Extraction cost: before or after harvesting? Economic and environmental consequences

We consider a discrete time, infinite horizon dynamic game of groundwater extraction. As usual in this kind of models, the marginal extraction cost depends on the level of the groundwater. The goal of this paper is to point out the importance of the moment where this cost is announced to the players. We consider the case where the cost is announced before the extraction is made and the case where is announced after extractions. For both cases, we also analyse the possibility of taking into account the rainfall or not. The current literature considers only the case where the cost is announced before rain and harvesting.We characterise the equilibrium in the linear-quadratic case. We compare solutions as functions of the discount factor, with the particular cases of zero discount (static model) and no discount (maximisation of the steady state) from the economic and the environmentalpoints of view. We show that when the level of the groundwater is small, announcing costs after harvesting and rainfall is better from the economic and environmental point of view than the case of announcing it before harvesting and rainfall.