## Thursday, April 30, 2009

### Eyeball Economics

Those of us who wear contact lenses always find ourselves doing a fun math problem that requires multiplying by two. For you who have perfect vision and you who choose spectacles, this is an exercise in commonplace approximation and ordinary economics. For my fellow contact wearers, consider this math problem to be our secret handshake!

Suppose you have two eyes and you need one contact in each eye to see properly. Contacts cost money -- \$25 per box. Contacts also wear out every couple of weeks (or in my case four months). There are six contacts in each box. With a different prescription in each eye, a person needs two boxes to function as a normal human being.

As with most semi-durable, somewhat costly goods, several questions come to mind:
1. How long does a box last?
2. How many boxes do I use in a year?
3. How much do contacts cost per year?
To figure this out, we can use some staightforward eyeball math. Each contact lasts two weeks. With a different prescription (and separate box) for each eye, each box lasts 12 weeks. That's 52/12 or 4.33 boxes per year... per eye.

Unfortunately, they don't sell boxes in 0.33 units. They're sold in whole numbers. To cover our yearly eye demands, we need five whole boxes. Per eye, that's \$125 annually. For both eyes, that's \$250 per year. Yowza! Wearing glasses looks really smart now.

But, that's the calculation if you change your contacts every two weeks. If you stretch the limits of your contact lenses as I do, you can get away with cheaper eyewear. For example, I only switch lenses every four months. Annually, that's three contacts per eye, six contacts per head, and I only have one head. Because I have the same prescription in each eye, I can get away with one box per year. So, my contacts cost \$25 per year. What a bargain!

I need to insert a disclaimer. Stretching the capabilities of my contact lenses is not following doctor's orders. I am no doctor of optometry, but I am still sure it is bad medical advice to tell people to wear their contacts longer than prescribed. Don't take the fact that this is a bargain as an endorsement of wholesale neglect of doctor's advice. They probably know what they are talking about, and I bet I have worse eyes for the strain. If I abuse my eyes too much, there is a chance that I will die blind.

That doesn't change the fact that rational people make the calculation to not follow doctor's orders. Given my own incentives, I suspect other contact-wearing individuals make the same calculation and a similar decision. This year alone, I saved \$225 over the alternative. That's no small potatoes. If I place a low likelihood on dying blind (or less severely, having eye problems when old), saving \$225 every year until I start having those problems may be the right calculation.

That's what our incentives tell us, but our incentives are not aligned with the doctor's advice. This leads me to have a couple of questions for the readers:
1. Given our incentive to not follow their advice, do you think eye doctors give stronger (or weaker) advice regarding the care of our eyes?
2. Aside from threatening blindness, can you think of any strategies eye doctors can use to make us account for the costs of not following their advice?
3. Vision insurance may make these costs a moot point for incentives, but only for a select group of people. How many people have vision insurance anyway? And, why might they sign up?

Eye doctors face a difficult problem in communicating the right information with the right incentives to ordinary people. I wonder if some other system would make everyone better off.