Should old women pay for the health of old men?

Several years ago, Richard Posner conjectured that old women should pay for the health care of old men. The reason is that old women tend to live longer and appreciate the company of men, thus they would be happier if they lived longer. This is a purely theoretical argument as in all industrialized economies health care is state provided, at least in retirement. But note it leans on one important assumption: old women are happier if married.

Christoph Wunder and Johannes Schwarze test this using the German Socio-Economic Panel, an endless source of insights. And they find that widows are just as happy as married women quite rapidly after the loss of their husbands. I would conjecture that retirees are quite prepared for such eventualities, and the loss of a partner affects them less than earlier in life.

However: what about the men? Would they like to live longer? Is the marginal utility of an additional year of life at age x higher for a man than for a woman? This will never be measurable, but this should be the real question to ask.