This note offers a proof of the necessary conditions for optimal control problems that involve a finite number of discrete switches in the objective functional over the planning horizon.

Common wisdom suggests that a fully-funded actuarially fair social security system must increase welfare when households face longevity risk and annuity markets are missing. This wisdom is based on the observation that social security pays benefits as life annuities and therefore appears to...

We study the optimal provision of social security in a dynamically efficient economy using a continuous-time overlapping-generations model in which consumers have short planning horizons. The short-horizon mechanism leads to dynamic optimization that is time-inconsistent over the life cycle. Our...

We revisit the role of social security in countering inadequate saving for retirement. We compute the optimal social security tax rate for households who lack the computational ability to solve dynamic optimization problems. Instead, they follow the simple rule of thumb of consuming and saving a...