The tragedy of annuitization

We construct a tractable discrete-time overlapping generations model of a closed economy and use it to study government redistribution of accidental bequests and private annuities in general equilibrium. Individuals face longevity risk as there is a positive probability of passing away before the retirement period. We find non-pathological cases where it is better for long-run welfare to waste accidental bequests than to give them to the elderly. Next we study the introduction of a perfectly competitive life insurance market offering actuarially fair annuities. There exists a tragedy of annuitization: although full annuitization of assets is privately optimal it is not socially beneficial due to adverse general equilibrium repercussions.