According to several studies, agricultural carbon sequestration could be a relatively low cost opportunity to mitigate greenhouse gas (GHG) concentration and a promis-ing means that could be institutionalised. However the potential for additional carbon quantities in agricultural soils is critical and comes from the agricultural .rms behaviour with regards to land heterogeneity. In this paper, our aim is to set incentive mechanisms to enhance carbon sequestration by agricultural .rms. A policymaker has to arrange incentives as agricultural .rms have private information and do not spontaneously switch to the required practices. Moreover, a novelty in our paper is to show that the potential for additional carbon sequestration is similar to an exhaustible resource. As a result, we construct an intertemporal principal-agent model with adverse selection. Our contribution is to specify contracts in order to induce truthful revelation by the .rms regarding their intrinsic characteristics towards carbon sequestration, while analytically characterizing the optimal path to sequester carbon as an exhaustible resource.