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# Thinking on the Margin

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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.

LD Bottorff writes:

I'm glad you covered "Anything worth doing is worth doing well." That has always bothered me, and now I understand why.

Dan writes:

I think economists pay too much attention to marginal effects of taxes on work. For most people it's the the average tax rate not the marginal that drives work decisions.

ZC writes:

@ Dan, "For most people it's the the average tax rate not the marginal that drives work decisions."

It's not economists fault that most people are stupid. There job is to educate people about such things, and that's exactly what this post does.

Rich Berger writes:

Dan-

Got anything to back your assertion up? I certainly think on the margin - but then I studied economics.

Dave writes:

Except, marginal is pretty much irrelevant if you work on salary.

Bob writes:

My example of marginal analysis.
I stopped studying for my PHD prelim about a week before the exam. I reasoned at that point the chances of my missing something that would be on the exam and the chances that it would make the difference between passing and failing were negligibly small.

Rich Berger writes:

Even if you work on salary, the evaluation of another job brings marginal thinking into play - how are the taxes, how is the commute (compared to your current job).

David R. Henderson writes:

@Dave,
Except, marginal is pretty much irrelevant if you work on salary.
Not true, partly for the reason that Rich Berger says and partly for the reasons I mentioned in the paragraph I quoted: working harder on the job to earn a raise or a bonus.

Dan writes:

"Got anything to back your assertion up? I certainly think on the margin - but then I studied economics."

There are many instances in which the standard "I put in effort X and get a bonus of Y" just doesn't hold.

I remember Tyler Cowen had a nice post describing how avg rather than marginal tax rates are more relevant for economic decision making.

ZC writes:

@Dan

Alright, you seem to wish to persist on your point that, "most people it's the the average tax rate not the marginal that drives work decisions."

Sure, many people make all sorts of decisions utilizing incorrect, outright wrong, biased, or inaccurate information. People are terrible about making medical decisions (usually incomplete information and a poor understanding of the outcomes of the possible choices), who to form relationships with (1/2 of marriages end in divorce, ends up being a pretty costly wrong decision for many), many people pay brokers and money managers far too much to achieve results they could obtain themselves at far less expense (they underestimate the lifetime costs of AUM fees) etc.

Heck, the majority of North Koreans probably think Kim Jong whatever is a deity and they live in the greatest county in the world. Just because lots of people think about something the wrong way, doesn't justify the utility of thinking about something that way.

ThaomasH writes:

This is the kind of thinking we need to apply to marginal increases in the CO2 concentration of the atmosphere. Early on the negative external of burning fossil fuels was low or zero (or maybe negative). But today we need to consider the marginal costs.

TMC writes:

Dan is correct, the higher marginal rates will kick in for this paycheck, but will eventually be taxed at a lower rate in April. (I'm assuming the decision is to work OT during a given week, not all year).

ThomasH: Odd thing with CO2, the marginal damage diminishes. At 280 ppm it took an increase of 280 ppm to add 1.5*. Now at 400ppm, it will take an additional 400 ppm for the same 1.5* increase.

Jesse C writes:

I find people heavily compensated via discretionary bonus (like me) think VERY MUCH on the margin. When I learn my bonus next week, it will determine how much time I choose to take for vacation this year, as this will be my first non-guaranteed bonus from my current employer.

Also, if salaried folk don't think on the margin, why do they ever work long hours? Seems like the only decision factors are marginal, apart from fear of unemployment.

Tom West writes:

Also, if salaried folk don't think on the margin, why do they ever work long hours? Seems like the only decision factors are marginal, apart from fear of unemployment.

Speaking for myself, but assuming it's true for most, it's because I want to feel good about myself, and that depends on doing a good job.

If monetary compensation and fear of job loss was the only motivation, my father, a university professor, could probably have worked 1/3 the hours he did.

Money is important, but at least among those I end up dealing with, it's fairly low among motivation for spending the time to do a job right. I get lots of excellent service from people I'll never see again and for whom I have no real ability to offer feedback.

I'm pretty certain my experience is fairly universal. If it wasn't, weak efforts wouldn't cause any outrage.

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