&NA; 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.

中文翻译：

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不确定性和空间存量外部性下的最优地下水提取

&NA; 我们引入了一个模型，该模型包含两个重要因素来估计地下水管理的福利收益：随机性和空间存量外部性。我们估计了在不确定性下的最优管理以及导致大型含水层缓慢枯竭动态的逐渐存量外部性所产生的福利收益。该地下水模型强加了可耗竭自然资源的一个重要方面，而没有传统的地下水提取单单元（浴缸）模型所必需的完全耗尽的极端假设。使用动态规划，我们结合并比较了独立同分布的随机性以及年降雨量的马尔可夫链过程。我们发现，对于堪萨斯州 Ogallala 含水层部分的参数化，含水层的空间枯竭对福利增益具有重要意义，范围从 2.9% 到 3.01%，这比之前在该地区发现的要大。令人惊讶的是，在降雨中加入随机性只会略微增加福利收益。