Agriculture is one of the main causes of biodiversity loss. In this work we model the interdependent relationship between biodiversity and agriculture on a farmed land, supposing that, while agriculture has a negative impact on biodiversity, the latter can increase agricultural production. Farmers act as myopic agents, who maximize their instantaneous profit without considering the negative effects of their practice on the evolution of biodiversity. We find that a tax on inputs can have a positive effect on yield since it can be considered as a social signal helping farmers to avoid myopic behavior in regards to the positive effect of biodiversity on yield. We also prove that, by increasing biodiversity productivity the level of biodiversity at equilibrium decreases, since when biodiversity is more productive farmers can maintain lower biodiversity to get the same yield