In this paper we show that, when elastic labor supply is considered via Cobb Douglas preferences, dynamic inefficiency of OLG economies, while being still a necessary condition, is no longer sufficient for an internal public debt increase to be welfare improving in the long run. This is due to the fact that the equilibrium interest rate can move in the ‘‘wrong’’ direction if individuals’ labor supply is sufficiently elastic. Consequently, raising the level of debt when the economy is experiencing dynamic inefficiency could even be welfare-worsening, in contrast with [Diamond, P., 1965. National debt in a neoclassical growth model. American Economic Review 41, 1126–1150].