Russ Roberts

Willingham on Education, School, and Neuroscience

EconTalk Episode with Daniel Willingham
Hosted by Russ Roberts
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Daniel Willingham of the University of Virginia and author of the book Why Don't Students Like School? talks with EconTalk host Russ Roberts about how the brain works and the implications for teaching, learning, and educational policy. Topics discussed include why we remember some things but not others (and what we can do about it), the central role of memory in problem solving and abstract reasoning, the current state of math education in America, and what makes a good teacher.

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0:36Intro. [Recording date: October 6, 2009.] Understanding how our brains process information. Claim: thinking is hard, brain tries not to do it. What do you mean? We think of ourselves as the pinnacle of creation exactly because we are so good at abstract thought. Compared to other animals, there is no doubt. When you compare the mental processes involved with abstract reasoning, high level thought, dealing with novel problems, to other mental processes the mind and brain handle, they are not all that effective. Compare vision--unbelievably reliable. Walk into a room and in less than one second, appreciation of the objects in the room and almost never wrong. Thinking processes--very slow, unreliable, effortful. Vision takes no effort; after an hour of hard work thinking about a difficult problem people will say they are tired out. Most of the time we will avoid thinking if we can; refuge we move to is memory. In our everyday lives, constantly encountering problems that if we wanted to we could think about them in novel ways. Go to grocery store; confronted with three dozen varieties or more of bread. Could compare them all on price, visual appeal, nutritional content. But most of the time you just buy what you've bought before. Most of the time we just move to memory; but memory isn't as reliable as vision. We think our memory is not that good, but it is actually pretty reliable, and certainly more reliable than high-level thinking is. What gets into our memory? We think everything's in there if we could just tap into it. What gets into short- and long-term memory? Common myth that memory works like a video camera. Can never prove that that's not true. Most cognitive psychologists think that memory is fairly selective. Surprising thing is the selection process. Used to think things got into memory if you tried--that's what studying is. As an adult, rarely study but things constantly get into your memory--current events, what friends are up to, movie plots. Some sticks, some doesn't. Wanting to remember something does nothing--know that from looking up the same word four times. Where your keys are. Principle seems to be the extent to which you think about things deeply and carefully; and connecting things to things you already know about. Implications for students and also for teachers. Ask student years later what they remember and the things they remember are the things that were important to them, not to you as a teacher. Ask students after class what they got out of it; often not what you put in.
7:43Work on this. Students remember jokes, stunts, the projector falling off the podium. After a year, you remember about 50% of what you learned a year earlier. Takes sustained work to affix something in memory. Remember what we think about--sounds like a throwaway, but a little more complicated. Can't store everything. Memory system lays its bets in a very intelligent way: whatever you are thinking about now is something you are likely going to need to think about later. The longer you think about something, the more likely you are to hold onto it. Also the features you were thinking about at the time--thinking about the meaning of something versus the sound of something versus what something looks like. Barking dog--black and brown dog versus characteristic of the dog's bark versus meaning--likelihood dog will bite you. If you are thinking about what the dog looks like, that's the part you are likely to remember. Implies that you have some control about what you remember. If you are not trying to remember anything about the dog and it just scares you, if someone later asks you what color it was you are less likely to remember. If you have a reason to remember the breed of the dog, conscious effort, make connection with other Dalmations you've seen or think of the movie. Encourages you to control your thoughts at that time. In a laboratory you tell people that they will see a series of words come up; for each word, think about how much you like the word, pleasant or unpleasant word and rate on scale of 1 to 7. For the other half, you do the same and also tell them that later there will be a memory test for these words. The people who know there is a memory test coming later don't do any better than those who didn't know. Tell people you will pay them by the more words they remember, still no difference. Wanting to remember something makes no difference. It's the rating process.
12:38Next level: Role that memory plays in abstract reasoning. Mnemonics: people like the idea that you go to a cocktail party and to remember someone's name you attach it to something. Ty Cobb's batting average is 367--stuck with that one, in the hard drive. Deeper point: abstract reasoning, which we amateurs think of as thinking really hard. Tell students that to do well in class, have to spend time thinking. Imagine them puzzling over economics problems; but most people don't know how to do that. A lot of what we think of as abstract reasoning is really synthesizing things that are in memory and applying them from previous examples, looking for analogies. Psychologists have been working on reasoning a lot and the extent to which memory of the particular topic you are trying to reason about is important to memory. One extreme view: memory is completely intertwined with reasoning and if you don't know something about it, reasoning about the topic is utterly hopeless. Other extreme view: reasoning is a skill, a muscle, and once you are good at reasoning any problem that comes down the pike you can handle it. Looks like the former is probably more true than the latter, but certainly not the whole story. Knowledge is really important for reasoning; many times we are drawing analogies to previous problems we've encountered, but analogies often don't occur to us. Example: Give people a medical problem to solve that doesn't require any background knowledge about medicine--trying to save a patient's life and patient has tumor, can use special rays. Then give them a problem that is conceptually identical but it's in a different cover story--a military story. Even immediately after either solving the medical problem or being told the solution, they still see the analogy. Depressing. A lot of times in economics like incentives matter; prices adjust, shouldn't hold constant--do whole set of examples and go to apply it to something else and sometimes the students don't see that it's the same underlying example just with different surface structure. Change things a little bit and students don't understand that it's the same. With enough experience, you do get around that problem, else you'd never learn. Expertise does develop and can see that deep structure. Knowledge important: school context, scientific reasoning or historical analysis examples. In history, trying to teach how historians think; sourcing is important, who wrote it, what was their reason, who was their audience. Easy enough for students to memorize that, but quite another matter to actually do it. Student may ask the source of a document--letter written home by an American soldier to his brother, written in 1917, brother in Arkansas. Fine, but what do you do with that? Have to know something about WWI. Is Arkansas relevant? Background knowledge necessary to deploy thinking skills. Tradeoff and connection between facts and reasoning. Modern American education--retrieval of facts, not a lot of abstract reasoning. Need to know year United States entered the war, who was the President. Rewards good note takers. But to get to the next level you've got to know that stuff. Facts are easy to denigrate as an educational goal, but they are crucial. Yet if they are the only goal, it's a waste of time. Sweet spot between memorization, stock of factual knowledge, and taking it to the next level. Facts are necessary but not sufficient. Facts are easy to test, seem objective; set standards that are largely fact-based. Students' proficiency with factual knowledge probably correlated with deeper knowledge. The tests probably are measuring something important but lead to terrible consequences in the classroom because of the way they are structured. In economics education, the multiple choice exam: The marginal rate of substitution is a. the ratio of the prices, b. the ratio of marginal utilities, etc. All that really does is get people to know the definition; but that's not what economics is. Shouldn't be the finish line, but the starting line.
23:04Example in book: farmer's got a field of a certain width and length, rectangular field, wants to seed it with a certain crop, knows how much seed he needs per square foot and cost of seed; has to figure out expenditure. Basic word problem in high school algebra. Then ask about painting the side of a barn and the students don't recognize it as the same problem. Economics example, will answer in comments to this podcast after responses: If you put a tax on coffee by the cup, which Seattle was thinking of doing--$.10 tax on every cup of coffee in Seattle; let's say $.50 per cup to make it more dramatic. What happens to the size of the cup of coffee if that tax passed? Bigger, smaller, stay the same? Students have trouble getting started; a few can see it, most don't; let them get started; show why wrong answers don't work, let them see how you approach the problem yourself; then show them the right answer. Try to show them how that response to a change in prices and intervention in markets has parallels to other examples. One view: they have to work at it, try it themselves; another is that if you show them enough variants they will start to get it. Pedagogical approach of students watching Russ work problems that are not simple versus them struggling, unable to do it, till maybe some of them get it. Middle approach. If you really have got the students engaged and ask them to do the problem themselves--from the point of view of memory is that they are going to remember the incorrect solution. Discovery learning: unguided discovery, have at it and see if you can solve this problem. Proposed in the 1960s, but it has problems: lots of students don't get the solution, get frustrated. Worry that they will remember the wrong answer. It can work really well--situation specific. Think about kids learning computer software. With no instruction they fiddle with it and learn. That's because there is immediate feedback in the environment telling them whether they have been successful. Discovery learning probably fine for computer software. Frog dissection, not so much. Fiddling with a frog to figure out how it works, probably not going to learn that much. Economics probably more like frog. Guide students. Study groups in graduate school; bad paths shot down immediately by the brighter and more intuitive students; iterate your way towards the right solution but in real time. Ideally a good study group was a group honest enough to say when things were wrong. Grad school students highly motivated with a great deal of background knowledge. Different than trying to do that with a fourth grade class. Romance about that kind of learning at the lower grades.
30:25Dan Pink podcast--proponent of drawing on the right side of the brain. Claim: left side once was road to success, good at math, engineering, analytical stuff, would make a good living; harder to do now and right-brain creativity, empathy will be increasingly important. Haven't read his book. Neuroscientific, approximation; somewhat out of fashion. When you think about being creative--creativity requires a lot of expertise. Difficult to be creative if you haven't done a lot of the linear thinking. Big emphasis, high schools trying to teach creativity. Can you teach creativity? Can try to create a habit of mind to be somewhat irreverent and try to think problem through in own way. Hunch is that a lot of this is cultural. Americans don't need a lot of instruction to think of ourselves as individuals; value in every individual's opinion; don't take everything as received wisdom. Compare to some east Asian cultures, probably east India as well; anecdote. Some very prepared to be creative thinkers, frequently will discuss that they were not encouraged to be creative in school or at home or anywhere else. Encouraged to respect authority. Not great empirical data, but makes some sense, intuitive. Could look at innovation. Highly likely that sociologists have thought about this. "Thinking outside the box"--critical of that phrase in the book. Applying problem-solving strategies where you would normally use memory. Lots of times when you are drawing on memory. Driving home. Could think outside the box--is this route the fastest, the greenest in terms of fuel economy--but unlikely to do that. Didn't mean to be critical of it; but you can't think outside the box all the time. Big issue in curriculum design in K-12 education. Creativity is a wonderful thing. Alfred North Whitehead: Civilization advances by maximizing the amount of stuff we don't have to think about. Driving home, thinking about what we'll do tonight, thinking about the financial crisis--productive not to think outside the box. Shave-time problems: when you first start shaving you have to think about it, but later not. Practice conserves mental energy. Balance--could be automatically doing something in a really dumb way. Want reliable guide to know when to reconsider. That's what friends are for. That's what markets are for--sometimes markets tell us, special and you try a new kind of bread; or friend suggests a better route home. Social interactions.
38:54Example of thinking outside the box down to a smaller level: Math education. Trend toward understanding the process. Can always look up facts on the internet; have a calculator; better to know the process, can always figure it out on your own if you need to. National Math Panel report written at request of President Bush--need to have three types of knowledge. Need to know math facts, have memorized the multiplication table and simple addition and subtraction; need to memorize procedures, long division; conceptual knowledge--need to know why these things work. We are doing okay on the first two in America; but terrible on conceptual knowledge. International comparisons--the younger kids are the better they [Americans] do. At that age, factual knowledge and procedures take you pretty far on those tests. The United States starts to get bad relative to international is high school. Conceptual knowledge means why the procedure works. Why when you are dividing fractions the thing to do is to invert and multiply? Remarkable statistic: high percentage of sixth graders don't really understand what an equals sign is, what it means. Lots of them think it means put the answer here. Don't understand that it signifies equality. Algebra will be very confusing. If you don't understand division conceptually, you will have trouble with factoring later. Pitched as too much emphasis on facts. We need to maintain the factual knowledge. Inverting of fractions--akin to driving while talking on cell phone, eating at the same time--something a human can do and not have an accident most of the time. Tradeoff between getting kids to invert and knowing why you invert. Difficult tradeoff. Can't let it be a tradeoff; have to make target that they have both. Math hierarchical; really true at the conceptual level. Procedural approach is recipe for getting kids to hate math. Flip side: right answer is not really important, it's understanding the fundamentals. Those arguments not really embraced by very many teachers. Three million teachers in this country, big diversity of opinion; many pick and choose among the theory and don't go for ideas way out on a limb. Useful to do back-of-the-envelope calculations--how many mortgages in the United States? how big might the ultimate cost of the crisis be and what does that translate per capita? Don't want to do a precise calculation.
46:52Related question: use of statistical analysis to bolster a viewpoint. Empirical work in education of the efficacy of empirical work. Difficult to measure correctly; axes being ground by people pushing an agenda. In neuroscience? Not writing for the academy--writing for teachers; relative newcomer. Status of empirical research in education--very bad reputation in colleges, particularly in colleges of arts and sciences. A lot of good empirical research gets done, but whether it's heard is the problem. Difficulty in getting that research heard is a function of the way education schools are staffed. Decision for school of education programs to put all kinds of scholars into the same school--historians, psychology, critical theory, etc. can be made relevant to education. Idea is to lead to interdisciplinary flowering of thought; but instead everyone has different definitions of what it means to know something, what should be considered persuasive evidence. Equally true in the college of arts and sciences, but psychology professors don't talk to English professors too much and no one expects them to; working on different problems, each have important issues. In an Ed-School, expected to talk; result is cacophony; no one's voice is being heard. As parents and teachers we want to know what works, which is hard to discover. Does this work: Take the great teachers, don't take the great subjects. Great teacher can make anything an intellectual journey. What makes a great teacher? Difficult problem. One step back: what makes a successful teacher depends on definition of what you think the goal of school is. Americans don't agree on this. Bill Ayers, terrorist with whom Barack Obama was palling around: he is more recently a professor of education at the University of Illinois, Chicago; interested in social justice education. At the forefront, it's on getting people to think for themselves with an emphasis on this not being a just world; goal of students and teachers is to make the world a more just place. Insidious and unproductive because we all disagree about how to make a just world. Ayers can't believe anyone would see things differently: we may disagree about methods but surely we'd agree that that's the goal of education. Contrast that with Partnership for 21st Century Skills, outfit in southwest trying to serve as a catalyst between business interests, government, and schools--now have 13 states that have signed on to their goals; serious commitment, rewrite standards, re-do education of teachers and assessment. Their idea is that the goal of education is to be able to get a job. No one is talking about what the goals of education ought to be, not a conversation that is being had in any state. Education is at the state, not federal, level. We have an intuitive sense of what a good teacher is, but defining it independent of the goals is impossible. Almost anybody would say that a teacher students enjoy learning from and from whom they actually learn something--can start there. Use that as a starting definition.
56:05Different dichotomy: a lot of people who want their kids to like school; a lot of popular teachers are entertaining but not terribly informative. "She's a great teacher because her class is so much fun." Easy to make a class fun if there is no content. "He really knows his stuff but he can't communicate it." Maybe he doesn't know his stuff; maybe he just looks like a genius because he's so complicated and convoluted, versus parsimonious thought. High school and grade school: popular teachers are often not the best--can be, but not always. Teacher/student relationship counts for a lot. Best learning takes place when we respect those teachers. Good data, especially for early grades; older, more resourceful, easier and more strategies to get past the fact that they don't like the teacher. If a first grader is fearful or doesn't like a teacher, deal-breaker. Teacher needs to be well organized. Best data from college students--talk to undergraduates, boils down to those two dimensions: did they seem like a nice person and did they come to class well-organized. Passion; like to think it counts for a lot; maybe just comforting. Don't know. Enthusiasm in the classroom: if the professor seems bored, why on earth would you be interested? Teaching principles of economics, 390 students in class, didn't use microphone, thought if microphone use would lose students or if used, would have to be really pumped up.
1:00:41If you could change one or two things what would they be? Wouldn't be based on insights from neuroscience. Would get policy-makers to rethink the jobs of all of the adults in the system--not just teachers but the people writing the standards for each state, administrators, professors of education--from the point of view of cognitive science. We are posing cognitive problems that are impossible to solve. Nobody could do what is expected of a teacher; most can't, so they do something else.

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COMMENTS (63 to date)
Benj writes:

Good podcast, thanks. Regarding the coffee tax...

If a flat tax of $0.50 is levied on each cup of coffee, my guess is that in the short term the average size of the cups sold will go up, or the quality of the coffee will go up--probably a bit of both. I might be willing to pay $3.00 instead of $2.50 for a grande (medium) at Starbucks, but I will be less willing to pay $1.50 for a cup of gas-station coffee that was previously $1.00. Similarly, at Starbucks an upgrade from the smallest size to the largest size will be more palatable if I'm spending more on either size.

Of course, the prices will adjust--maybe the prices of the largest sizes will increase by a little more than $.50 and the smallest sizes by a little less.

The tax will also somewhat reduce coffee consumption in the long term.

This sounds sort of like the choice of different grades of gasoline.

Jason Woertink writes:

At first I think the coffee sizes will go in all directions. Some will sell the coffee in larger sizes thinking that consumers care about the per volume cost. Some will keep it the size the same thinking that the given coffee cup size is ideal for consumers. And others will shrink the size to maintain the current price that consumers are used to. Then the market will decide which way is best based on how consumers consume coffee. Most likely stay the same or shrink since I don't think people buy coffee by looking at the cost per ounce.

Bo Zimmerman writes:

Since every other answer has been given already, I'll go ahead and defend smaller. The higher price causes demand to shrink, while capacity to supply remains unchanged. Producers will lower price and size to keep the market clearing.

BoscoH writes:

Not every possible answer has been given yet. The actual sizes are a sunk cost, so to speak, especially at the branded chains. According to my Starbucks app for iPhone, a "Tall" is 12 oz, a "Grande" is 16 oz, and a "Venti" is "20 oz". Off the menu, you can order an 8 oz "Short".

There is a pre-tax distribution of coffee orders among these four sizes at *$. The question asks how the post-tax distribution would be different. With a fixed per-serving tax (same amount regardless of serving size), the incremental cost between sizes for the consumer is lower post-tax than pre-tax. Those that say consumers would migrate to larger sizes are depending on this psychology. But then, why not make the tax $10/cup? Surely that would make everyone by Venti, no? In actuality, people would buy a lot less coffee.

Coffee tends to be a spare change product, much like fast food. If you have $3.50 and that Grande including 50 cent tax is $3.75, you're getting a Tall instead. However, per stiff serving tax does encourage two people to buy one Grande or Venti and split it instead of 2 Shorts or 2 Talls.

So my final answer is that the tax squeezes out the middle. The post-tax distribution has a lower proportion of Grandes and Talls, and a higher proportion of Shorts and Ventis than the pre-tax distribution.

[Incidentally: Great podcast. I've listened 3 times today. There is another podcast with him here (18 minutes).]

Nicholas Conrad writes:

Remember, it's not the coffee that is being taxed, only the cups. Therefore, before answering the question of cup sizing, we can first assume that the total number of cups of coffee sold will decline. The question is from which side of the size scale those cups will leave.

Highly elastic coffee consumers will opt to buy smaller cups. However, very price conscious people are probably mostly buying the smallest size already, meaning that they will be pushed out of the market altogether.

Meanwhile, somewhat inelastic consumers will attempt to game the tax. A customer who knows he wants a coffee now, but is unsure of whether he will also want a cup later, becomes more likely to simply upgrade his cup size to avoid the second instance of the tax. Highly inelastic consumers will adopt the same policy. However, these customers will likely want their coffee prepared in thermal mugs to keep them warmer longer.

This dual effect of pushing out a large number of the people who would slide down the size scale, and giving everyone who is still willing to buy at the artificial price an incentive to slide up the size scale will cause the average size of cups sold to increase.

Tanya U writes:

I'm a long time, almost religious listener to this podcast, but this is the first time I'm commenting here.

I am a physics postdoc trying to make the jump to the professor level. Naturally, I am very interested in how to become a better teacher, especially of the stuff that I love and research. Being in the field of natural sciences and dealing mostly with math, I was very intrigued by what Dr. Willingham was saying.

I find that often practice and repetition are also a good way to get the retention and even the analytical insight into a problem. The difficulty is finding the incentives to motivate the student to actually go through the that repetitive problem. As my PhD advisor said very "tongue in cheek": "Education is the key to repetition" :)

When you were talking about being able to drive a car effortlessly, there was once a time where you actually had to pay attention to every detail in the car, you had to understand why the car moved a certain way, when you applied the brakes. Repetition taught you what was a good reaction time, no matter how many times you had it on a test, actually doing it over and over again, you learned to drive. But you had an incentive! Maybe you wanted to impress your peers by driving that car, maybe you had an actual economic gain by saving time over taking the bus. Regardless, the car is a status symbol and the driving license is one of the requirements to getting that status symbol.

With math education it is quite the opposite. In high school the guy or gal that is interested in math gets labeled a geek and made fun of. And while people find what I do interesting now that I'm in my 30s, in high school it was not like that. Many kids get turned off by math education, because their peers say it's not cool, hence there is not incentive. The result is that kids in high school "miss out" on doing repetitive "understanding" motions, which are part of math and analytical thinking, because they don't see the advantage of doing so.

I always try to somehow incorporate some sense of advantage in my physics/math teaching. Some relation to the real world, but it's still very difficult to do for every thing. Sometimes you just want to yell: "Trust me on this, learn it, you'll know it in the future and it will be useful!"

As for one of your last points, I totally agree that passion is very important for relaying the message. In physics there is this running joke: "How can you tell an extroverted physicist? He looks at *your* shoes when talking to you!". But get me talking about my subject... oh boy! Yes, my students look at me strangely, but they feel that if that strange lady in the front is so excited about it, maybe there could be something there...

Anyway, thanks so much for your podcasts. As a non-economist I love you relaying interesting economic topics to us laymen.

Oh, and the cup of coffee problem...
So the price of coffee goes up by 50c. The first thing that happens is that people are going to buy less coffee. Some coffee shops might go out of business, but the rest of them are making less profit (not per cup, but they sell less cups). So there are two ways that something can go. The first possibility is that they make the cup smaller to offset for the losses from the number of coffee cups sold, so their profit / cup goes up. Unfortunately what ends up happening there is that the people will buy even less coffee that way and it will be a deadly spiral. The second possibility is that they make the cup larger. That way they might make a little less profit / cup, but the public will probably buy more coffee again on the notion that the larger price in coffee is offset by the larger size. Unless the coffee shop is operating so closely at the margins that a small percentage drop means ruin, the slightly larger cup and slightly lower profit / cup will not drive them out of business and they will get to sell lots of coffee again.

Ok, maybe I butchered it, at least I have the excuse of not being an economist, haha

Kind regards

Tanya

Chris Funk writes:

Russ -

Quite frankly, I apologize for such a long-winded response, but it is truly a compliment of sorts: your podcasts are highly educational and thought-provoking.

--

I think there is an ironic lesson here. Consider Dr. Willingham's suggestion that what we think about controls what we remember, in relation to the posted comments.

You posed a simple, but intriguing question which required some careful thought: the effect of a tax on each cup of coffee sold. Yet the vast majority of the podcast was on much broader issues relating to memory, learning, and education.

What does it say that only one of six responses has addressed the ostensible theme of the podcast, while the rest have run with your thought exercise? This isn't meant to be derogatory to anyone involved; I just found it fascinating.

Perhaps it is unsurprising given the economic focus of the podcasts. After all, most listeners come to the podcast 'thinking' of economic theory.

Moreover, as both you and Dr. Willingham suggest, we require a certain facility with facts before we can employ advanced reasoning. When confronted with a discipline with which we have limited familiarity (cognitive psychology), we may naturally be reticent to engage in too much analytical reasoning.

This latter situation certainly affects me with regard to economics!

Still, even though I have been involved in a teacher education program recently (and still have a significant amount of interaction with teachers and teacher educators), I too found that I instinctively remembered and wanted to address your question--at the expense of tackling some of the other important issues Dr. Willingham raised.

The question is, why? Why does your simple, throw-away question stick to our minds, in an almost involuntary way?

I have only a partial answer. Somewhere between the states produced by overly controlling pedagogical techniques (e.g. excessive repetition of specific behaviors/processes/procedures, nonstop didactic lecturing) and overly permissive pedagogical techniques (leaving students to puzzle out problems on their own without any feedback, accepting 'close' as 'good enough') lies an optimal state of enticement to engage in self-invested learning.

Posing an open ended question with the promise of a follow-up discussion of solutions by an expert (which is what you did), entices the mind to seek solutions.

You have given us three messages in the briefest of exchanges: 1) here is an intriguing question, even to an expert (such as yourself); 2) you think your listeners (us) are capable of coming up with valid solutions; and, 3) that the expert (again, you) will discuss the solutions with us after the thought exercise is finished.

This provides some of the most important conditions for what Mihaly Csikszentmihalyi terms "flow" or 'optimal experience': 1) the creation of a challenge which piques our interest and is within our capability; and, 2) the presence of clear feedback at the end of the challenge.

I highly recommend Mihaly's book, "Flow: The Psychology of Optimal Experience." In the book he suggests that individuals are happiest--and, crucially, perform their best--when they are 'autotelic' ('auto' meaning 'self', and 'telic' meaning 'directed or tending towards a goal or purpose'; e.g. self-goal-directing).

One of the key issues confronting educators is creating 'autotelic' students: students who take 'ownership' of their own educational goals.

Thus, one of the most crucial questions to consider when looking at our educational system is how and why our system fails to consistently produce such behavior in students.

A related question would be: do the incentives in our economic system help produce this behavior?

As always, a very thought-provoking podcast!


P.S. I feel obligated to provide some sort of answer to your thought exercise (though hardly an original one).

If the market is already mature and competitive, there would likely be very little space in the sales margin for the companies to offset the increase in price with greater efficiency. Some innovations might take place, but the vast majority of the cost must be borne by the consumer.

Similarly, in an immature, non-competitive market, there will be little competition to force companies to *not* pass the cost on to the consumer. The companies will have to determine a reasonable exchange between loss of sales and erosion of margins, but there is little pressure for them to resolve that problem in favor of consumers.

So, in both cases, the majority of the tax costs are likely to be borne by the consumer in the form of increased prices at each price-point.

Price increases are unlikely to lead to increases in consumption. Sales should decline as prices increase, with the relative size of the decline determined by the ratio of the price increase to the original price. Sales of higher price-point items may decline less, as a percentage, than lower price-point items, but sales at all price-points should decline in absolute terms.

Given that other fixed costs of producing a cup of coffee remain the same, the decline in sales by volume should lead to a decline in sales revenue.

Declines in revenue must be matched by declines in expenses for a company to remain profitable. Unless previously-unknown increases in internal efficiency can be found, the only way to decrease expenses would be to decrease the volume of product delivered at each given price-point (decrease the fixed costs by decreasing the materials used).

Thus, the tax, over time, should lead to a gradual reduction in the volume of coffee served at each price-point.

Or, at least that's my very uneducated guess.

Don Venardos writes:

Increasing the size of the cup lowers the effective tax rate on the cup of coffee and would therefore be the logical response to a per cup tax since it would have a greater impact on marginal revenue than marginal cost; assuming the demand for the product is not highly inelastic.

Alex Moore writes:

I also think that the size of coffee cups will increase assuming that demand for the product isn't very inelastic.

When the tax is put into place, it will effectively raise prices for the consumer causing the amount of coffee demanded to fall. What happens at that point is that, the coffee industry (assuming they are price takers - a fair assumption in Seattle!) would either face lower prices or, since the tax is fixed per cup, they could virtually lower the prices (per unit of coffee) by reducing the tax burden through increasing cup sizes (so that marginal cost again equals price), thus bringing the supply and demand curves closer to equilibrium. They would choose this second choice because the first coffee shops to do this would be able to capture some profit initially until everyone jumps on the band wagon.

Seth writes:

Great podcast. People remember stories. I give presentations in my company and have found that when I wrap my points in stories, they have much greater impact. They may even think my stories are boring and mind numbing at the time (which many have said), but six months or a year later they come back and retell my story and then share a similar story they experienced.

I make sure to go through my presentation before hand and do my story check. I look at the facts and figures, but ask myself what story I'm going to tell to bring that fact or figure to life.

People will drink more tea. In gas stations, the size will go up. People there buy on value and try to get the most for their money. They see value in $/oz.

At Starbucks, I'm not sure a small flat tax would have much of an effect. People there tend to buy less on $/oz and more how much coffee they like to drink at a time. The value prop is different.

I'm sure I'm wrong.

David writes:

Professor Roberts: I don't often write a comment to your podcasts. But, I listen to your show every Monday. You provide a great service to your listeners. Thank you.

As for the coffee problem, here is my amateur opinion --rendered, by the way, as I sit in a Seattle coffee shop. I would think that the demand for coffee is fairly elastic. For caffeine addicts, there are a number of substitutes -- Red Bull, Jolt, tea, etc. But, that does not end the analysis, because the problem does not ask about coffee per se, but rather coffee sold by the cup (assuming that the tax would not apply to coffee brewed at home, but only to that sold by the cup). Cups of coffee, like steak dinners, are more or less a luxury item. If the price got too high, people would presumably quit going to their local coffee shop, indicating that demand is relatively elastic. On the other hand, even with a 50 cent increase in cost, a cup of coffee is still a relatively low budget item. Furthermore, aside from the coffee itself, many people want the social experience afforded by their favorite coffee shop. This social benefit may not be readily substitutable.

These considerations, on balance, lead me to believe that a 50 cent tax would be unlikely to significantly deter people from buying cups of coffee. However, I think that merchants would end up bearing most of the tax burden. To make up for the resulting "sticker shock", they would likely increase the size of cups or allow free refills, cutting into their revenues. This would also decrease the number of cups of coffee sold. There is already a 10% sales tax on a cup of coffee in Seattle -- I just paid $2.20 for a $2.00 espresso. If the end result is to sell less cups of coffee, I wonder if the suggested tax would end up generating much revenue or if it would simply cut into profits of the coffee shops.

David writes:

I forgot to comment on the podcast itself. I have two school age children, a sixth grader and a second grader. I've been very disappointed with the way math is taught in their school. Very little time is spent on the basic facts -- multiplication tables and addition facts are all but neglected. Instead, they are given abstract word problems and puzzles. When I've complained to the school, I've been told that the children are being taught how to "think mathematically." That may be true, but if they don't know their multiplication tables or how to do long division, I doubt that knowing how "to think mathematically" is going to do them much good in the long run. It seems to me that this is a very poor way to teach mathematics, at least at the elementary school level. I have the same complaints about their english composition lessons. The teachers spend little time on grammar and sentence structure.

I went to Catholic schools as a kid. We spent the first five years or so of elementary school learning the basics. While it wasn't much fun and didn't require a lot of imagination, I learned to write a sentence and it made high school and college math understandable and, even, fun. I've often wondered if the way my kids are being taught is effective. It seems to frustrate them more than anything.

steve b writes:

Great podcast,
In regards to the question....The sizes of cups of coffee will get smaller, and bigger. The assumption is that it is a competitive market, with very low profit margins per cup, so the producers could not eat the tax if coffee were exceedingly inelastic.
Before the tax is imposed, the market had determined how much coffee should be sold and for how much. The tax imposes higher cost on producing and selling coffee. In order to pay for this extra cost, either the price each cup of coffee must go up, or the size of each cup must go down by an amount sufficient enough to cover the cost of the tax, or a cup must be sufficiently bigger to cover the tax.

In the first case, an increase in price will reduce the market size, but shrinking the size of the cup is not such an obvious signal, and it may mask some of the lost value.
For high quality coffee, the shrink in size of the cup will not be too large as it is already much more expensive. However low quality, low cost coffee will see a much higher relative increase in cost. The producer of low quality coffee would not be able to shrink its cup sizes enough to cover a 50 cent tax(they would be too small to be viable) or make the cups a size that could cover the increase in tax ( a cup can only get so big until its either too much coffee, or more likely, gets cold before you can drink it all) so they must either produce high quality coffee, or drop out of the market.

The net effect is smaller cups of coffee, and higher quality, more exotic coffee drinks.

This is all disregarding the people on the margin that choose to drink coffee at home, or find a substitute (tea) at the coffee shop.

Stan R writes:

Great podcast. Most teachers would probably do well to read Dan and Chip Heath's Made to Stick. Making important concepts "sticky" so they stick in memory and can anchor related concepts fits right in with Willingham's work.

The elements driving stickiness:
1. Simplicity
2. Unexpectedness
3. Concreteness
4. Credibility
5. Emotions
6. Stories

Kahneman's study of colonoscopies, Ariely's studies of "fudging" students, and of course, the original Tulip Mania are all incredibly sticky when told well. I would wager everything that students remember a year or more after their class could also be explained by the stickiness of the idea's presentation.

On a completely different note, I should have recommended Elinor Ostrom be invited for a podcast pre-Nobel, and now I'm sure she's far busier than she could have ever expected. She was #1 on my list for deserving the recognition of a Nobel, but I was still really surprised by it. Russ, I was curious if you'd heard of her before the announcement?

Russ Roberts writes:

Tanya U,

The late great econ teacher Paul Heyne talked about romance vs. tools (or something like that). We hook students with the romance, the cool stuff, the counter-intuitive insights of economics. Then we teach them the analytical tools. Or poetry vs. prose. The tools are the prose. The poetry is the cool stuff, the fun results.

I think it's very hard to get students (especially kids) to work hard mastering difficult techniques while promising them it will be useful some day. And of course sometimes it isn't useful, it's merely beautiful or helps your brain work better. That is why i think the younger the student, the more important are external motivators such as grades or the respect of the teacher. And that's where passion and charisma and caring come in to make a great teacher.

Russ Roberts writes:

I appreciate all of your efforts to get at the coffee problem. Here are some reactions and some hints. The hard part of this kind of problem is recognizing that the current pattern of size options is not random. Don't start from scratch. You want to think about how the tax changes the incentives given the current set of offerings. And you want to simplify the set of offerings so that's easy to see. So here are some hints:

Try to show the incentives facing buyers to switch their buying habits. In general, there is a trade-off between small and large sizes before the tax. Large cups are cheaper per ounce but cool off. Small cups are more expensive per ounce but the coffee stays hot. That is, suppose cups of coffee before the tax are available in 8 oz and 12 oz sizes. For people who drink 24 ounces of coffee, some choose three of the 8 oz cups, some choose two of the twelve. How does that incentive change with the tax?

Or look at the seller. Suppose there is only size of cup available before the tax, a 12 oz cup. Does the tax create a profit opportunity for a seller to start offering an 8 oz cup? Or a 24 oz cup? Both?

I would ignore price elasticity. I don't think it has anything to do with the problem.

Russ Roberts writes:

Stan R,

Thanks for the book recommendation. I'll check it out.

I had heard of Elinor Ostrom. Long ago, I studied how people dealt with the tragedy of the commons in grazing and fishing. Her work is central to that question.

The importance of her work is showing the creativity and flexibility of voluntary arrangements. People often contrast the market with government. The right contrast for me is top down vs bottom up. Ostrom studies bottom up solutions. Sometimes these are what we call markets. Sometimes they are norms and other mechanisms that emerge as people find ways to deal with problems.

Matt writes:

It would probably stay the same. As far as I know there has always been twenty cigarettes in a pack of Camels.

George writes:

For the coffee question, given its context in the podcast, it seemed the goal might be to find an analog then apply the analog to the coffee situation. The analog I'd pick is the airlines' charge on pieces of checked luggage. This is a relatively recent event and, in effect, is a per unit tax like on the coffee cup. I think what we've seen with checked luggage is, first, a marginal decline in the demand for this service and, second, a shift to larger suitcases. Translating this to coffee: a lowering of coffee sales and a shift to larger cups.

Brendan H. writes:

Hmmmm. As a pricer I can't resist this coffee question.

First, some research, because although I'm a coffee addict I brew my own at work, so I headed down to the Starbucks here in the office building and found:

Drip:
1.59/1.69/1.79

Cappuccino/Latte:
2.39/2.99/3.29

Given that the Tall/Grande/Venti sizes increment by 4oz each, with the Venti almost twice the size of the Tall, I'm guessing that their COGs is not actually much of a factor -- staffing and real estate probably cost them a lot more than coffee grounds, milk and water.

Thus, they're mainly sensitive to two metrics:

1) Margin per cup (above cost of goods -- to which we should add the .50 tax in this case)
2) Number of cups sold

The trade off for them is going to be of profits per cup vs. number of cups -- and I'm guessing that anything which reduces the number of cups is going to hurt them more. If I'm right that their margin over COGs is 80%+, a hit to their number of cups needs a very large increase in the profits per cup to make up for it.

If I were pricing for Starbucks, I'd first see if we could increase the increment between sizes, go from 12/16/20oz to 10/15/20, or possibly (if the cost of stocking four sizes wasn't too great) go 8/12/16/20.

The key, as I see it, would be to keep your entry price point low enough that you don't see much drop in volume of cups sold, even if that means becoming less profitable at point of sale by eating some of the cost of the tax and finding other places to work it out of the business. (Close lower traffic stores, try to upsell more sandwiches and pastries, etc.) Obviously, the current coffee shop business model is based on operating expenses supported by that 80%+ margin per cup in terms of cost of goods. So to the extent that this tax turned coffee into a 70% or 65% margin business, it would require that coffee shops reduce OpEx in order to stay in business.

The overall goal of pricing in response to the new tax would be to assure that the cups of coffee sold volume reduces by no more than 10% in the short term, and rebounds to the prior level in the long run. Secondary goal is to keep the average margin per cup as close to the prior levels as before in order to avoid having to restructure to reduce operating expenses.

My pricing for either a 10/15/20oz lineup or a 8/12/16/20 one would be focused on having a base line product no more than $0.10 more expensive than the old entry level price, in order to assure that you don't price customers out of the market, with the 20oz size being 2.39 for drip and 3.99 for cappuccino/latte in order to support your overall margins. The 20oz size would still be the cheapest coffee per ounce (and even more so given the time cost of walking down to a Starbucks again later) so I think you'd have hourglass shaped demand, with most people gravitating toward either the cheapest cup or the largest quantity.

Bingo little writes:

What is this Mr. Roberts? You're doing a rap video of some sort?!2

Jeff N. writes:

The size of the cup is likely to get larger.

From the buyer's point of view, it makes sense to decrease the marginal tax rate by choosing the 12oz cup. The difference in marginal tax rates becomes even greater when deciding to buy 2 12oz cups vs. 3 8oz cups. The trade-off is that relatively slow drinkers may have to consume cold coffee. On the other hand, it would also mean fewer trips to the coffee stand which could be considered a net positive.

From the seller's point of view, the new tax does provide the opportunity to introduce a 24oz cup. What the seller may not know without empirical data is if the savings provided by reducing the marginal tax rate is enough to offset the unpleasantness of having a cup of coffee that may be too large to fit in all car cup holders and is likely to cool off before being entirely consumed. It would certainly be worth the experiment to see if revenues could be increased with the larger cup.

Pyrrhon writes:

There is yet another answer to the coffee cup conundrum: it is impossible to predict how the cup size will change after the introduction of the tax, notwithstanding the confidence with which economists will spin their arguments. We are talking about human behaviour, not the movement of planets. There are countless factors, each of them decisive, but any simplistic model that economists love to toy with must ignore almost all of them.

Don Venardos writes:

Okay, from the buyers POV if there are 8oz and 12oz cups available and I drink 24oz of coffee, after the tax the option of buying three 8oz cups of coffee is relatively more expensive so I would have an incentive to switch to two 12oz cups of coffee.
If I drink 14oz of coffee and I buy two 8oz cups with some left over because I like the coffee hot, again, I would likely switch to a 12oz cup and not drink quite as much.
However, if I drink 10oz of coffee I may be willing to switch to the 8oz cup and not drink quite as much.
If I drink exactly 8oz or 12oz my choice would probably remain unchanged.

I predict that multiple cup of coffee drinkers will switch to a larger size and single cup of coffee drinkers with some left over would switch to a smaller size, and those drinking the exact size would buy the same size. Therefore, whether or not the mean size is smaller or larger would depend on the ratio of multiple cup drinkers to single cup drinkers with some left over.

Yifan writes:

Coffee question;

Price goes up, some ppl will decide not to buy coffee.
Some ppl will decide to downgrade and consume less.
So the resultant mixture means a greater proportion of coffee sold are in smaller cup sizes.

I find the argument for upgrade unconvincing because after the tax, it becomes more expensive to upgrade now than before. So why upgrade now?

Blake Riley writes:

On the coffee cup question, my initial guess is that a tax per cup could make cup size move either direction depending on the consumer's preferences. Both the number of cups and total ounces sold will fall according to the law of demand. The main question is the relative importance of cups vs ounces.

If the consumer is primarily concerned about the total amount of coffee they consume, cup size will increase because this lowers the price per ounce. Number of cups sold would fall sharply. On the other hand, if the consumer is primarily concerned with the cups bought, because they value trips to the coffeehouse, the social experience, or routine, cup size will decrease.

I really enjoyed the rest of the podcast. My wife and I are both new grad students, her in English and me in economics, and are on both sides of the student-teacher relationship now. We've both been thinking hard about how to apply economics in the classroom. If anything, I am reminded of one of the first EconTalks, with Don Cox, where he talked about taking his infant daughter out of the hot daycare to put her winter clothes. Are there any analogous teaching tips to better align teacher and student incentives?

Chris Funk writes:

Dr. Roberts -

Please correct me if I'm wrong, but you seem to be saying that the existing "pattern of size options" derives from the varying value consumers currently place on temperature and volume, and assumes that the two are (loosely) inversely related.

E.g. Some consumers are willing to trade large volumes for sustained hot temperatures, others are willing to trade sustained hot temperatures for large volumes, still others occupy places in between these two extremes.

If you will, temperature and volume form an axis, along which consumers cluster in terms of their preferred position between the two. By looking at these clusters, existing products have been sized to offer maximal coverage of profitable consumer profiles.

Implementing a tax alters the value relationship between temperature and volume, and we should expect consumers to alter their behavior accordingly.

Consumers will have to recalculate how much they value the coffee's temperature vis-a-vis its volume given the new pricing. We will get different clusters on the axis between volume and temperature, and businesses will make adjustments to their product lineup as a result.

Is this the general idea?

If so, from a consumer's perspective, the price premium for hot coffee has gotten larger. So I would expect some consumer movement towards valuing volume more highly. This would provoke a response in vendors to provide more volume, until a new balance had been achieved.

Netsp writes:

Prof. Roberts,

I would be fascinated to know which hints you have tried before and which work best.

I see that your tip is try to think what caused current prices. I would supplement this by saying that Economists like examples that apply widely. If your solution about coffee cups doesn't apply to televisions, it's probably not what the economist had in mind.

My instinct about good thinking tools/tips would probably be along the lines of extreme examples. Instead of thinking about a $0.50 tax, think of a $5 or $50 tax.
If the tip is part of a repeatable process (it works for many problems), it can become an aid to abstract thought.

There's a pretty interesting question here (I think). What makes a tip a good one. I think it's interesting because a tip is a way of letting a student 'sit and think' or 'own the problem,' without letting them become too frustrated.

emerich writes:

Russ's hint obviously implies that cups will get bigger. But the tax also changes the incentives between drinking untaxed coffee at home and taxed coffee at the coffee shop. What if people are buying not hot coffee so much as caffeine and a coffee break? If I exceed my quota of caffeine I'll snap at my boss and get fired, but I have a choice between drinking untaxed cups at home and taxed cups at the coffee shop. With the tax, I'll drink more untaxed coffee at home before leaving for work, and a smaller, taxed cup, for my coffee break. I keep my coffee break, get the same amount of coffee and caffeine, but the cup I buy in the coffee shop is smaller.

Otherwise the podcast was also interesting but frustratingly inconclusive. Russ, if you haven't read him, read E.D. Hirsch on core knowledge (http://coreknowledge.org/CK/index.htm). He has found based on extensive research that children--as well as the rest of us--need a strong foundation of existing knowledge to put new knowledge to productive use. The more you know about a subject, the faster you can learn more about that subject. The more you know about a subject, the more easily you can put that knowledge together in creative ways.

Chris Funk writes:

Netsp -

You bring up a valuable point. In education circles, the method to which you are referring is known formally as 'scaffolding'.

Whether we call it a 'tip' or 'scaffolding', the intent is the same: to provide a small rung on a ladder, which allows the learner to pull themselves up, without excessive (and sometimes counter-productive) help from the teacher.

In the case of the 'tip' in question, it has helped me to think about the way a tax changes the incentives acting on consumers (or the way in which the tax changes the value judgments made by consumers).

The difficulty for me has been trying to identify correctly the most salient incentive principles at play.

I had never given much thought to the value questions involved in deciding what size cup of coffee to purchase, but Dr. Roberts discussion of the trade-off between size and temperature makes sense.

It's a new, somewhat foreign, but exciting way to think about the purchase of a cup of coffee, and I'm understandably not very good at it yet.

Mort Dubois writes:

Russ: are you asking what will actually happen or what an academic economist predicts will happen based on elegant theories? And what kind of time frame are you talking about? I don't know any theory, so my prediction of what would actually happen is that no size change will occur. In the real world there's considerable momentum to the existing choices:

- existing inventory of cups

- existing signage/menus and cost of changing them

- existing restaurant infrastructure.

- existing habits of patrons. Say you order size X every day - how often are you to change to size y simply because the price changes? We're used to the idea of changing prices, much more than the idea of changing sizes.

In the short term there's little incentive for the seller to change anything - too expensive and troublesome. In the long run people tend to accept price changes, particularly for addictive substances like coffee.

In my area, Philadelphia, we have a dominant local convenience store chain called Wawa. Several years ago, they raised prices on all of their coffee by about 25%. This caused raised eyebrows for a day or so, but people keep buying the coffee and no new sizes have been introduced. Wawa is a very well run organization, so regardless of theory, there's your answer.

Mort

Adam writes:

The discussion about how students have trouble drawing analogies when there's a different "surface structure" reminds me of the beginning of Tobias Dantzig's book, Number. He talks about how before we had a number system like the one we use today, we had words that meant a specific number of a specific thing--say a word that meant two geese, and then a different word that meant two cows. He posed the question: who was the first person that realized that there was a "twoness" in common with both concepts?

I'm not going to answer the coffee question because I took your class and that would be cheating :D

If I had to name the one thing that has stuck with me from your class, it would be the discussion of The Problem of Social Cost, where you talked first about the consequences of rules about what happens when a pitch hits a batter, and then about car radios. It really helped me think about trade-offs in a way I hadn't quite considered before.

And incidentally, I know a few of my fellow classmates who have used your pistachio story in casual conversation with non-economists. (I think one was a lead up to a comment about the difficulty of finding straight men in San Francisco...maybe not exactly the application that you had in mind)

Anon writes:

Average size of cups consumed gets larger. Prices and sizes already incentivize consumers to buy larger cups as they are a better deal $/oz. A flat tax of 0.50 on all cup sizes reinforces this incentive towards larger cups. +.50/12oz is cheaper than +0.50/8oz

Netsp writes:

Chris Funk,

Thank you for the term. I will remember it. The reason I find 'scaffolding' so interesting is that I expect experimentation with different types of scaffolding to yield insight into how a mind works.

In this case I happen to know the principle being referred to, so I defer to the principle, the effect of a per-unit tax. The 'story' of how it happens is something I construct after. I never would have thought of heat retention. For this reason, I am slightly handicapped when trying to explain it.

I found Prof. Roberts' surprising, because it is so specific to this example when the principle we are trying to see in action is a general one. I can see three possible ways of 'scaffolding' (can this be used as a verb?).

1)per specific case- I suppose this encourages students in economics to see the mechanics of the principle at work in the example without knowing the principle. This is what he ave us.
2)hinting at the principle- This would help students see the principle, and apply it wherever it fits. An example of scaffolding here could be "Instead of cofee, think of drinks. If every glass at a bar had a $5 tax, would you drink pints of pots?"
3) General thinking tools that can be used widely. An example here would be "Instead of a $1 tax, try think of a $10 tax or $1 subsidy."

As I said, my instinct is to prefer 3. Because it is such a general principle, it feels less like cheating. Also, I feel like it is just more useful in your toolkit. I would be very interested to know if there are any rules about how to use scaffolding.

Phil writes:

Re coffee and the discussion about applying what is learned in one problem to another: consider analyzing the problem with a $2,500 tax on cars, regardless of size. Now consider a dealership with only 2 size cars, small for $15,000 and large for $30,000. Add the new tax, and car sales will drop sharply at both sizes. The question is which sales will drop more, the large car or the small car? If you need a car, a price increase from the tax will probably lead to greater sales of small cars.
Unless cars (or coffee) are a very unusual category of products (Geffen goods) in which case the demand for larger more expensive products go up.
Incidentally, consider that the Cash for Clunkers program was a temporary negative tax that drove up sales, and that the end of the program was the functional equivalent of raising a tax leading to lower sales when the program ended.
The key from the taxing authoriy's standpoint is to raise a tax that is high enough to generate new revenue, yet low enough to allow the coffee merchant to remain in business and profitable. This isn't any different than how a landlord has to consider raising the coffee shop's rent.
Or, think of this as either a parasitice or symbiotic relationship. If it is parasitic, the parasite (taxing authority, landlord) has to charge just enough and not too much to kill the host. If it is symbiotic, the taxing authority, or landlord has to provide some new or enhanced benefit (cleaner streets, larger signage, a police station across the street that enhances the demand for coffee in the neighborhood).

Crosseded and Painless writes:

Love your podcasts!

This one reminded me of this lyrical gem from my misspent youth:

Facts are simple and facts are straight
Facts are lazy and facts are late
Facts all come with points of view
Facts don't do what I want them to
Facts just twist the truth around
...

Crosseyed and Painless
Talking Heads
Remain in Light '80

You don't have to squint too hard to see how the entire song in so many ways reflects the truth/sadness/irony of our current situation.

http://www.youtube.com/watch?v=bOOhfS1hZVo

http://www.lyricsfreak.com/t/talking+heads/crosseyed+&+painless_20135079.html

emerich writes:

It occurs to me that the coffee question isn't the greatest illustration of students' failure to apply a general principle to a specific problem. In fact, someone who'd taken economics would naturally start thinking about supply and demand and elasticities because it was presented as a problem in economics. In fact it's a logic problem and economic principles are misleading--e.g. one is tempted to assume demand will fall because of higher price, so cup size will fall. My wife, who's never taken economics, immediately said cups would get bigger. My son, who has taken economics and is a professional currency trader, said cup size would fall as a response to price.

wbond writes:

Prof. Roberts:

It strikes me - perhaps incorrectly - that the hint you gave and many of the responses here assume that the cost of the coffee itself is the primary source of "overhead" cost that goes into the price of the product.

Wheras, it seems to me that the coffee itself is probably quite inexpensive to the coffeeshop (even the good stuff) and that most of the overhead that needs to be supported in the price is to be found in the rent, equipment, and labor costs.

So, the answer to the question would be different if discussing more expensive goods, or goods with a secondary market, for example.

I suspect the answer is more nuanced, then, depending on how much the tax actually would influence behavior to decrease total sales and you might see solutions such as using coffee sales as somehwat of a loss leader in order to sell other items with higher profit margins and lower taxes. If the cost of the diffent size of the physical (paper, or whatever) cups themselves doesn't matter much, and the coffee itself is the cheap part, I suspect you would also see larger cups.

Fun stuff and excellent podcast.

You are an excellent teacher to this non-economist who enjoys listening.

Name [Required] writes:

[Comment removed for supplying false email address. Email the webmaster@econlib.org to request restoring this comment.--Econlib Ed.]

I Can CUP writes:

In response to the coffee question, I think I would stop selling by the cup, and start selling mugs of coffee instead thus avoiding the tax. Or I would sell empty cups and allow anyone who purchases an empty cup a free serving of coffee which also avoids the tax.

Floccina writes:

Maybe some coffee shop would start to sell a large cup of coffee and an untaxed empty cup for those buying coffee in couples.

Sean writes:

How can you argue with the empiricism of Matt (Oct. 14, 12:12 PM)? "As far as I know, there have always been 20 cigarettes in a pack of Camels".

Joe writes:

If I were a seller I would start selling coffee by the pot, or in quart sized insulated cardboard containers like Dunkin Donuts sells. I think it would also create an incentive for offices to buy a coffee maker.

Andrew writes:

There are a lot of ways to look at this. One is to assume a multistage budgeting process on the part of consumers, i.e. a utility tree. Given the average price of coffe relative to other goods, a consumer chooses to allocate expenditures to coffee (or not). Coffee expenditures are then allocated to various sizes (say L, M , S). In this context, coffee prices are given since the individual consumer can not affect them.

A per unit tax will have two effects, (1) total coffee expenditures will go down because coffee is now relatively more expensive when compared to other goods. Less expenditures will be allocated to coffee. The second effect is more theoretical. Some of you may know that a conditional demand system (demand for different coffee sizes as a function of total coffee expenditures and size prices) is homogeneous in prices. This is to say that a proportional change in prices should not change the allocation mix. A per-unit tax is not proportional and would make larger sizes relatively less expensive when compared to smaller sizes (assuming that larger cup sizes sell for higher prices). A greter share of coffee expenditure will be allocated to larger sizes.

Recap...
(1) A smaller share of the consumer's budget is allocated to coffee.
(2) Conditional on total coffee expenditure, larger sizes would account for a greater share of total coffee expenditures, hence the average size will increase.

Steve450 writes:

Excellent work Mr. Roberts! This is by far the most comments I've seen to any of your podcasts so far.

Perhaps a similar thought and discussion provoking example should be a regular element of your show.

davehedengren writes:

The Whitehead quote appears in Hayek's "The Use of Knowledge in Society" but appears without citation.

Thanks to the wonders of the internet however I was able to check the source, certainly an important operation, with hardly any thought at all. It comes from Whiteheads' An Introduction to Mathematics (1911) p 62.

http://www.archive.org/stream/introductiontoma00whitiala#page/60/mode/2up

Pietro PC writes:

Coffee problem: the tax will cut into the profits so the seller will try to recoup in other ways: probably the coffee pot will sit longer out on the burner and thus coffee won't be as hot, making the trade off between smaller and larger cup only a monetary one. On the other hand, it might also be costly to offer a wide variety of sizes, so there's also an incentive to restrict the amount of choice in cup sizes. This seems to suggest that the cups will stay the same, or at least narrow around the average size, but the coffee will be colder, on average. I haven't read previous comment, so I might be repeating.

Mort Dubois writes:

I can't resist adding a few more real world coffee observations. To me, the tax is just another cost, similar to the cup itself. Think back to the following innovations in coffee service:

- The cardboard ring that goes around the hot cup

- An assortment of very fancy lids

- All kinds of different flavor and brew permutations

- Nicer coffee house interiors

- etc, etc, etc.

Did ANY of these change the size of the portions on sale? Anyone notice this anywhere, anytime? I can imagine lots of responses to changes in cost, but I've never observed changes in the relatively standard sizes (12, 16, 20 oz). Coffee sellers, like any business, have a variety of responses to cost increases. For whatever reason, it seems that changing the size is not high on that list. Since the tax is just a cost increase, I don't expect it to change the cup size at all.

Mort

More Like Water writes:

Perhaps the coffee cup would stay the same size, but the actual coffee would start tasting a bit more like water.

MR writes:

The Market in a Cup
-------------------

Like all questions in econ this is empirical (which informs our guess) and more importantly, the result of a *discovery process* (our guess is, and can only be, a guess); I am somewhat surprised that Dr. Roberts seems to have a specific and precise answer in mind, though perhaps not, and I include a question for you, Dr. Roberts, at the end.

Question: A 50cent tax is imposed on a cup of coffee. What happens to cup sizes?

Answer:

(1) given the standard market in cup sizes, the cups themselves will likely not change in size, so the question is not "what happens to the cup size?", but "what happens to the distribution of cup sizes bought?" [of course, given a big enough tax this assumption breaks down]. So step one is reposing the question.

(2) The size of the tax will dictate what happens. In general, with a flat rate the relative cost of a higher priced good will fall, making it cheaper and thus more likely to be bought. But there are confounding several factors at play here: if the price increase is near zero, no change will occur, if it is huge everyone who still buys will get the biggest cup [and throw out the additional coffee if they don't want it]. In the middle there will be a tendency for the big cup, which is countered by the tendency to save money, as well as other aspects (such as a tendency not to waste), the break point of switching size will depend of the individual and precise costs. The precise distribution of personal preferences which informs choice, being preferences, are not "rational", i.e. computable.

The general story is of countering incentives: bigger to get a relative savings, smaller to get an absolute savings, which is anchored by the quantity of coffee that is enjoyed which is a force for "no change" (if the old prices didn't distort your quantity preference too much... If there is significant distortion, then this is no longer an anchoring force, but one for change - again, bigger? smaller? depends on the person). If I only enjoy a small coffee it doesn't matter - to me - if large is only 1cent more, if I don't value the extra coffee I will not spend the 1c, even though 1c is effectively nothing - I dis-value throwing out the extra coffee and wasting a penny everyday for the rest of my coffee drinking existence. Someone else will say "who cares? It's one penny, and I might want one one more sip before dumping it".

(3) Empirically coffee, according to Brendan H., is about 1.59/1.69/1.79 for S/M/L. A 50cent tax takes this to 2.09/2.19/2.20 - given that 10c is approximately zero in many peoples minds, they would likely take the biggest cup if they would enjoy drinking that much, or at least not care about throwing out some coffee and extra mass of garbage. Of course, the post tax prices charged by the sellers would *change* to maximize the total profit, but since Dr. Roberts emphasizes a larger tax hike we must play to the exam - he is **looking** for the answer of "bigger" and wants us to speak to that incentive.

Tisk-tisk, rewarding students who learn to write to the test is a public bad, if one takes the strange view that education should be aimed at learning truth and how reality functions versus sorting people by their ability to please test writers, i.e. learn how to gain power via politics [I tease, Dr. Roberts clearly values education and is a liberal].

(4) But the real answer, fit for post test discussion or for essay style questions, is "unknowable": markets respond in unexpected ways, which is why we want markets, and in doing so they find solutions while giving us information what people value & how they think - this is the beauty and power of markets. For example, cups cost money - and one way to counter the tax is to give a discount if you bring your own cup (a discount proportional to the cost to the store for the cup). Thus stores can and will act to bring down the effective tax retaining more price discrimination, will people respond? Most stores right now offer such a discount, but will it become more important to a consumer and thus be taken up more? Depends on the consumer. The stores may be inspired to find a way to bring down costs, allowing more room in pricing, and any such finding will propagate through the market, etc.

(5) In summary: The relative importance one places of absolute cost, and reducing waste will tend to keep the cup size bought the same or move to reduce it, this is counteracted by the relative savings which will tend to increase cup size as for the possibility you had drank less than you would have preferred based on old prices, confusing the issue even more - as long as old prices did not distort the quantity drank too much, on average, quantity enjoyed will be a force for "no change". Each individual will react in a different way, and stores will attempt to counter the undercutting of their ability to allow price discrimination - any success will be replicated by other stores.

More interestingly, most individuals *themselves* likely would not know how they would react prior to actual action. Ask people what they would like, they will say one thing, but when it comes time to do it the importance of the decision (versus a cheaper hypothetical) will make one seriously consider the action. Markets collect both collective decisions as well as "discover" individuals.

The result? Unknown. Forced to bet, I would say "bigger". I would be completely unsurprised if I lost the bet.

Dr. Roberts: I now pose a question for you.

Preamble: I would expect most liberals, who value personal choice and see many aspects of life simply as preferences that should not, and cannot, be judged as intrinsically better or worse, and also tend to believe that such variation both exists and is legitimate and is even good (spice of life! more aspects to combine into interesting new things!), would also be unsurprised if the summing and averaging and settling of preferences via the market post this change turned out different than they expected.

Based on this general attitude towards people and their preferences, which informs choices made, there would also be a tendency to intuitively understand the market is a discovery process - which is uncomputable, and where effects can be accurately made only for extreme and strong changes.

Question: Is a given precise answer to this question meaningful? If someone said "bigger" on a test you gave, would they be marked correct or incorrect? Would some econ profs give this question as a multiple choice rather than a short essay question? Any given answer is quite possible, with "bigger" being the first order guess one naturally leans too and that your posing of the question indicates you are looking for (sub-question: am I right in this inference?). But without any sort of empirical consideration in order to inform a guess, or acknowledging of the unknowable nature of the answer (i.e. it is *only* a guess), a solid "bigger" seems worse than no answer at all - that answer, "bigger", discounts the discovery process of the market, both of individuals and group preferences and of means of effectively fulfilling them, and the liberal world view that is implicit behind that understanding of the market. In an econ class discounting the liberal view is fine, though it would be strange for you to do so, but a precise answer of "bigger" seems to miss the whole idea of what markets are about and how they work.

Question, reposed: Strong clear statements are good, when they can be supported. This coffee question does not seem to be one of those situations. Perhaps I am missing the big picture of what econ is about and its ability to judge outcomes and being overly cautious in what one can say, but to me the question seems to be either seriously ill posed - if a precise and absolute answer is expected - or an elegant koan-like question to force the student to realize what economics is. So, here is my question in final form: is the coffee cup question a koan, or am I making an error in my estimate of what econ can predict and a single clear answer exists?

Eric Fisher writes:

Consider the distribution of coffee sold in a given store. Since the status quo is a long-run equilibrium, we can assume that there is a fixed supply of n_s small coffee cups and n_b big coffee cups and that the two markets markets will clear at p_s and p_b respectively. It is reasonable to assume that p_b > p_s. Now a uniform specific tax will raise the the price of the small cup by a larger percentage than it will raise the price of the big cup. Hence the percentage decrease in the quantity of small cups bought will be larger than that for larger cups. As long as the elasticities of demand are roughly comparable, a larger share of coffee will be sold in large cups. Hence the average size of coffee cups will increase.

Since the two goods are substitutes, the ancillary demand effects will further reinforce my solution.

Russell, since I answered this one correctly, will you please say yes and be my Facebook friend?

Deuce writes:

Matt and Sean make a lot of sense. I don't have the time currently to write 3k words on my thoughts so I had to relate it back to something I know. If there is a $.50 tax on beer I may drink less (prob not) but I would still drink it 12 oz at a time. There will be those that want to get more for the buck but they are doing that with 30 oz. bottles of beer (I mean coffee)

Great Podcast, I look forward to it every week.

make it a double writes:

Does a 24oz coffee drinker really order 2 x 12oz just to keep his beverage hot? when 1 12oz = 1.50 and 1 24oz = 1.70? Maybe it depends on the refill policy of the coffee seller.

There are people who take their coffee on the road, and others who sit in the shop all day. There are different options available to each group - refills cost much less if you are on the sofa at Starbucks then if you are trying to keep a 70MPH pace down I-5 from San Francisco to LA.

My sense is that the average size would increase, as my personal inclination would be to seek a better average cost per oz. I can live with a luke-warm java.

But since you mentioned that price elasticity is not key to the solution, I'll sit here drinking my free coffee from the office and ponder my Econ GPA from years ago, awaiting the answer...

excellent podcast, fantastic series. thank you.

Nicholas writes:

I grew up in Seattle, and I can assure you that Seattle boutique coffee shops do usually allow customers to bring in thermal mugs to have their coffee prepared in. Therefore this idea of coffee getting cold is a red haring. As I alluded to in my previous response, consumers will invest in thermal mugs to keep large cups as warm as small cups would be.

Charlie writes:

The coffee problem seems like a very standard application of the Alchian and Allen Theorem that adding a per unit charge to the price of two substitute goods increases the relative consumption of the higher price good.

I first heard of the type of question on MR as Tyler refers to it (don't remember ever encountering it in undergrad or graduate econ). Here is an example from long distance relationships (http://www.marginalrevolution.com/marginalrevolution/2006/09/trudie_on_longd.html). I had to look up the name of the theorem, but I remembered enough about the original example to find the post easily with a search.

Tyler links to the definition I use above. I would have had trouble explaining it so well, but intuitively I understood the answer.

I hope that this gives Russ some solace, as it seems this is how econ education should and does work. I heard an explanation for a hypothetical problem. I understood, and in some sense memorized the reasoning. And then when a similar problem arose I applied the old reasoning in a new application.

Gary Dean writes:

OK, I just listened to the podcast, am intrigued, but have not read all previous comments-- so I apologize for any redundancy.

Here are my thoughts:

1. "Cup" is a defined and accepted unit of measure. Perhaps not the specific intent of the legislation, but for someone (a court) having to interpret that would have to be the application. That said, a per unit of measure tax would have no direct impact on the size of the coffee receptacle. There would, however, be an impact on the amount of coffee sold, and the increased price would lead to a decrease in overall consumption.

2. If the "per cup" tax is not a per measure tax, then it would have to be a tax on the coffee receptacle (i.e., cup) provided by the seller at place of sale. [Which raises the interesting question of whether the tax applies to the sale of empty "coffee cups".] With that being the case, then there would be no tax on the sale of the product, coffee, itself -- if there were, then we would be at #1 above. This would result in the overall reduced sale of coffee receptables at the point of sale of coffee [which would be a positive environmental effect and, therefore, be sufficient rational basis and legislative intent], and instead coffee sales would migrate heavily towards "provide your own coffee cup" sales -- i.e., we would have "fills" in addition to refills. As to the impact on the size of coffee filled coffee cups being sold, I would think that they would increase for the reasons some previous commenters put forth.

3. Lastly, if none of the previous applies and the "per cup of coffee" tax is for what we colloquially accept as "cup of coffee sales," then we would see the rise of "private coffee clubs" along the lines of after-hours liquor sales, wherein for paying $X in advance I can come in and fill/re-fill my cup at will (or set # of times perhaps). I could, naturally, join the "club" at the first time I walk into an establishment, again just like after-hours liquor sales at "private clubs." The impact on the size of cups of coffee sold to non-club members would most likely be akin to #2.

Thanks for this neat exercise.
I am looking forward to the schoolbook answer.

Gary Dean writes:

Russ,
Given the wide range of responses and differing analysis, I think this question would make for a great EconTalk round table discussion with 2 or more opposing economists.

Hubert writes:

I will be glad if ‘the solution’ will be revealed tomorrow because the problem of the coffee cup size keeps my mind engaded. Deciding whether to buy a small or large cup will never be the same again. Its difficult to add to all the response above. I think the major effect of the per cup tax is through multiple cup drinkers that substitute less bigger cups for more smaller cups. More bigger cups will be sold. The supply side will probably respond to this by offering (slightly) lager cups or adding an extra large (super size) cup to the range available. I do not think there would be an effect, if there where no multiple cup drinkers.

Like many said before I agree this is difficult to predict an the market should find out. So is there an analogy for which we can test the predicted effects. One I analogy thought of is the window tax (http://en.wikipedia.org/wiki/Window_tax) (applied in the UK from 1696 to 1851) applied in The Netherlands in the 19th century. Like the cup tax this tax was also a fixed amount per window independent of window size. Would people have substituted less bigger windows for more smaller windows then? So was average window size larger during this tax regime? I heard this claim once for houses in Delft, but I doubt if it is true. Houses build in the 19th century do not seem to have bigger windows. There is significant prove of the volume effect though: a lot of windows where blocked and the effects are still visible today (Photo window tax, illustrating reduced output, http://www.panoramio.com/photo/17402340, http://www.flickr.com/photos/designerd/123789711/)

An other example would be the ‘bit tax’. This would probably result in bigger bits.

PS. Whats and ‘oz’? My advise would be to move from oz to ml, metric units are so much more efficient.

Jake Russ writes:

I think this explanation is originally from Lancaster (Kevin?), but no one has said it to this point, so I'll add it now.

Ultimately, utility is what we get from consuming coffee. Assume that the consumer drinks coffee but really values coffee because of the caffeine in it. So consumers demand coffee but are actually deriving utility from the caffeine content. The standard maximizes their utility subject to a budget constraint (income) assumption applies.

Lancaster defined quality as Q = units of attribute / units of good.

For coffee, Quality = Units of Caffeine / Oz of Coffee. So "better" coffee has more caffeine per ounce than weak coffee does.

Think about the size differences. Keep it simple and assume only small and large. In addition to all the other factors suggested above temperature etc... Consumers are revealing how much caffeine they want when they purchase certain sizes of their coffee. All else being equal, large cup people are getting more total caffeine than small cup people.

If an excise tax, a tax on # of cups sold, is enacted then it will give an incentive towards increasing the quality of coffee. The number of overall cups sold will decrease as consumers substitute towards stronger cups and less repeat purchases in order to achieve their desired consumption of caffeine. Avoiding some of the tax.

Think about a consumer who buys two cups in a regular day to get her needed caffeine (Which size doesn't matter). After the tax, she may just demand one really strong cup in order to get her total caffeine intake to the desired level and avoid paying the tax twice.

This is not to say some of the answers above were wrong, but just another way to think about the potential effects of this tax. It seems this puzzle really struck a chord with other listeners.

Jonas Kölker writes:

I think the problem is unsolvable as stated. Why?

First of all, I take it the problem is not of the field study variety (i.e. we are not here to lobby our representatives, then go and observe the real world) but a mathematical one.

What we can reasonably assume is that the market clears (pre-tax), and that we are given supply and demand schedules for coffee at the pre-tax cup sizes.

What we don't know are the supply and demand schedules at different cup sizes. It could be the (highly contrived) case that consumers want at least X mililiters of coffee, but are outraged if that uses more than Y grams of plastic foam for the cups (it's bad for the environment), and thus are only willing to buy cups at exactly one size.

Contrived, but could be. Draw the demand curve for this contrived example. Then draw two different and more reasonable demand curves. Then, what arguments do we have for believing one of the more reasonable demand curves over the other? Other than empirical ones, that is (and we aren't given that data).

Are we to rely on common sense? I point to all the answers already given---many seem common-sensical, and some of the common-sensical ones disagree. Which piece of common sense trumps which?

Does anyone know the minimal set of assumptions one needs to make to prove "the right conclusion"?

karl writes:

Lets say they offer 3 sizes and prices are posted:

s 100 ml $1
m 150 ml $1.40
l 200 ml $1.80
smiles free

Medium gives you 50% more but you only pay 40% more. Not a bad deal. Large gives you 33% more than the Medium but you only pay 29% more to step up. To go from a Small to a Large, you pay 80% more to get 100% more liquid.

Adding a flat 50 cent per cup tax (regardless of size) results in these after tax prices:

s 100 ml $1.50
m 150 ml $1.90
l 200 ml $2.30
smiles $.50

To step up to the Medium you now pay 26% more to get 50% more. (Remember before the flat tax you were paying 40% more money to get 50% more liquid.)

To step up to Large you now pay 21% more to get 33% more than Medium. (Before the flat tax you were paying 29% more money to get 33% more liquid.)

To go from a Small to a Large you pay 53% more to get 100%. (Before the flat tax you were paying 80% more to get 100% more.)

If coffee sizes remain the same, it becomes way more advantageous to get a Medium or Large.

One might assume Starbucks wants to ensure you get 50% more liquid for 40% more money after the tax is applied on a Medium and 33% more liquid for 29% more money for a Large after the tax is applied.

It doesn't really cost Starbucks 40% more money to give you 50% more coffee, however. Starbucks really wants you to move up to the large size. It seems the tax is a god send to Starbucks as customers will realize after tax the Large is the best value (Large costs you 1.15 cents per ml vs 1.5 cents per ml for the small).

So I don't see why Starbucks should even change sizes. It could make the Medium and Large even bigger to give the customer additional incentive, of course.

Alexander writes:

I don't like to write long winded responses. So i will try to keep it short.

If there is $.50 increase on a cup of coffee the amount of coffee consumed will decrease. The increased price creates and incentive for customer to reduce consumption (assuming they are not drinking crack coffee).Incentives are not absolute and changes in behavior are based or individuals preferences of consumption and social factors. There will be some individuals who will not change there coffee drinking behavior and there will be some who will consume less and/or move to a substitute(if one exists).

A good example of a how tax affects consumer behavior is one that is currently in play right now in Australia. There has been a recent tax placed on alcopops (Smirnoff,mike hard lemonade, etc..) The tax has clearly curbed consumption of alcopops. Some consumers still pay the higher price but, most have moved to substitutes.

great podcast Russ..

Gerry writes:

my guess:

a flat tax, itself, on a cup of coffee will have no actual affect on the size of the coffee. However, I think that the seller might ALSO increase the price AND the size of the coffee in order increase the value of (or justify) the coffee and its new price... So that when the consumer sees the new price of coffee they compensated for the extra dimes spent.

Now if the consumers know the tax is coming, I don't believe there is anything a company can do to prevent its sells from suffering in the short-run--whether it's a bigger or smaller or same cup size. In the long run, good marketing might bring their sales back to where they once were.

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