Agricultural households use assets not only for production as a source of income generation but also for protecting consumption from negative economic shocks. We show a model of household dynamic decisions on investment in agricultural productive assets under credit constraints and non-convex production technology. We test and estimate the model with data from Kagera, Tanzania in order to show its usefulness for quantifying the relative magnitude of potential determinants of poverty dynamics and effectiveness of counter-factual policies for poverty alleviation. We ask whether there is a poverty trap and a threshold in dimension of assets and productivity which determines household’s forward-looking behavior and welfare status in the future.