press. Frederick, S., G. Loewenstein, and T. O’Donoghue. 2002. “Time Discounting and Time Preference: Amer. J. Agr. Econ. A Critical Review.” Journal of Economic Literature XL(2):351–401. Gelburd, D.E. 1963. “Managing Salinity: Lessons from the Past.” Journal of Soil and Water Conservation 40(4):329–31. Gewirth, A. 1981. “Are There Any Absolute Rights?” Philosophical Quarterly 31(122):1– 16. Gigliotti, G.A. 1983. “Total Utility, Overlapping Generations and Optimum Population.” Review of Economic Studies 50(January):71–86. Good, D.H., and R. Reuveny. 2006. “The Fate of Easter Island: The Limits of Resource Management Institutions.” Ecological Economics 58(3):473–90. Hardin, G. 1968. “The Tragedy of the Commons.” Science 162(1968):1243–48. ——. 1998. “Extensions of the Tragedy of the Commons.” Science 280(5364):682–83. Heal, G. 1998. Economic Theory and Sustainability. New York: Columbia University Press. Heerink, N. 1994. Population Growth, Income Distribution, and Economic Development. Berlin: Springer. Hemminki, E., Z. Wu, G. Cao, and K. Viisainen. 2005. “Illegal Births and Legal Abortions—the Case of China.” Reproductive Health 2(5):1–8. Hunt, T.L., and C.P. Lipo. 2001. “Cultural Elaboration and Environmental Uncertainty in Polynesia.” In C.M. Stevenson, G. Lee, and F.J. Morin, eds. Pacific 2000: Proceedings of the Fifth International Conference on Easter Island and the Pacific. Los Osos, CA: Easter Island Foundation, pp. 103–15. Jacobsen, T., and R.M. Adams. 1958. “Salt and Silt in Ancient Mesopotamian Agriculture.” Science 128(3334):1251–58. Johnson, D.G. 2000. “Population, Food and Knowledge.” American Economic Review 90(1):1–14. Kavka, G.S. 1982. “The Paradox of Future Individuals.” Philosophy and Public Affairs 11(2):93– 112. King, M., and C. Elliott. 1997. “To the Point of Farce: A Martian View of the Hardinian Taboo— The Silence that Surrounds Population Control.” British Medical Journal 315(7120):1441– 43. Kirch, P.V. 1997. “Microcosmic Histories: Island Perspectives on ‘Global’ Change.” American Anthropologist 99(1):30–42. ——. 2005. “Archaeology and Global Change: The Holocene Record.” Annual Review of Environment and Resources 30(November):409–40. Levy, A. 1992. Economic Dynamics. Aldershot, Australia: Avebury. Lotka, A.J. 1925. Elements of Physical Biology. Baltimore: Williams and Wilkins. Good and Reuveny Lucas, R.E. Jr. 2002. Lectures on Economic Growth. Cambridge, MA: Harvard University Press. Mäler, K.G. 2000. “Development, Ecological Resources and Their Management: A Study of Complex Dynamic Systems.” European Economic Review 44(4):645–65. Malthus, T. 1798. An Essay on the Principle of Population. New York: Penguin. Nagel, T. 1981. “Libertarianism Without Foundations.” In J. Paul, ed. Reading Nozick: Essays on Anarchy, State, and Utopia. Oxford: Basil Blackwell, pp. 191–205. Nordhaus, W.D. 2007. “A Review of the Stern Review on the Economics of Climate Change.” Journal of Economic Literature XLV(3):686– 702. Nordhaus, W.D., and J. Boyer. 2000. Warming the World: Economic Modeling of Global Warming. Cambridge, MA: The MIT Press. Nozick, R. 1974. Anarchy, State and Utopia. New York: Basic Books. Obstfeld, M., and K. Rogoff. 1998. Foundations of International Macroeconomics. Cambridge, MA: The MIT Press. O’Hara, S.L., F.A. Street-Perrott, and T.P. Burt. 1993. “Accelerated Soil Erosion Around a Mexican Highland Lake Caused by Prehispanic Agriculture.” Nature 362(6415):48–51. Ostrom, E. 1990. Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge: Cambridge University Press. Parfit, D. 1984. Reasons and Persons. Oxford: Oxford University Press. Perman, R., Y. Ma, J. McGilvray, and M. Common. 2003. Natural Resource and Environmental Economics. London: Pearson/Addison Wesley. Pezzey, J.C.V., and J.M. Anderies. 2003. “The Effect of Subsistence on Collapse and Institutional Adaptation in Population-Resource Societies.” Journal of Development Economics 72(1):299– 320. Ponting, C. 1991. A Green History of the World. New York: Penguin Group. Reuveny, R., and J.W. Maxwell. 2001. “Conflict and Renewable Resources.” Journal of Conflict Resolution 45(6):719–42. Reuveny, R., and C.S. Decker. 2000. “Easter Island: Historical Anecdote or Warning for the Future?” Ecological Economics 35(2):271–87. Romer, D. 2001. Advanced Macroeconomics. Boston: McGraw-Hill. Samuels, M., and J.L. Betancourt. 1982. “Modeling the Long-Term Effects of Fuelwood Harvests Social Collapse 17 on Pinyon-Juniper Woodlands.” Environmental Management 6(6):505–15. Sen, A. 1983. “Evaluator Relativity and Consequential Evaluation.” Philosophy and Public Affairs 12(2):113–32. Smith, V.L. 1975. “The Primitive Hunter Culture, Pleistocene Extinction, and the Rise of Agriculture.” The Journal of Political Economy 83(4):727–56. Stephens, J.L. 1969. (1841) Incidents of Travel in Central America, Chiapas, and Yucatan, vol. 1. Mineola, NY: Dover Publications. Stern, N. 2007. The Economics of Climate Change: The Stern Review. Cambridge: Cambridge University Press. Stuart, D.E. 2000. Anasazi America: Seventeen Centuries on the Road from Center Place. Albuquerque: University of New Mexico Press. Tainter, J. 1990. The Collapse of Complex Societies. Cambridge: Cambridge University Press. Thompson, W.R. 2004. “Complexity, Diminishing Marginal Returns, and Serial Mesopotamian Fragmentation.” Journal of World-Systems Research X 3(Fall):613–52. Tomlinson, R. 1975. Demographic Problems: Controversy over Population Control. Encino: Dickenson. Turnovsky, S.J. 2000. International Macroeconomic Dynamics. Cambridge, MA: The MIT Press. United Nations. 1948. Universal Declaration of Human Rights. General Assembly Resolution 217 A (III), New York. ——. 1975. Report of the United Nations World Population Conference, Held in Bucharest, Romania. A/Conf. 60/19. New York. Van Tilberg, J.A. 1994. Easter Island: Archeology, Ecology, and Culture. London: British Museum Press. Volterra, V. 1926. “Fluctuations in the Abundance of a Species Considered Mathematically.” Nature 118(2972):558–60. Weitzman, M.L. 1999. “Just Keep Discounting, But. . .” In P.R. Portney and J.P. Weyant, eds. Discounting and Intergenerational Equity. Washington, DC: Resources for the Future, pp. 23–30. ——. 2007. “A Review of the Stern Review on the Economics of Climate Change.” Journal of Economic Literature XLV(3):703–24. World Bank. 2003. World Development Report. Washington, DC. Yoffee, N., and G.L. Cowgill. 1988. The Collapse of Ancient States and Civilizations. Tucson: The University of Arizona Press.