A theoretical model of aquifer exploitation, where groundwater is devoted to agricultural production, is presented here. As new aspects with regard to other models found in literature, the model has explicit formulations for the number of production units and the natural discharge of the aquifer. It is specialized to competitive and optimal control strategies, and a comparison between steady states and trajectories under both strategies is made for ideal aquifers of very different dimensions. The commonly accepted conclusion of little differences between control and no control results to be expected in aquifers of a high storage capacity is confirmed for the area-times-storativity dimension but not for the vertical dimension of the aquifer, for which the conclusion could be quite the opposite. Sensitivity analyses are also carried out on both versions of the model where it is shown that a limitation to the entry of production units is the best instrument to improve important features regarding the competitive steady states and also to bring closer control and no control strategies.