Optimal Groundwater Extraction under Uncertainty and a Spatial Stock Externality

Abstract

We introduce a model that incorporates two important elements to estimating welfare gains from groundwater management: stochasticity and a spatial stock externality. We estimate welfare gains resulting from optimal management under uncertainty as well as a gradual stock externality that produces the dynamics of a large aquifer being slowly exhausted. This groundwater model imposes an important aspect of a depletable natural resource without the extreme assumption of complete exhaustion that is necessary in a traditional single cell (bathtub) model of groundwater extraction. Using dynamic programming, we incorporate and compare stochasticity for both an independent and identically distributed as well as a Markov chain process for annual rainfall. We find that the spatial depletion of the aquifer is significant to welfare gains for a parameterization of a section of the Ogallala Aquifer in Kansas, ranging from 2.9% to 3.01%, which is larger than those found previously over the region. Surprisingly, the inclusion of stochasticity in rainfall increases welfare gains only slightly.