Why do we invest in useless health care?

Robin stumped us with this in health econ class. Here's a first cut:

Investing in health care is inefficient ex post, but ex ante the uncertainty is so great that trading $ for health care makes sense. The uncertainty arises from the mystery of the human body, and from rapid, and eratic medical innovation. Thus, there is some chance, however slim, that the average benefit will increase in the future. If someone values 1 year of additional life at $100M, and the average benefit of $1M of health care is zero, but there is a 1% chance that the average benefit will become 1 year of additional life, then the costs are $1M and the benefits are 0.01*1 year=0.01 year=3.65 days=$1M. Thus, assuming risk neutrality, it makes sense to invest because this someone is betting on innovation. Further, it makes sense to spend more money as time goes on, since medical technology is always improving. And this is what we see, that the bulk of health care $ are spent in the last 6 months of life. Also, there's little incentive to save up for the future at that point.

These are small numbers, and if they're realistic, that may partly explain why the RAND Study showed zero marginal benefit of health care. But even if there truly was zero marginal benefit over this period of time (seven years, 1975-1882), I think it was not irrational to expect innovation. Using the numbers above, that would mean an innovation occurs only once every 100 years, and so maybe no significant innovations were picked up during the RAND Study.

Correction: Here is the other first cut.