Optimal pay-as-you-go social security when retirement is endogenous and labor productivity depreciates

This paper considers an overlapping-generations model with pay-as-you-go social security and retirement decision making by an old agent. In addition, the paper assumes that labor productivity depreciates. Under this setting, socially optimal allocations are examined. The first-best allocation is an allocation that maximizes welfare when a social planner distributes resources and forces an old agent to work and retire as she wants. The second-best allocation is an allocation that maximizes welfare when she can use only pay-as-you-go social security in a decentralized economy. The paper finds a range of an old agent's labor productivity such that the first-best allocation is achieved in the decentralized economy. This differs from the finding in Michel and Pestieau (2013) that the first-best allocation cannot be achieved in the decentralized economy.