Spatially and Intertemporally Efficient Management of Waterlogging

Agricultural production is as a major contributor to numerous environmental problems. Most of these problems have a dynamic aspect and, moreover, the magnitude of these environmental problems depends on the distribution of the characteristics of the land. Therefore, policies designed to establish the social outcome need to be simultaneously targeted site specifically and time specifically. This paper integrates both aspects and presents a theoretical model that allows us to determine the socially optimal outcome over time and space. Moreover, the applicability of our approach, defined as optimal control in two stages, is demonstrated by reformulating the mathematical model such that it can be solved with standard mathematical software. For this purpose, we present an empirical study based on the cotton produced in the San Joaquin Valley in California and determine the socially optimal water price in the presence of waterlogging.