Harvesting the Commons

Environ Resource Econ https://doi.org/10.1007/s10640-018-0221-4 Harvesting the Commons Partha Dasgupta1 · Tapan Mitra2 · Gerhard Sorger3 Accepted: 17 January 2018 © The Author(s) 2018. This article is an open access publication Abstract We study a socio-ecological model in which a continuum of consumers harvest a common property renewable natural resource. Markov perfect Nash equilibria of the corresponding non-cooperative game are derived and are compared with collectively optimal harvesting policies. The underlying mechanisms that drive open-access commons in our model are shaped by population size, harvesting costs, and the ecosystem’s productivity. If other things equal population is small relative to harvesting costs, unmanaged commons do not face destruction. More strikingly, they are harvested at the collectively optimal rate. Property rights do not matter in that parametric regime because the resource has no social scarcity value. However, if other things equal population is large relative to harvesting costs, openaccess renewable natural resources suffer from the tragedy of the commons. Property rights matter there because the resource has a social scarcity price. The population size relative to harvesting costs at which the socio-ecological system bifurcates is an increasing function of the ecosystem’s productivity. A sudden crash in productivity, population overshoot, or decline in harvesting costs can tip an unmanaged common into ruin. The model provides a way to interpret historical and archaeological findings on the collapse of those societies that have been studied by scholars. For their comments on a previous draft of this paper, we are most grateful to Paul Ehrlich, Ingmar Schumacher, Daan van Soest, Robert Solow, and an anonymous referee. B Partha Dasgupta Tapan Mitra Gerhard Sorger 1 Faculty of Economics, University of Cambridge, Sidgwick Avenue, Cambridge CB3 9DD, UK 2 Department of Economics, Cornell University, Ithaca, NY 14853, USA 3 Department of Economics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria 123 P. Dasgupta et al. Keywords Tragedy of the commons · Renewable resource · Intrinsic growth rate of resource · Human population growth · Cost of harvesting · Markov perfect Nash equilibrium JEL Classification C73 · Q20 1 The Problem The economic theory of common-property resources, or “commons” for short, has for the most part remained confined to a timeless setting. Dasgupta and Heal (1979: Ch. 3) formulated the situation to be studied as a one-stage symmetric game involving herdsmen grazing their cattle on a piece of communal land. It was shown that if, as is typically the case in village grazing fields in South Asia and sub-Saharan Africa, access to the common is restricted to a well-defined group of herdsmen, the implicit rent each herdsman earns in a non-cooperative equilibrium is less than what each would have enjoyed had they cooperated. The authors also showed that if the size of the group was to increase indefinitely, each herdsman would introduce a vanishingly small herd, but the total number of cattle in the field would expand to the point where aggregate rent is zero. The distortion created by each herdsman is no doubt small if the group size is large, but the sum of those small distortions is not small. The situation where access to a common is unrestricted was first studied by Gordon (1954). Although he did not offer a formal analysis, the methods deployed by Dasgupta and Heal (1979) can be extended to complete his account. Suppose the number of potential herdsmen is unlimited but entry into the common involves a small fixed cost. The situation can be modelled as a two-stage non-cooperative game: Herdsmen decide whether to enter, following which those who have entered choose the size of their herds. It can be shown that in symmetric sub-game perfect Nash equilibria the number of herdsmen who enter tends to infinity and the aggregate rent from grazing the common tends to zero as the cost of entry becomes vanishingly small. Rent dissipation is a reflection of overgrazing. But there is a further concern, that in time overgrazing could lead to the common’s destruction even if it was in the herdsmen’s collective interest to preserve it over an indefinite future. The situation would be as though each herdsman discounts the output from the commons at a higher rate than he would have, had the group acted collectively. In his famous paper on open-access resources, Hardin (1968) implicitly considered a dynamic setting. The grazing field can then be thought of as a renewable natural resource. If the rate at which cattle consume fodder exceeds the field’s regenerative capacity by a finite margin, it is doomed. Although Hardin (1968) did not offer a formal analysis, he insisted that unrestricted freedom in the commons leads in time to their ruin. And he dubbed the processes unleashed by that freedom, the “tragedy of the commons”.1 1 Global commons such as the atmosphere and the high seas are open-access resources. Unfortunately, Hardin (1968) chose to illustrate the tragedy of the commons by imagining the fate of grazing fields, which are geographically localised resources. His conclusions about the fate of local commons have been countered in an extensive empirical literature. Scholars have uncovered a variety of communitarian institutions that have evolved over the centuries to protect and promote local common-property resources. Many of the most striking studies have been of village and coastal communities in South Asia, sub-Saharan Africa, and South America (Jodha 1986, 2001; Cordell and McKean 1986; McCay and Acheson 1987; Feeny et al. 1990; Ostrom 1990; McKean 1992; Noronha 1997). The connection to the literature on social capital is self-evident. However, Ghate et al. (2008) contains a revealing set of empirical studies of local commons in South Asia, where communitarian institutions have been found to have eroded to the point where the commons resemble open-access resources. Dasgupta (2010) is a review of both strands of the literature. 123 Harvesting the Commons Identifying Hardin’s processes in situations where agents choose the size of their herds strategically over time has not been found to be easy; which is why the theoretical literature on the fate of commons in dynamic settings remains sparse.2 It has been customary to study strategic behaviour among a group of identical agents consuming a common-property renewable natural resource. The payoff to an agent is the discounted sum of net utilities (utility minus harvesting costs) over time. Utility is assumed to be a monotonically increasing, concave function of personal consumption, and harvesting costs are linear and independent of the resource stock.3 The optimal rate of resource exploitation when the agents fully cooperate has been characterized by Clark (2010). The idea here, on the other hand, is to determine (symmetric) Marko (...truncated)