Spatial-dynamic seawater intrusion and pumping cost externalities in a confined aquifer

This paper analytically develops the economic theory of seawater intrusion in confined aquifers and, in the process, creates generally applicable solution methods for illuminating steady-state spatial externality relationships for other spatial-dynamic diffusion resource management issues. By linking a confined aquifer and its unconfined recharge region with a dynamic boundary condition neglected in the economics literature, we introduce the physical realities that generate spatial externalities in all renewable confined aquifers. We derive spatial-dynamic first-order conditions for optimal extraction and characterize the policy relevant spatial-dynamic pumping cost and seawater intrusion cost externalities with hydrological assumptions appropriate to the different dynamic timescales of system components and the focus on seawater intrusion. For confined aquifers, we prove the marginal seawater intrusion cost externality decreases linearly in distance from the coast. Moreover, we demonstrate that the marginal seawater intrusion cost externality generally exceeds marginal pumping costs near the coast, implying substantial divergence between optimal and common property extraction near the coast, and significant divergence may extend to the inland aquifer boundary depending on both the magnitude and shape of the revenue function relative to extraction costs and aquifer parameters.