Demographic structure and overlapping generations: A simpler proof with more general conditions

d'Albis (2007) considers a continuous-time general equilibrium overlapping-generations model with age-specific mortality rates. His proof of the existence and uniqueness of the steady-state equilibrium, which can be extended to other overlapping-generations models, relies on the shape of a function that appears in the equation defining the equilibrium. By focusing on the mean age as a function of the stable population growth rate instead of the function used in d'Albis (2007), we provide a simpler proof with more general conditions. We also obtain useful properties about the first and second derivatives of the mean age function that can be applied in future work.