David R. Henderson

Think on the Margin

David R. Henderson*
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I start every course I teach with what I call The Ten Pillars of Economic Wisdom.1 The third pillar is "Economic thinking is thinking on the margin." I find that this is the toughest of the 10 pillars for my students to grasp. But once they get it, it changes how they think about many things in life.

Most issues in economics and in life are not all or nothing, but more or less. That's where thinking on the margin comes in. So, for example, I assert that if gasoline prices rise by 50 percent due to a reduction in supply, many people will drive less. When some people hear that statement, they react, thinking that they are disagreeing, with comments like "I would still drive to work." They probably would, but this reaction shows a failure to think on the margin. Notice that I did not assert that all people would stop driving to work. A few would, but most probably wouldn't. It's an issue of more or less, not all or nothing.

When you start thinking on the margin, you notice that, for many decisions, the margin is more important than the average. Consider two examples, one from the supermarket and one from the tax code.

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.

Consider the tax code in the United States, where, as in most other countries, the higher your income, the higher your tax bracket. Most middle-income people in the United States pay a fairly low percent of their income in federal income taxes, typically under 10 percent, along with a payroll tax for Medicare and Social Security of 7.65 percent. If they don't understand the system, they are often surprised when they work a lot of overtime or get a big raise or bonus. They expect to keep over 80 percent of their overtime pay, bonus, or raise. Instead, they keep less than 70 percent. Why? Because many of them are in a 25-percent tax bracket. Although their average income tax rate is relatively low, at 10 percent or less, their marginal income tax rate, 25 percent, is hefty. That, along with the 7.65 percent payroll tax, leaves them with less than 70 percent of their pay increase.

 

For more information, see Marginal Tax Rates, by Alan Reynolds, Concise Encyclopedia of Economics.

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.

Thinking on the margin also helps us understand one pitfall of means testing for government benefits. Imagine that the government announces that, say, starting in 2020, recipients of Social Security benefits will lose $1 of benefit for every $3 they get in other income over $50,000 a year. The goal of such a policy, of course, would be to focus the benefits on those most in need while saving substantially on Social Security expenditures. Such a policy would probably achieve its goal. It would also impose large marginal tax rates on the middle-income elderly.

Why? Because for every dollar of income over $50,000, the Social Security recipient will lose 33.3 cents, implying a marginal tax rate from that one provision alone of 33.3%. Add that to the 15% marginal tax rate the person is already paying and, say, a 6% marginal tax rate at the state level, and he is paying a marginal tax rate of 54.3%. If the additional income that he receives is self-employment income, there's an additional 15.3% tax, and he now pays a whopping marginal tax rate of 69.6%!3

I first "got" the power of thinking on the margin—although I can't say that I fully integrated it into my thinking—when I was 9 years old and saw the movie A Hole in the Head. The character played by Frank Sinatra wants to keep his son but needs a certain amount of financial stability to do so. He tends to think all or nothing, needing "the big win" that will help him keep the hotel he owns. But along the way, he fritters away bits of wealth. When he has a good day, he buys a somewhat nicer car; when he has a bad day, he trades down. And each time, he loses a little wealth because of the illiquidity of cars. Add up all those bits of wealth he loses on each transaction and the total might have been enough for him to save his hotel. Obviously, I didn't use the term "marginalism" when I watched the movie, but I knew enough from the adults around me to know that constantly trading cars up or down destroys a lot of wealth. Sinatra's character never learns to think on the margin.

Interestingly, the theme song of the movie, "High Hopes," which is one of my favorite inspirational songs, has a "thinking on the margin" part to it. It's about a ram trying to butt a hole in a dam. It sounds impossible, but the idea is that each head butt does a little damage to the dam and the damage is cumulative. So with enough butts, the dam goes down.

Thinking on the margin is also key to deciding the optimal amount of something to buy or the optimal amount of an activity to engage in. Take crime. Assume that we all agree (I realize that we don't) about which activities should be criminalized and which should not. Would it make sense to eliminate all crime? Thinking on the margin leads to the conclusion that it does not. If we allocate resources efficiently, we will go after the crimes that are most beneficial to prevent and least costly to go after. But some crimes would not be very beneficial to prevent and would be costly to prevent. Imagine, for example, trying to prevent all petty shoplifting. The marginal cost of preventing such crimes would exceed the marginal benefit. So the optimal amount of crime is greater than zero.

 

For more on Nobel Laureate see James M. Buchanan, see his biography in the Concise Encyclopedia of Economics.

Thinking on the margin sheds light on that old maxim that many of us heard from a parent or an elementary school teacher: "Anything worth doing is worth doing well." Steven Rhoads writes:

Nobel laureate James Buchanan suggested that an economist can be distinguished from a noneconomist by his reaction to that statement. Another economist actually polled a group of his fellows to judge their agreement or disagreement with this and four other maxims. "Anything worth doing..." was by far the least popular, with 74 percent of respondents disagreeing. 4

Thinking on the margin can also help you when you face a monumental task. The key is to divide the task up into smaller steps. Lao Tze, a pre-classical Chinese scholar, suggested, "A journey of a thousand miles begins with one step." The way to get something done is to start. It's like the old joke: "How do you eat an elephant? One bite at a time."

To take another example of thinking on the margin, bicyclists and backpackers often lighten their load to make traveling easier by following the maxim: "Take care of the ounces; the pounds will take care of themselves."

 
"The idea of thinking on the margin can even be, dare I say, inspirational."

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.5

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.

 

For more ideas and information about thinking on the margin, see "De Minimis", by Allen Sanderson, Library of Economics and Liberty, September 3, 2007.

Thinking on the margin can even help you build your wealth and becoming rich slowly. But that's another story.

Whether the issue is working harder to earn more or allocating your time, thinking on the margin is a powerful tool for thinking clearly and making good, and sometimes great, decisions.


Footnotes
1.

For a complete statement of the ten pillars, see David Henderson, "The Ten Pillars of Economic Wisdom," EconLog, April 12, 2012.

2.

If you itemize your federal taxes, you can deduct the state income taxes you pay from your income and so your effective marginal state income tax rate is actually slightly lower than it appears. With a 6% state income tax rate and a 25% federal income tax rate, for instance, someone who itemizes pays an effective marginal state income tax of 4.5% (= 6%×(1 − 0.25)). For ease of exposition, I assume that the taxpayer does not itemize.

3.

Actually, the rate is slightly lower. Even if person does not itemize, he gets to deduct half of the self-employment tax from his adjusted gross income. Therefore a couple in the 15% bracket would pay, not 15.3% but, rather 15.3% minus 0.15×7.65%, which nets to about 14.1%. So the combined marginal tax is "only" 68.4%.

4.

Steven E. Rhoads, "Marginalism," in David R. Henderson, ed., The Concise Encyclopedia of Economics, Indianapolis: Liberty Fund, 2008.

5.

I recount this conversation with my therapist in David R. Henderson and Charles L. Hooper, Making Great Decisions in Business and Life, Chicago Park, California: Chicago Park Press, 2006.


*David R. Henderson is a research fellow with Stanford University's Hoover Institution and a professor of economics at the Graduate School of Business and Public Policy at the Naval Postgraduate School in Monterey, California. He blogs at EconLog.

For more articles by David R. Henderson, see the Archive.

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