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Costs and Benefits
An economist friend of mine once confessed ‘you know, some days I’m not sure I have any other way of making decisions than by cost-benefit analysis’.
You might think he was getting a little carried away. But then again, I’ll bet that you use cost-benefit analysis more than you think. When considering whether to buy apples or bananas at the supermarket, you weigh up the prices with your enjoyment of each fruit. When storms in Queensland caused the prices of bananas to spike a few years ago, fewer consumers bought them.
Cost-benefit analysis doesn’t just apply to market decisions. Economists studying crime have found that measures which raise the ‘cost’ of offending – such as more police on the streets – tend to lower the amount of crime. Some crimes are irrational, but it’s a mistake to assume that criminals aren’t savvy enough to weigh up costs and benefits too.
When it comes to financial decisions, one of the challenges of applying cost-benefit analysis is uncertainty. How do you treat something that’s a 50 percent chance of happening? How can put something on the cost-benefit scale when it’s there half the time, and gone the other half?
It turns out economics has a fairly well established answer to this problem, which is something known as ‘expected value’. In short, if something has a 50 percent chance of happening, you should divide it by two.
One easy way to see this is to suppose that I offered you the following deal based on a coin toss. Heads, you get $1. Tails, you get nothing. How much should you be willing to pay for the coin toss?
As long as we’re dealing with small amounts of money, the answer simply comes from dividing the value of the payoff from the chances of it happening. So a 50 percent chance of winning $1 has a value of 50 cents. Put another way, if you have the opportunity to enter a coin toss competition of this kind, you should do so only if the entry fee is 50 cents or less.
Expected values are particularly useful when deciding whether to buy insurance. Suppose you are wondering whether to pay $50 to insure your $500 smartphone. The answer is that you should buy the policy if you think that the odds of losing your phone are more than 10 percent, which is $50 divided by $500.
In practice, people often buy insurance in this kind when they would be better to skip the policy. Unless you’re particularly clumsy, small product insurance is often a bad deal – particularly given the speed with which a new phone drops in value after you walk out of the store.
One of the simplest examples of where you can apply cost-benefit analysis is in considering whether to pay more money to reduce the excess on a rental car. I remember once being asked whether I wanted to pay $20 to reduce the excess by $1000. My response was that if I thought the odds of crashing were as high as 2 percent, I wouldn’t be renting the car at all!
By contrast, I’m happy to pay an insurance premium equal to around 0.1 percent of my home value, since I figure that the odds of my house burning down this year might well be as high as 1 in 1000.
Using expected values also helps when considering how to invest. If you’re putting half your money into government bonds yielding 5 percent, and the other half into shares yielding 15 percent, then you can expect an average return of 10 percent.
The insight in expected value isn’t the maths, but the way in which it uses probabilities to put a bit of certainty on things that are inherently uncertain. When we were planning the guest list for our wedding, my wife and I had to consider who we could invite, given a limited number of places. Because we were getting married in the United States, but many guests lived in Europe or Australia, we figured that some guests were a much lower chance than others of attending than others.
The solution we hit upon was to put a probability on each person we were inviting. That meant we could keep a reasonable track of the likely number of people who would attend. If we guessed someone was a 20 percent chance, we put them down as a 0.2. If they were an 80 percent chance, we put them down as a 0.8. We then sent out invitations so that the sum of the probabilities added to the number of guests we could invite. In the end, we managed to do a reasonable job of guessing the probabilities, and didn’t break the wedding budget.
Life is full of tough decisions – many of them involving things that aren’t quite certain. Using cost-benefit analysis helps make a complex world a little more manageable. I can’t promise you that thinking like an economist will always get you the perfect answer, but it will help on average. Or put another way, the expected value of your happiness will be higher if you use expected values.