Spatial externalities in aquifers with varying thickness: Theory and numerical results for the Ogallala aquifer
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This paper studies the divergence in the planning and equilibrium solutions for a multicell
aquifer with heterogeneity in cell depths. A spatial model is developed that explicitly accounts
for the lateral movement of water between cells. The optimal planning problem maximizes the
discounted stream of rents earned from irrigation over an infinite horizon. The optimal steady
state of this problem is derived and compared to the competitive equilibrium steady state, which
results from myopic rent maximization among users. Studying the steady-state conditions in the
two outcomes allows for the nature the spatial externalities to be characterized and reveals the
effects of varying cell depths. In a two-cell specification of the model, closed-form expressions
are derived for the difference in optimal steady state water table elevations between the two
cells. The gap in optimal heights is shown to depend on an interaction between the speed of
lateral flows in the aquifer, the asymmetry in cell depths, and the curvature properties of the
irrigation benefits function. The 2-cell model is then applied numerically to quantify the spatial
externalities and asymmetry effects in Sheridan County, Kansas, which overlies the Ogallala
aquifer. Simulated welfare losses in this model are relatively large and are sensitive to the
asymmetry in cell depths.