The two Feature Articles for January are out this week and the first one is by me. The title is “Think on the Margin.”

A few years ago, I went to the supermarket to buy my favorite beer, Heineken, for my birthday party. I faced a choice between two different sized cases of beer. The 18-bottle case sold for \$22 and the 24-bottle case sold for \$24. It just so happened that the Heineken man was standing beside me. He saw me studying the situation and said, “Yeah, the average cost per bottle for the 24-bottle case is less than for the 18-bottle case.”

“True,” I said, “but that’s not what I’m figuring. I’m seeing that 6 more beers cost me only an extra \$2 and I’m trying to decide whether that’s worth it.” It was. I thought 18 were all I needed, but the marginal cost of 6 extra beers was low. The mistake of buying an additional 6 would be minimal.

On taxes:

One implication of the distinction between average and marginal tax rates, which follows directly from the above analysis, is that an important factor when deciding whether to work overtime or work harder for a raise or a bonus is the marginal income you get to keep. To calculate that, you multiply the sum of your marginal tax rates (federal income tax rate plus state income tax rate2 plus payroll tax rate) by the increased income to compute the taxes paid. Then you subtract those taxes to compute your net income. Imagine, for example, that you live in high-tax California and are, like many middle-income people, in a 6 percent state-income-tax bracket. Assume, also, that you are in a 25 percent federal bracket. Then, your combined marginal tax rate is 25% plus 6% plus 7.65%, or 38.65%. So that \$1,000 raise that you got? You pay \$386.50 in taxes on it and keep only \$613.50.

Finally, on how thinking on the margin helped me finish my dissertation:

The idea of thinking on the margin can even be, dare I say, inspirational. When I was a Ph.D. student at UCLA, trying to make progress on my dissertation before going to my first academic job at the University of Rochester, I found myself avoiding working on it. So desperate was I that I went to see a therapist named Roger Callahan. Roger got right to the point, asking me how long I wanted to work on my dissertation each day. Here is how the conversation went:

David: At least four hours and more like six.
Roger: How long are you working on it now on an average day?
David: On an average day, zero.
Roger: Then here’s what I want you to do starting tomorrow morning. Sit down and work on it for two hours.
David: Two hours? That’s no good. At that rate, I won’t be finished nearly in time.
Roger: But you’re asking how to get from here to there. Right now you’re not working on it at all. Two is greater than zero.

His method worked. Gradually, I raised my number of hours from two on a bad day to as many as ten on a good day. He helped me see the problem “on the margin.” Fifteen months later, I had my Ph.D.