We adopt an imagined exchequer, the functionary responsible in an early polity for securing resources from its agrarian subjects, and we develop a feature-rich demographic and environmental model to explore the population ecology of agricultural production in the context of population growth, Malthusian constraints and economic exploitation.  The model system allows us to (i) identify and characterize a peak of surplus production early in population growth, prior to density-dependent constraints and (ii) characterize the taxation potential of a population at its Malthusian equilibrium.  For a fixed total level of taxation the exchequer has two options: a small population taxed at a high rate, unstable to small perturbations, or a larger population taxed at a lower rate, which is stable.  In a small and growing population it is more effective to tax goods; as the population approaches its density-dependent equilibrium it becomes more effective to tax labor.  We likewise show that early agrarian states afflicted by stochastic variation in agronomic output face an extinction risk dependent on the level of taxation and magnitude of yield variation.  Successful agrarian states balanced resource exploitation against dynamic population ecology constraints; we propose that fiscal mismanagement should be among the hypotheses for polity failure.