The expected monetary value of insurance is negative (or rather, negative in real dollars. It can be positive in nominal dollars but underperform inflation.)
But the utility is not linear in money. Losing e.g. $10,000 might be 20 times as bad as losing $1,000. If so, you should pay $1,000 100% of the time to avoid paying $10,000 8% of the time.
The insurance company averages out over many buyers, so their utility is roughly linear.
Insurance is just trading against different utility scales.
Yep. Also note that if you had $1M in the bank, you would then not prefer to buy insurance for something on the order of $10k.
Hey, everyone! So I've been reading an article about the expected utility, apparently to figure out whether the risk is worth taking you multiply expected value of the outcome by it's probability.
And apparently insurance companies can make money because the expected utility of buying insurance is lower than it's price.
So why would buying insurance be the rational action? I mean intuitively it makes sense(you want to avoid the risk), but it doesn't seem to fit well with this idea. If insurance is almost by definition is worth slightly less than it's price, how is it worth buying?
(sorry if it's a dumb question)