The commons with capital markets
The authors propose and explore a two-period model for dynamic commons, with capital market access to resources. A complete characterization of the model is provided for the symmetric consumption and the extraction behaviour in four environments: under strategic and competitive equilibrium concepts, as well as with and without market access. The effect of market access is identified on the depletion or extinction of the commons. An another result is that, controlling the communal endowments per capita, the strategic equilibria dominate the competitive ones. This is because while the agents may disagree over how to divide the resource, they all would prefer it to be larger. The strategic concept allows the agents to anticipate the returns to their conservation and to take into account the effect of their extraction on the commons. As the number of agents becomes infinite, the strategic outcome converges to the competitive; as the number of agents falls to one, it converges to the planner's. An interesting set of results refers to the welfare effects associated with the market access, two opposing effects being described. Positively, the market access allows consumption and extraction smoothing while, negatively, the market access creates an outside option to the commons: under autarky, the commons is the only source of consumption utility, encouraging its depletion. A sufficient condition for autarky to dominate market access for some levels of communal endowment is that the world market discount factor exceeds the subjective discount factor. Conditions are derived under which equilibria with multiple extinction dates do coexist. The conditions for multiple equilibria are more restrictive under the strategic equilibrium concept. In both cases, the multiplicity depends on strategic complements: when other agents extract sufficiently quickly to extinguish the resource rapidly, the rapid extraction is a best response. When the agents extract slowly enough to ensure its presentation, slow extraction is a best response. Conditions for the unique extinction dates are also provided, upper bounds on the slopes of the best-response functions of agents being placed.
scientific article; zbMATH DE number 5135812