The main purpose of this paper is to analyze problems of financing an old-age insurance when birth rates are low and population declines or fertility fluctuates with time. A government then searches for optimal policies to cope with such problems. A first criterion could be seen in the Pareto principle. But we all know that there is no way out of PAYG unless at least one generation has to pay for the transition. Therefore an optimal policy is concerned with intergenerational redistribution and optimal growth.
In the absence of public pensions the economy will in the long run converge to a steady state which is not optimal in the sense of a golden rule. This dynamic “in”-efficiency results from the decentralized decision making by the consumers and the firms. If the PAYG system influences the savings ratio of the economy, public pensions can be seen as an instrument to implement a modified golden rule.