How sustainable are old-age pensions in a shrinking population with endogenous labour supply

In this paper we model an OLG-economy where labour supply is endogenously determined and where we assume that there are two pension systems, namely, a pay-as-you-go system and a funded system. The main question is whether there is an equilibrium involving an old-age pensions system, partly financed by PAYG and partly by a capital reserve system, and what will be the size and the composition of the pension income. We also look at the consequences of increasing preference for leisure on the design of the pension system. We assume the population growth rate and the technological growth rate to be endogenous; they are assumed to be correlated with the labour supply. Negative population growth is admitted for by the model. The main conclusion is that there is in any economy an equilibrium, but that the numerical outcomes heavily depend on the attitude towards leisure and the capital production elasticity.