## HCOL 196, March 14, 2011

I showed several of the things that I got as a result of my work on the Hubble Telescope.

I then asked how it is that people are willing to buy insurance, even though it is priced high enough that the insurance company is virtually certain to collect more in premiums than they pay out in benefits. First we reminded ourselves of what the “utility” curve looks like for a typical risk-averse person. In particular, we found (for one of the students) that \$25,000 loss for sure is equivalent to a \$100,000 loss in terms of the person’s risk profile.

This led us to draw a decision tree for a 1% chance of loss of \$25,000 (say totalling a car). Replacing the actual monetary amounts by their utility (or loss in this case) of \$100,000 gives us a tree that says that this student would be willing to pay up to \$1,000 in premiums to avoid losing the \$25,000. The problem is resolved by this method. For, if we only put \$25,000 as the loss, then the most the student would be willing to pay in premiums is \$250, which is less than the insurance company is going to offer the insurance for (since their expected loss would be \$250, and they want to make a profit, pay shareholders, pay salary, pay for their buildings, etc.) Insurance would not work in that case.

But from the insurer’s point of view we have another diagram. Because the insurance company has so much money, there isn’t a significant curvature of its utility function, so the loss of \$25,000 if there is an accident is just \$25,000 in utility. That means that if the premium is between \$250 and \$1000, the customer will be willing to buy. So the insurance company can add a profit and salaries and stuff to the premium, maybe having a premium of \$400 for example, and still make money since the customer will be willing to buy the insurance. A deal can be made.

I asked why the insurance company doesn’t just price it at \$1,000 and make more money. The real reason is that it is not a monopoly. There are other insurance companies around, and if one company prices at \$1,ooo another one can price it at \$500 and steal all the customers from the first company.

I asked how it is that you are willing to buy anything at a price higher than the store cost is, for example, a gallon of milk. One student noted that it’s the same thing at work. You want the milk more than you want the money, and the store wants the money more than it does the milk, so everyone is better off (from their point of view) if the customer buys the milk.

Finally, I pointed to the last question on the problem set due on March 23, noting that to answer it you are going to have to put a dollar value on human lives. We discussed this briefly and will continue the discussion on Wednesday. I asked you to think about it in the meantime.