Nash bargaining in a general equilibrium framework: The case of a shared surface water supply

We extend the axiomatic Nash bargaining approach to the context of interregional water sharing in order to assess the approach’s normative implications in a general equilibrium (GE) framework. The GE model is applied to a water development project proposed for the Wasatch Front and Cache Valley regions of Utah — the Bear River Development Project (BRDP). We demonstrate conceptually how an allocation rule and attendant net regional welfare measures are endogenously determined as equilibrium solutions to the bargaining problem. Numerical analysis, based upon a simulation model calibrated to current data, reveals that Nash bargaining is generally infeasible as a solution mechanism for sharing surplus water supplies generated through the implementation of the BRDP, with or without potential ex post side-payments made between Cache Valley and the Wasatch Front. Only in the special case of (1) larger future regional population sizes, (2) a hypothetical, joint per-capita cost-share arrangement where total project (i.e. fixed) costs are shared equally across the two regions, (3) hypothetically larger water augmentation rates, and (4) the ignoring of potential environmental costs, is the Nash bargaining solution viable. Otherwise, for all other scenarios where the analysis is based upon current or future population sizes, joint- or region-specific cost-share arrangements, lower or higher water augmentation rates, and internalized or externalized environmental costs, the Nash bargaining solution is found to be unattainable as a potential mechanism to share surplus water supplies produced by the BRDP.