Can population ageing imply a smaller welfare state?

Razin et al. [Razin, A., Sadka, E., Swagel, P., 2002. The ageing population and the size of the welfare state. Journal of Political Economy 110, 900-918] find a paradox in a two-generation OLG model that the higher the dependency ratio, the smaller is the welfare state. I generalize their model by replacing (i) the identity of the benefits of the old and young by proportionality, (ii) the absence of correlation between current contribution and future old-age benefit by a (weak or strong) correlation and (iii) the independence of the interest rate of the dependency ratio by a decreasing function. This generalization radically narrows down the domain of RSS's paradox in the enlarged parameter space.