## Wednesday, November 28, 2007

### The Utility of Money

Some financial decisions, particularly about insurance, must take into account what is called the utility of money to get the right answer. Normally the concept of utility is explained in very mathematical terms, but it doesn’t have to be. Let’s take a fun example straight from a game show.

You’re standing beside Howie Mandel playing a super-sized version of Deal or No Deal. You’re down to just two amounts left, 1 cent and \$3,000,000! You get the following offer: take \$1,000,000 now, or take a 50/50 chance at the \$3,000,000. What should you do?

If you got to do this many times, then on average, taking the chance you would win half the time and get an average return of \$1,500,000. This is more than the million dollars you were offered, and so you should take the chance, right? Not so fast.

Most people would correctly figure out that they should just take the million dollars. The reason is that the first million would make a huge difference in their lives, and an additional two million doesn’t have the same impact. This is exactly what we mean by the utility of money: how useful the money is to you. The more you have, the less useful the next dollar is to you.

So, if you are already rich, the first million isn’t as big a deal, and you should probably take a chance on getting the full three million. But, if you aren’t rich, and that first million would completely change your life for the better, then you should just take the million that was offered.

One simple model for the utility of money is to view things in percentage terms. Suppose that everything you have in the world, including future earnings above the amount you need to live, adds up to \$250,000. Then a million dollars increases your net worth by 400% to \$1.25 million. Adding another two million dollars to this is a 160% increase, which is less than the first 400%. So, the extra benefit of taking a chance in the game isn’t worth the risk. For a rich person who starts with a net worth of \$4 million, the first million adds 25% to make \$5 million, and the next two million adds 40% more. For this person, the risk is worth it.

All this explains why a car insurance company with deep pockets is willing to take on risk, but individual drivers are better off paying a little extra to reduce risk. In the next post, I’ll show how the utility of money can be used to make decisions about other types of insurance.