This paper focuses on one possible explanation for the empirical evidence of (a) income convergence among the world's poorest countries and among its wealthiest countries, and (b) income divergence among most of the remaining countries.  The model incorporates the assumption of subsistence consumption into the neoclassical exogenous growth model yielding outcomes that are consistent with the convergence-divergence empirical evidence.  While subsistence consumption can lead to negative saving and disaccumulation of capital, it can also coincide with positive saving and accumulation of capital.  The model predicts that the poorer the country, the lower its saving rate, a result that also appears to be borne out by the evidence provided here.