The geometry of life annuities

Straightforward geometry can be used to explain the role for life annuities in smoothing individual consumption during retirement. In the aggregate, there is a surprising analogy with a standard diagram from trade theory. That diagram takes careful account of the government revenues forgone when there is a move from tariffs to free trade. Here we find a similar geometric interpretation of the proceeds from deceased estates which need to be accounted for when comparing a noannuities economy with its annuitized counterpart. By the same token, there are considerable gains from opening up a market for life annuities, even after deceased estates are taken into account.