Marginal Thinking

Howard Baetjer: This is the third lecture on basic concepts of economics and the main topics for this lecture are marginal, the meaning of marginal, thinking at the margin. We’re going to distinguish marginal from total and distinguish marginal from average. Then I’m going to briefly [00:00:30] tell you what a former colleague of mine at Towson calls the rule of rational life, which is a nice little way of thinking at the margin, a statement about how we should think at the margin. At the end of this I’m going to talk about some of the nuances of meaning of margin. There really are different meanings to it that are appropriate at different times and it’s worth putting those on the table. So that’s what we’re going to do now.

First of all, what do we mean by [00:01:00] the marginal and thinking at the margin? Has any of you ever been in a situation where you were deciding whether or not to have another piece of pie at a buffet? Have any of you ever been in a situation where you were trying to decide whether to hit that snooze button on the alarm and get a little bit more sleep before getting up? Any of you ever been in a situation where you’re working out your schedule at college and deciding whether to take another course or not? Should I take six courses this term or only five, or five [00:01:30] instead of four. Presumably you’ve all been in that situation. Yes? The additional piece of pie is the marginal piece of pie. The additional half hour is the marginal half an hour of sleep. The additional course that you’re considering taking is the marginal course. By marginal, we mean additional, or one more, or sometimes one less. It’s a matter of the increment, a little more or a little less, that’s what the margin [00:02:00] refers to.

Good economic thinking is almost always marginal thinking. Thinking in terms of a little bit more, or a little bit less. Thinking for example of the costs versus the benefits of a marginal piece of pie. What’s the benefit of one more piece of pie? It tastes good. What’s the cost of it? I’m already overweight, I should be trimming back on my calories. We think about [00:02:30] the costs and benefits of that marginal, the one more piece of pie, hour of sleep and so on. The term marginal is very important, has been particularly important in economics since the 1870s because in the 1870s there occurred what’s known as the marginal revolution. That was when value theory made the transition from the labor theory of value, which is as we said [00:03:00] is wrong and misleading, to the subjective theory of value, which is also sometimes known as the marginal theory of value. It puts the focus not on the totality of something but on the value of a little bit more or a little less, or the cost of a little bit more or a little less.

Famous in this respect is the Water-​Diamond paradox, which was the question that bedeviled [00:03:30] people until the 1870s when it was sorted out as to why water, which is essential for life costs so little … I should say it has such a low price, whereas diamonds, which are used primarily for decoration and ornamentation are so expensive. Why isn’t water, which is necessary for life more valuable than diamonds, which we use as [00:04:00] bobbles and decoration? The key is to think at the margin of a little bit more water or a little bit less water, or a few more diamonds, another diamond or one fewer diamond. The theorists who worked this out pointed out that we value things at the margin. When we think about the value of water we’re thinking about the value of another cup of water or another bottle, given that we already [00:04:30] have a fairly nice supply and because happily for us we’re well supplied with water, the value of one more glass is not very high.
On the other hand because diamonds are so rare and people like them because they’re so few the value of one more diamond is much greater because there are so few. Now if the world were as strewn with diamonds the way it’s strewn with [00:05:00] water … Suppose we had oceans of diamonds, that’s a good way to think about it, Atlantic Ocean, water, Pacific Ocean, diamonds. Which would be more valuable in that? Which would be more valuable at the margin? What would people value more, one more glass of water or one more diamond? Probably one more glass of water, wouldn’t you think because the water is necessary to life but if we’re already using diamonds to [00:05:30] pave our streets with, you know who the hell cares? So what makes that one more glass of water of lower value at the margin is that we already have so much. What makes the diamonds more valuable at the margin is that we have so few. So we do our thinking, our valuing at the margin.

You want to distinguish marginal costs and marginal value from total costs or total value and from average [00:06:00] costs or average value. I like to illustrate the distinction between marginal and total with a hypothetical. Let’s suppose that you’re a college student, it’s the end of a term and you have your economics exam the next day but you also have recently gotten into a delightful, romantic relationship and your boyfriend or girlfriend has finished his or her exams and says the night before your economics final, “Let’s go [00:06:30] out. The weather’s nice, we’ll go and we’ll walk and we’ll smooch and it’ll be great.” You think, well I need to study for economics and you say to your boyfriend, girlfriend, “I can’t I need to study for my economics final.”, and he or she says, “What’s more important, our relationship or economics?” What’s wrong with the question? What’s more important, [00:07:00] our relationship or economics?

Student: He or she compares the total value or average value by-

Howard Baetjer: Yes, the question implicitly contrasts the total value of the relationship with the total value of learning economics but that’s not what’s at stake tonight, right? What’s at stake the night before the exam?

Student: The different between a C or a B or an A.

Howard Baetjer: That could be the value of [00:07:30] the study. What’s at stake is marginal hours spent on economics versus marginal hours spent holding hands and walking around and spooning, right? That question, probably not intentionally, maybe sometimes intentionally wants to divert you from what’s really at stake, which is how are you going to spend those hours tonight to the totality of the relationship. Now if you’re in that situation I recommend that you say … If [00:08:00] you’re alert and you’re thinking as an economist and you can find a diplomatic way to do it, you would say, “My dear, if I had to choose between our relationship and passing economics, I would immediately choose our relationship and take an F in economics but at the margin one more night spent with economics is more valuable the night before the exam than one more night spent with you.” I don’t know how you say that diplomatically [00:08:30] but the issue there is that what’s at stake is a few more hours studying or a few more hours romancing.

So the decision needs to be made on that basis. What’s the value of going out with your boyfriend, girlfriend? It’s whatever it is. You contrast that to the value of instead, spending the time on economics and presumably you make the decision on to spend the hours wherever they’re more valuable [00:09:00] at the margin, okay? So there’s the distinction between marginal and total. Here’s another one, a thought experiment, the point of which is to distinguish marginal from average. The way I set this up intentionally tries to put you off saying things clearly so let’s see how you handle this. Let’s imagine that you are flying from [00:09:30] Baltimore to Providence, Rhode Island. It’s a trip I make once in a while on Southwest airlines. Let’s suppose that the total cost normally of a flight for Southwest airlines for flying an airplane from Baltimore to Providence is $5000 and let’s suppose, just to use round numbers, that the plane carries 100 passengers, okay? So, $5000 for the flight, 100 passengers normally, suppose you come in at the last [00:10:00] minute to the ticket stand and say, “Can you put me on a flight to Providence?”

Let’s suppose they have space on the airplane, so there’s some available seats. Basically $5000 to fly there, 100 seats, not all of them occupied. What price must Southwest charge you to come out ahead on the deal? How much must Southwest charge you to [00:10:30] come out ahead? One way to ask this is-

Student: A dollar!

Howard Baetjer: What will it cost Southwest airlines to fly you to Providence? Now while you’re thinking, the way I set this up is to say the erroneous thinking I want people to do so I can show them the distinction is think, well if it costs $5000 to fly up there and the plane takes 100 passengers, well that’s $50 per passenger [00:11:00] so they’ve got to charge at least $50 in order to cover the cost. If it’s fewer than 100 passengers on there, they might divide differently. To make it worthwhile to Southwest they’ve got to take your proportional share of that $5000, but that’s wrong. Thinking at the margin, what’s the lowest price Southwest should be willing [00:11:30] to charge you and still come out ahead?

Student: A penny!

Howard Baetjer: How do you come up with a penny?

Student: At zero, they would break even and the lowest cost, once you consider sunk cost, the fact that they’re already flying is a penny that they make a profit on.

Howard Baetjer: All right, that’s very good. I want you to think a little bit more precisely. If you get on that airplane what’s going to be different for-

Student: The weight.

Howard Baetjer: Weight.

Student: The extra carrying they would use to-

Howard Baetjer: The extra mass so there’s going to be additional fuel they’re going to pay for to accelerate your [00:12:00] mass up to Providence. What else? Have you ever been on Southwest? What do they give you during the trip?

Student: Drinks, I guess.

Howard Baetjer: They give you soda-

Student: Drinks or food.

Howard Baetjer: Peanuts, pretzels and so on. So the marginal cost to Southwest of flying one more passenger up there is the fuel they need to accelerate your mass, one bag of pretzels, one bag of peanuts and a half a can of soda. So I wouldn’t say a penny [00:12:30] but say $1, $2. It makes sense for them to let you on the airplane if you pay more in the price of your ticket than the cost to them of flying you up there. So they would come out ahead at say $3 or $4, whatever amount of money was necessary to cover the peanuts, pretzels, soda and the flight fuel. So when making these sorts of decisions, you want to think at the margin in [00:13:00] terms of the additional benefits and additional costs rather than the average benefits and average costs.

By the way, I’m told that many businesses miss this and they make mistakes in their pricing. They think, well we’ve got to cover our average costs but often it doesn’t make sense. They need to cover their average costs on the whole over time but on any particular time they just need to cover that marginal cost in order to come out ahead. [00:13:30] So make the distinction between marginal and average, make the distinction between marginal and total.

The rule of rational life is the next topic here and I’ve implied that. The rule of rational life is that, goes as follows. As long as the marginal benefit exceeds the marginal cost, do it. Take the example of studying for the exam when your girlfriend [00:14:00] or boyfriend wants you to spend time with him or her instead. As long as the benefit to you of additional study is greater than what you give up, the time spent on this attractive relationship, keep studying. After that point, then go do something else. Take the case of hitting the snooze button on your alarm clock in the morning. As long as the benefit of additional sleep is greater than [00:14:30] what you give up, the studying, making breakfast, getting to breakfast perhaps. As long as the benefit of the additional whatever is greater than the cost of the additional whatever, it makes sense to do it. That’s the rule of rational life. I think that originated with Professor Jerry German at Towson some years ago.

Next main topic, the nuances of this term marginal. Sometimes, as in the examples I’ve given you, [00:15:00] well no, even the examples I’ve given you this other can apply to. In textbook analysis marginal means additional with the implication that the additional hour, the additional good that you purchase is identical to the previous one. In supply and demand graphs we assume that all the units being bought or sold are identical but often it’s going to be useful [00:15:30] to think of marginal in a slightly different way. It’s not actually identical units because often when we talk about a marginal student or a marginal hour of sleep, we recognize that the next one we go to isn’t quite as valuable or important. Take the case of hitting the snooze button on your alarm, is that additional hour of sleep going to be … Or let’s say half an hour. Is the additional half an hour going to be as valuable as the previous half hour? Probably not [00:16:00] if … The first sleep you get is more important than the extra.

Is the additional piece of pie … It might be an identical … Well the pie would be identical. You get an identical piece of pie. It’s not as worth as much to you, one more is not worth as much but it’s identical, but that hour of sleep is not identical. Marginal also, an additional hour of studying. Is an additional hour of studying going to be as valuable [00:16:30] as the previous hour of studying?

Student: Not if you study intelligently.

Howard Baetjer: Usually not, not if you study intelligently because toward the end of your studying time it’s going to be more review rather than then really consolidating the ideas in the first place. How about when a farmer grows a marginal bushel of wheat? The bushel of wheat would be identical. Let’s assume the bushel of wheat is identical but is he going to grow that on an identical [00:17:00] piece of land? Probably not. In order to grow more wheat he’s got to bring marginal crop land into production. He’s going to use his best fields first, then if he’s going to produce more, then he’s got to use his not so good fields and irrigate them more, use more fertilizer perhaps on the additional fields. So marginal sometimes means additional and not quite as good.

[00:17:30] I think in this regard of the marginal students at Towson, I’ve got some really good students, the students who are first admitted. Those who are admitted later, they’re more shaky, they’re not quite as good students. Be aware of that distinction, sometimes marginal means one more identical unit, [00:18:00] sometimes it means you’re scraping the bottom of the barrel. All right, and finally I want you to consider the … We’ll go over an example that illustrates what we mean by marginal and the importance of thinking at the margin and incentives at the margin. For that I want to give you this table, which will show you what’s known as the low wage [00:18:30] trap. Let me explain what you’re looking at here. This comes from Edgar Browning’s book “Stealing From Each Other”, a wonderful book about welfare.

It looks at the way the numbers worked for a family of three, a single parent with two kids in Philadelphia in 1996. The reason he goes back that far is … First of all the book was published sometime ago but 1996 [00:19:00] was the last year in which these data were available. Let’s start it this way, look up here a second. Suppose I were to ask you this, would a person sensibly want to work for a pay of $30,000 if taxes took out of it $10,000 some so that [00:19:30] your take home pay out of that $30,000 you were paid after taxes was $19,837? Could we imagine people choosing to work for that if they’re taxed at that rate?

Student: Yeah.

Howard Baetjer: Sure, it’s about what kind of a rate, about how much?

Student: 30%

Howard Baetjer: About 30% or about a third, all right? That would be thinking on the whole, looking at the tax rate on the total income. [00:20:00] When we look at it that way, sure it makes sense for somebody to work if you’re being taxed a third, that’s okay. Often the kinds of decisions people make are at the margin where the margin is, should I work a little bit more? Should I earn a little bit more money? For people in the welfare system this is very much the case because they don’t have a job and they’re offered a chance to work part-​time, so that’ll be a little bit more income. If they do well, then they might be promoted or get some [00:20:30] more hours and work more. Look at the really tragic way the decisions at the margin play out for a single parent like this.

Suppose it’s you, if you have no earned income thanks to medicaid, food stamps, the housing subsidy, aid to family with dependent children and the name of that has been changed, it’s now temporary assistance for needy families or TANF. EIT is the earned income tax credit, taxes speak for themselves. [00:21:00] In 1996, a single parent of two in Philadelphia got government benefits worth $19,217. Now let’s suppose that’s you. You have to opportunity to work and earn $5000 worth of income. What approximately is the marginal tax rate on that income? That is, out of that $5000 about how much do you get to [00:21:30] add to your disposable income? It goes up by the difference between [$19,000 and $20,700 00:21:37] it’s about $1500, right? $1500 more disposable income.

Now we say that means you have a marginal tax rate or a tax rate on that additional, that new $5000 of income of how much? Out of that $5000 how much is taken away if you’ve got $1500 more disposable?

Student: Negative 15?

Howard Baetjer: Well [00:22:00] no, it’s 35 … Out of that $5000 about $3500 gets taken away, right? So your tax rate on that marginal income is more than half out of the $5000, $3500 is taken away. We can figure that out, make that calculation but it’s a 60, 70 some percent tax rate so to speak on that marginal income. You get that $5000, you [00:22:30] still get your medicaid but your food stamps are reduced, your housing subsidy is reduced, your welfare is reduced, you get an earned income tax credit, which increases your income and when all that is said and done, instead of $19,217 you now have $20,700 to pay. What do you think? Is the marginal benefit greater than the marginal cost for such a person in that situation? Depend on the person but that’s a high marginal tax rate, which [00:23:00] certainly reduces your incentive to work for that additional $5000, right?

Look at the next line, your boss says, “You’re doing great work, I’d like to double your hours. Take you from $5000 to $10,000.” How much of that gets taken away? How much of that additional $5000? We say what is the marginal tax rate on that marginal $5000? How much of it is taken away?

Student: $7500.

Howard Baetjer: More than $5000, [00:23:30] so this is what makes it a trap and a terrible policy problem for us to deal with because the food stamps go down further, the medicaid gets zeroed out, the housing subsidy goes down, their earned income tax credit increases but taxes are in there also and so you have less disposable income. So we’ll let the example go at that, the point here is that people make decisions at the margin using the rule of rational life. Is the benefit [00:24:00] of this additional $5000 pay greater than the cost? When people make decisions like that they look at the marginal effects and this is one reason why the welfare system is such a problem. It’s so difficult to get the incentives right.

All right, and with that let’s quickly review what we’ve talked about is, thinking at the margin. Marginal means additional, one more or one less. Distinguish marginal from total. [00:24:30] Distinguish marginal from average. The rule of rational life, as long as the benefits of a little more are greater than the costs of a little more, keep doing it. Remember marginal sometimes means identical additional units, sometimes it means not quite so good additional units. The welfare trap example speaks for itself.

There’s one more thing I want to say about this welfare trap example. When you look at these numbers, [00:25:00] when I look at these numbers it makes me feel very good about humanity because so many people despite this, despite the fact that their disposable income goes down and down and down until they get to earning $30,000 where it’s finally the take home pay is above what it was when they weren’t working at all, despite that so many people do get out of the poverty trap. People have enough [00:25:30] wisdom to see that if I don’t start to get out of this, I’ll never get out so I’ve got to take the loss to my disposable income, get a job and get out. Okay, questions on margin, the margin, marginal?

Student: How do your students who favor welfare programs react when they see those graphs?

Howard Baetjer: [00:26:00] All of my students react to this with horror and the more progressed minded, if they engage with me further on it, I point out to them that this is a really hard problem. It wasn’t until this summer that I saw that proposal from Anthony Davies that seems maybe to be a way to get around this. If you’re going to have things like medicaid and food stamps and so on, it [00:26:30] seems almost impossible to structure it in a way that isn’t going to have these horrible incentives in it. I’ll put it back to the progressively minded students, this is something that you need to address, if you’re going to favor government intervention, government welfare, you need to be sensitive to this problem. I don’t know how to do it, maybe you can figure it out. I often leave it at that so that [00:27:00] they … I hope they’ll go away more thoughtful and start to question their … Perhaps to little question the belief and extensive government welfare.

If time goes on further, I’ll talk about the fraternal associations that provided welfare services. There are things like insurance, there are things like charity, there are all sorts of civil society voluntarily contributed [00:27:30] to ways of taking care of the poor that I believe would work better. Depending on the time we have and the student’s interest I get into that more or less [00:28:00] deeply.