Model

The household’s utility function sees a change in its weights after a certain period of time, owing to changes in the ages (and hence leadership roles) of household members. For instance, the oldest generation’s preferences may carry a bigger weight in the beginning (e.g., the first 10 to 20 years), after which time the middle generation’s preferences become dominant for another 10 to 20 years, until the newest generation’s preferences take over. I assume here that the oldest generation places a relatively higher weight on natural capital (groundwater) in the household’s utility function, because it ensures a prolonged agricultural lifestyle. The middle generation may be forced to alter this weighting by placing higher weights on the human capital of the youngest generation, which comes at the cost of lower weights on natural capital. The youngest generation eventually alters these weights in favor of human capital. It is important to emphasize here that the decision making body comprises all three generations of the household, who maximize overall utility across time. The assumption that weights on the arguments in the utility function are dynamic reflects the fact that, as time passes, household preferences shift away from natural capital and towards human capital. This assumption also draws support from collective household models used in the microeconomics literature, wherein several decision makers within a household, who vary in their preferences, cooperatively interact to optimize their household utility function (e.g., Vermeulen, 2002).