Aging, Retirement and Social Security in an Interest Groups Model

What is the influence of aging on the duration of retirement and on social security transfers? A model of political economy permits to investigate the duration of retirement and the social security transfer at equilibrium with the total number of elderly. In an overlapping generation model with interest groups, an increase in the proportion of elderly tends to increase the total social security transfers. However, if the pressure exerted by a group is described by a function with decreasing marginal returns to size, an increase in the number of elderly decreases the duration of retirement and may decrease the per head social security transfer