Economic and Political Equilibrium for a Renewable Natural Resource with International Trade

International natural resources are typically subject to intense conflict, something likely to increase with population and economic growth. International cooperation over natural resources and the environment is the subject of a substantial literature (Kolstad), and is normally formulated as a game with given payoff functions for the individual countries. Within the literature on international rivers (the motivation here), Ambec and Sprumont (2002) assume a strictly increasing and strictly concave water benefit function, while Ambec and Ehlers (2007) assume that the benefit function exhibits satiation. Both of the papers are cooperative games. Ansink (2009) analyzes self-enforcing agreements on water allocation in a bargaining game. Fundamentally, the resource conflict might stem from the self-perception that an individual country will gain with additional resource allocation. This is reflected in the associated economic literature which is typically sector-level models with monotonic welfare functions. The overall objective of this work is to consider a broader setting such that cooperation over the natural resource might be joint self-interest for the political entities. The analytical framework is economic and political equilibrium when countries with joint resource access also trade produced goods/services. General equilibrium prices are functions of the water allocation, and these in turn identify country welfare as affected by water allocation. Political equilibrium is formulated as a game-theoretic problem. Here the welfare functions from the economic model are the payoff functions for individual countries, and standard solution concepts identify negotiated water allocations. A complete analytical solution is derived with this setup. Autarchic country welfare is increasing in water allocation as expected. However, with free trade the welfare functions can be non-monotone in some instances: starting from some initial allocation, it can be self-interest for one country to give up water to another country. Furthermore, there can be instances in which the highest level of welfare for one country is achieved with joint use of the resource as opposed to having a full allocation of the resource. At a minimum, where productivity coefficients imply a comparative advantage such that trade occurs, then the level of conflict as measured by the gains from an additional allocation of the resource will be reduced.