Here is a question from the final exam for my public finance course:
A typical person’s demand for potato chips is given by p=5-q where q=the number of packages of chips purchased, and p is the price of chips in dollars per package. The marginal cost of producing potato chips is $1 per package. The potato chip market is competitive, so p=MC. Dr. Economides estimates that each package of potato chips consumed creates marginal damage of $0.50.
- Illustrate these facts with a diagram.
- Define the phrase “Pigouvian tax”
- Show how a Pigouvian tax could be used in this example to improve efficiency.
- Calculate the revenue raised by the Pigouvian tax. Show on your diagram, and calculate, the efficiency gain created by the tax.
- Opponents of the tax on potato chips take a careful look at Dr. Economides’ study. It turns out that the only people harmed by potato chip consumption are potato chip eaters themselves, as potato chip consumption is associated with bad skin, weight gain and depression. Does this strengthen or weaken the argument for taxing potato chips?
Solutions to parts 1 to 4 are here. The interesting part is question 5: if potato chips only harm potato chips eaters, does that strengthen or weaken the case for taxation? Vote here to express your opinion (only the first 200 answers will be counted).
"Pigouvian taxes" are imposed to make people take into account the full impacts of their actions. The classic example is a carbon tax. Whenever people produce or consume carbon-based fuels they harm other people, from those who breathe in exhaust fumes to future generations affected by climate change. A carbon tax makes people recognize the full cost of their consumption and production choices, thus creates incentives for people to change their behaviour.
The potato chip example, however, is different: the chip eater in the exam question isn't harming other people. The bad skin, weight gain, and depression is experienced by the chip eater himself. It is not obvious that a Pigouvian tax is needed to make chip eaters take into account the harms that they causing – why not just tell people that potato chips cause bad skin, and if people think the chips are worth the zits, let them munch away? They're only harming themselves.
Interestingly, a few of my students thought that this additional information about who is harmed by potato chip eating strengthened the case for imposing Pigouvian taxes.
Why is that?
One possibility is that the students were inadequately taught, or simply didn't study the material.
Some students disputed the basic premise of the question, the idea that potato chip eaters are only harming themselves. Bad skin, weight gain and depression, they argued, are harms to others, because we have a public health system. Yet the starting point for the analysis is that potato chips create damage of $0.50 per package. If chip eaters take any of any of that damage into account when making chip purchasing decisions, the case for taxing chips weakens. Also Canada's public health system often does not cover skin creams, anti-depressants and counselling, so the link between bad skin and depression on the one hand, and health care spending on the other is not obvious.
What interested me about this response was how "health" becomes a lens through which public policy issues are viewed, and a justification of policy choices. Perhaps, though, the students were just mislead by the wording of the question. Guessing that the specific details about bad skin, weight gain and depression must matter in some way, they figured that the question must be asking about health care.
Finally, it seems that some students really don't believe that people are rational decision-makers, fully taking into account the long-term effects of their consumption choices. Even when people are only harming themselves, they support Pigouvian taxes on paternalistic grounds, to stop people from harming themselves.
Today's Chronicle of Higher Education has an article arguing that mainstream economics is dominated by a "free-market fundamentalism," one tenet of which is that people are rational decision-makers. While this may be true, it's far from obvious that mainstream economists are successful proselytizers, bringing others around to their way of viewing the world.
Update: 62 responses to the survey so far, 87% have responded "weaken".
Worthwhile Canadian Initiative 
My immediate thought was: “do the chip eaters know eating chips causes zits?” Then I realised that even in the extreme case where none of them know this, all this means is that the case for the tax is neither strengthened nor weakened.
Ummm, the $0.50 number was pulled out of thin air?
The voodoo of the “Dr.” before the guys name doesn’t make the $0.50 any more of a fact about reality than if a wild monkey somehow generated to number.
Did any student call BS on the notion apt hat a made up “fact” is somehow a fact because it is made up by a “Dr.”?
A famous expire meant of a “Dr.” in a white lab coat instructing people to shock people comes to mind ….
Does anyone realize that the leading free market thinker of the last 100 years rejected this picture?
“mainstream economics is dominated by a “free-market fundamentalism,” one tenet of which is that people are rational decision-makers.”
Mainstream economics in the U.S. is dominated by Democrats, who make up a majority in the discipline.
There is a lot of muddle and myth about economics and the profession packed in the sentence.
“it’s far from obvious that mainstream economists are successful proselytizers”
How hard do you try? I can’t say that I have ever seen an economist, or anybody, trying to convince people that they are rational. 😉
Greg: “Ummm, the $0.50 number was pulled out of thin air?” “Did any student call BS on the notion apt hat a made up “fact” is somehow a fact because it is made up by a “Dr.”?””
Yup, as was the demand function and the stuff about potato chip markets being perfectly competitive. “Dr Economides” is actually the name of a grad school drinking buddy.
Excessive realism makes exam questions far too difficult. Students – being rational and self-interested – just want questions that are reasonably simple and straightforward, and ones that examine the material taught in the class (as opposed to stuff that wasn’t covered.)
Nick, exactly.
Frances: “Nick, exactly.”
Is that right? If you impose the tax then the chip eaters will bear the full harm twice. Once from the tax (that they know about) and then again from the zits (that they don’t). So they will consume the correct amount of chips and you will effect an additional random wealth transfer. So the tax is bad.
I would guess the majority of students who answered ‘strengthens’ fall into the first category (‘students were inadequately taught, or simply didn’t study the material’; I’m presuming the students are freshman or second year?). For the students who fall in the second category you can always add a statement along the lines of ‘assume all premise(s) of question are true’. For the third category, I will give some marks for ‘thinking outside the square’ but not full marks. I would give an extra mark if a student answers along the lines of ‘strengthens unless it can be shown people exhibit systematic cognitive bias towards consuming potato chips in which case it weakens the case’.
Btw, I like this exam question.
I don’t have an issue with the content of the typical freshman econ course (though I wouldn’t mind seeing more eclecticism) but I do believe not enough emphasis is given to distinguishing between positive and normative economics which is a problem. If most of the students who take econ 101 take no other econ course and during the whole of the course the difference between positive v normative economics is given no more than a couple of sentences for definition sake, and they’re being taught out of Mankiws book then I’m not surprised there is a general impression that “mainstream economics is dominated by a ‘free-market fundamentalism’”.
I just don’t think most undergraduate students are sophisticated enough to grasp the subtle difference between a policy which is ‘optimal efficiency wise’ (which is the position often being taught in class) and a policy which should be supported on normative grounds due to morality, ethics, socio-political factors etc. etc.
hence the belief that ‘economics is inherently ideological’.
*impression (instead of belief)
A part of my explanation – building on Coase – for the pathology which is “economic science” is that much of what is ordained as “science” has been driven by what is easy for professors to teach & test, e.g. Samuelson’s textbook was great for teaching to engineers & graded by TAs and even grading machines.
“Excessive realism makes exam questions far too difficult. Students – being rational and self-interested – just want questions that are reasonably simple and straightforward, and ones that examine the material taught in the class (as opposed to stuff that wasn’t covered.)”
I think the answer to 5 must be – you’ve never cleaned buses or cinemas.
Since the information in #5 states “the only people harmed by potato chip consumption are potato chip eaters themselves” I would write an answer that says the case for using a Pigouvian tax is weakened. But the actual wording of the question is: “Does this strengthen or weaken the argument for taxing potato chips?” So I had to ask myself “does the professor mean to include non Pigouvian taxes?” Here in New York and other parts of the US there are proposals to tax soda and other sugary drinks. The parallel between potato chips and soda led me to think that maybe the professor is referring to “sin taxes.” Thus, although the tax is not Pigouvian, the case for it still exists (is strengthened). Perhaps I would have known the professor’s meaning had I gone to lecture, but, alas, I overslept that day.
Michael,
good point. Both revenue and paternalism are perfectly valid reasons for a tax. If the effect is more concentrated, it may make the paternalism argument stronger not weaker.
Michael,
Assuming the same quantity of harm, the case for the tax is reduced. In both cases, the tax will result in the optimal amount of chip consumption. But in the case where the harm is to the consumer, there is an additional effect of an unjustified wealth transfer from chip eaters to the public. Including the resulting possible income effects means the tax is less justified.
K,
The health care economics textbook I used last semester has an entire chapter on “health capital.” The analysis is parallel to “human capital.” Could it be that the inefficiency you identify is simply an investment cost of health capital? As a parent of a teenager I would like her to reduce her consumption of chips and soda both today and in the long run. Today I am trying to modify her habits with respect to her long-run health not just her current behavior. Perhaps this is one of economic sciences’ limits: it takes preferences as given, I want to modify them.
….as potato chip consumption is associated with bad skin, weight gain and depression. Does this strengthen or weaken the argument for taxing potato chips?
If a close of you is depressive, you will be affected too…
Then revise your argumentation
K “Is that right? If you impose the tax then the chip eaters will bear the full harm twice. Once from the tax (that they know about) and then again from the zits (that they don’t). So they will consume the correct amount of chips and you will effect an additional random wealth transfer. So the tax is bad.”
Economic analysis tends to focus on efficiency. The way this question is structured, it turns out that, on the margin, the reduction in harm outweighs the reduction in chip eating enjoyment, so the tax increases efficiency.
Yet, as you rightly point out, there is also a redistributive effect – and for things like carbon taxes, the redistributive impact can be very large relative to the efficiency impacts. But because economists tend to ignore these redistributive impacts we’re left scratching our heads unable to figure out why people don’t like our carbon tax proposals.
Michael: “So I had to ask myself “does the professor mean to include non Pigouvian taxes?” ”
K gives a good answer to your concern. It’s a ceteris paribus thing. All else being equal, if people recognize harms that they themselves suffer, there a weaker case for taxing potato chips. Taxation is actually next term, and in that course I tell students that, if you’re going to remember anything from this course, its: broad base, low rate.
reason: “you’ve never cleaned buses or cinemas” 😉 True. That would strengthen the case for soda taxes, too.
DavidN ” policy which should be supported on normative grounds due to morality, ethics, socio-political factors etc. etc.”
We do some formal normative econ in the course, e.g. social welfare functions, social indifference curves, the utilitarian case for income redistribution. People typically don’t connect with it – perhaps because it’s taught in much the same way as consumer theory is taught, and students typically don’t enjoy that, either. It is something I need to find a better way of teaching.
Marc “If a close of you is depressive, you will be affected too…”
Exam questions very often taken the form “True, false, or uncertain: If A, then B.” The aim of the question is to see if students understand the nature of the relationship between A and B. A good number of students will generally reply “Not A.” Even if “Not A” is a perfectly reasonable position to take – potato chips make buses hard to clean, depression hurts other people – it doesn’t address the issue at hand, which is “If A, then B.”
What’s sometimes called “exam technique” is often just simple logic.
Michael – “Perhaps this is one of economic sciences’ limits: it takes preferences as given, I want to modify them. ” As I noted in the post, this is a very common position. With regards to your own children perhaps you have a right, even a duty, to shape their preferences. But do you have a right to modify or disregard mine? Perhaps I smoke ’cause I’m hoping for an early death, and I need to cling to something. So why take it away from me?
Frances,
I do not have the right to modify your preferences, but I do believe that through democratic processes the community has that right. I cannot imagine a society in which the community is not modifying and disregarding preferences. With democratic processes we humans are simply gaining some control over our social ordering. Ah, but this takes us far away from economics.
Michael : “I cannot imagine a society in which the community is not modifying and disregarding preferences.”
And it’s always been our most important social institutions that have modified preferences (and vice versa). Historically that was family, church, state. Now it’s Walt Disney and McDonalds. But when students have got their basic values from watching Family Guy, it’s really hard to even have a discussion about morality and ethics. People tend to like the idea of rights, but then the question becomes “what do we do when rights conflict?” When my right to eat potato chips conflicts with your right not to pay for health costs associated with self-inflicted harms. It’s one thing to talk about introducing values etc into economics, it’s less easy to do it when faced with a class of 60 (or 200) students, all of whom have different value systems.
“I do not have the right to modify your preferences, but I do believe that through democratic processes the community has that right.”
Perhaps, but countries like Canada are not merely democratic societies, we’re LIBERAL (small “L”) democratic societies, which usually take as their starting point the proposition that people should be free to do whatever they want unless there’s some offsetting harm to the broader community.
I suppose it’s a fair intellectual critique of economics that, as a social science, it starts from that proposition (although it’s not wholly surprising, given the intellectual origins of economics in the liberal enlightenment). That being said, given the liberal democratic nature of countries like Canada and the US, that’s hardly an unreasonable starting point for a social science. Moreover, I suspect that many of the people who would make that critique are somewhat selective in terms of the choices that they think community can constrain through the democratic process (i.e., the same people who are keen on having the “community” decide to tax potato chips likely wouldn’t be so keen on having the “community” decide to tax, say, abortions).
Michael: “Perhaps this is one of economic sciences’ limits: it takes preferences as given, I want to modify them.”
Some people, and especially kids, exhibit hyperbolic discounting. They are simply unable to coherently weight future consequences in their choices. It’s a case of severe time inconsistency and it’s hard to see it as anything other than irrational. Rather than modifying her preferences, I would see what you are doing as helping her become a more rational decision maker (not neglecting her future preferences). But certainly rationality is probably the most pervasively wrong assumption in economic modeling. And not coincidentally, also the most critical in producing parsimonious, elegant and mathematically tractable models.
Frances: “we’re left scratching our heads unable to figure out why people don’t like our carbon tax proposals.”
Of course, you are supposed to pay the revenues to all those who are harmed by the emissions, but if you just paid it out equally to all Canadians you might find overwhelming support. The evil-doers will be paying their fair share and Canadians would be grossly overcompensated since most of the harm is elsewhere in the world.
“The way this question is structured, it turns out that, on the margin, the reduction in harm outweighs the reduction in chip eating enjoyment”
I see that now. You make a good case for sin taxes. But it would be better if you could get the revenues back to chip eaters. Since giving them the money would defeat the purpose (unless you could deceive them as to the relationship to chip consumption which might not be too hard since they were pretty easy to deceive about the health effects of chips), maybe you could attach a Lipitor and a little tube of zit cream to each bag of chips. Or if, in fact, they suffer from hyperbolic discounting, just pay them in the future.
Bob: “A sin tax on abortion”
That’s disgusting, Bob. EeeeW. Apart from that I agree with you.
Mike Moffatt (citing other people) seems to lean toward: yes, that is an externality, or at least if we’re talking about time-inconsistent preferences. Or, at least, if a Pigovian tax creates time-consistent behaviour on inconsistent individuals, and causes increased total welfare, then the case for imposing them is not different than imposing such a tax to increase total welfare by removing the disutility caused upon others.
http://economics.about.com/b/2010/03/18/can-you-impose-an-externality-on-yourself.htm
K “Or if, in fact, they suffer from hyperbolic discounting, just pay them in the future.” interesting.
Kelvin: “Or, at least, if a Pigovian tax creates time-consistent behaviour on inconsistent individuals, and causes increased total welfare, then the case for imposing them is not different than imposing such a tax to increase total welfare by removing the disutility caused upon others.”
If a student gave a response along these lines, and correctly noted that this doesn’t strengthen the case for Pigouvian taxation, but just it leaves it unchanged (harms imposed on your future self are just as worthy of correction as harms on other people) they would receive full marks.
Terry McGarty comments on this post here http://terrymcgarty.blogspot.com/2011/12/pigou-and-potato-chips.html.
Terry, even if 80% of the costs are borne by non-chip eaters through health care expenses, the case for Pigouvian taxation is weaker than it would be if 100% of the costs were born by non-chip eaters.
Also, as Chris Auld has argued elsewhere, what matters is the net impact of smoking, obesity etc on expenditures. Just think of the savings to the Social Security system when chip eaters drop dead at 64.
Frances Woolley: “Even if “Not A” is a perfectly reasonable position to take – potato chips make buses hard to clean, depression hurts other people – it doesn’t address the issue at hand, which is “If A, then B.”
“What’s sometimes called “exam technique” is often just simple logic.”
That depends on what you mean by ‘If A then B’. If it means material implication, as it does by simple logic, then “not A” says that it is true. (Anything follows from falsehood.) And, since anything follows from falsehood, the students who answer “not A” are pointing out the weakness in the argument.
Let’s look at the statement in question in Q. 5: “It turns out that the only people harmed by potato chip consumption are potato chip eaters themselves, as potato chip consumption is associated with bad skin, weight gain and depression.” Exam technique is a game, and, since I know the game pretty well, I realize that the phrase, “It turns out” means that what follows is to be assumed in the answer. Students who don’t pick up that clue, or those who don’t care (and are willing to risk a bad grade on this question), will take the statement that the only people harmed are the chip eaters, not as an assumption or fact, but as a conclusion to a bad argument. They then will criticize the conclusion. Logic, as you say. 🙂
English not being logic, “if A then B”, often means “given A then B” or “assuming A then B”. With that meaning, then “not A” is irrelevant. The truth of A is assumed. I read “It turns out” as “Let us assume”. Suppose that the phrase were, “They claim” (“they” being the opponents of the tax). Then “not A” is quite relevant. Now, the question could have made the assumption explicit. For instance, “If the harm were limited to chip buyers, would that strengthen or weaken the argument for the tax?” Yes, that would make the game easier. But what do you want to test? 🙂
Frances: “interesting”
Yeah, but weird: selling chips with embedded 30 year bonds? Presumably people would just adjust their bond holdings. Unless there’s evidence that chip eaters (and smokers) don’t own bonds. Or maybe people are time inconsistent for lung cancer but not for dollars??? In which case it wont work at all. Seems to me like people just find ways to repress thinking about bad things like dying. In which case the best policy is to shove it in their face like we do with gruesome pictures on packages of cigarettes. Maybe we need to put really gross pictures of morbidly obese people on bags of chips. Enjoy!
“(i.e., the same people who are keen on having the “community” decide to tax potato chips likely wouldn’t be so keen on having the “community” decide to tax, say, abortions)”
That may be true, but surely taxing abortions would be much preferable to having them criminalised (then pro-choice people could switch to raising may to pay for them).
“Also, as Chris Auld has argued elsewhere, what matters is the net impact of smoking, obesity etc on expenditures. Just think of the savings to the Social Security system when chip eaters drop dead at 64.”
I think the full analysis of this is difficult. Maybe they drop dead at 64 after having had a stroke at 53.
Indeed, and taxing chips would be much preferable to having them banned, but I can understand why chip eaters might not really appreciate that distinction. (Plus, I don’t want to have to buy my doritos from the Hell’s Angels). The ability to visualize a worse alternatives doesn’t relly make a bad policy better.
I wrote: “Now, the question could have made the assumption explicit. For instance, “If the harm were limited to chip buyers, would that strengthen or weaken the argument for the tax?” Yes, that would make the game easier. But what do you want to test? :)”
Perhaps you wanted to ask something else, like: “If the chip buyers bear much of the harm, does that strengthen or weaken the argument for the tax?” 🙂
BTW, my answer would be, it would affect the size of the tax, not the argument. 😉
“I think the full analysis of this is difficult.”
Sure it is, but I believe that a number of valiant attempts have been made. In any event, even if you don’t think chip eaters impose a net cost on the fisc, that cost is likely to be significantly less than just the gross cost of treating chip related illnesses.
Bob Smith,
ah yes, but we live in an imperfect world. Sometimes a bad policy is an improvement.
Min: “Students who don’t pick up that clue, or those who don’t care (and are willing to risk a bad grade on this question), will take the statement that the only people harmed are the chip eaters, not as an assumption or fact, but as a conclusion to a bad argument. They then will criticize the conclusion.”
In general, yes, this is something that one encounters frequently when marking exams.
But wouldn’t the “conclusion to a bad argument” reasoning led students to answer “it weakens the argument for the tax, because clearly Dr. Economides’ study is totally bogus”? Whereas in fact a number of students wrote that the specific harms (bad skin etc) strengthened the argument for taxing chips.
On your suggestion for rewording: The question asked was: “It turns out that the only people harmed by potato chip consumption are potato chip eaters themselves, as potato chip consumption is associated with bad skin, weight gain and depression. Does this strengthen or weaken the argument for taxing potato chips?” Your suggested rewording is “”If the harm were limited to chip buyers, would that strengthen or weaken the argument for the tax?” Perhaps your wording is better – it’s direct, and less wordy, and my students frequently complain that my exam questions are too wordy.
My worry with your suggested wording is that the students would be at a loss to figure out what “the harm” refers to. I guess you could say “If the 0.50 marginal damage were limited to chip buyers…” But again, I don’t think they’d understand what that meant.
“ah yes, but we live in an imperfect world. Sometimes a bad policy is an improvement”
Sure, if were had a starting point where chips were illegal, I’d agree.
Min: “They then will criticize the conclusion” – so I guess the argument is that if harm to chip eaters = 0.50, then total social harm is 0.50+x, where x is the health care costs, so the case for taxation is strengthened.
So there’s this kind of health care costs “multiplier” which – like the multipliers cost benefit analysts know and love – can be used to blow up any effect to get you the results that you want.
I’m not sure I understand Nick’s comment. Are you saying that only in the case where no one knows the link is the case for the tax unchanged? I agree with that. But the more people know, the weaker the case,no? If all know, the WTP schedule is the Marginal net benefit – net of the .50 marginal cost of more weight or zits – and so a tax would distort, right?
@ Frances Woolley:
I don’t know about the best wording of the question, but I do like giving context, since that is closer to the kind of question students will face in real life. 🙂 Perhaps something like this:
Opponents of the tax on potato chips take a careful look at Dr. Economides’ study. It indicated that the potato chip eaters themselves were harmed, as potato chip consumption is associated with bad skin, weight gain and depression, and the $0.50 is his estimate of the harm to potato chip eaters. Does this additional information strengthen or weaken the argument for taxing potato chips?
Kevin, don’t have time to really think things through (am busy marking the question about the surgery on Prof Woofey’s dog) but your reasoning looks correct to me.
Min – that’s saying that the damage to chip eaters is $0.50, leaving open the question of whether or not there is additional damage over and above the original $0.50 estimate. The way I asked the question says the total damage is $0.50, and that harm mostly falls on chip eaters. But then again, I’m biased, so probably not the best judge.
Frances: I think this is related to the last paragraph of your post. When I teach commons goods, I go through a little model of traffic congestion. I show them that if the road were privately owned, the owner would maximize toll revenues by charging a fee equal to the Pigouvian tax. Then I say: or we could have the state charge the toll and send everyone a check at the end of the year equal to the total toll revenues divided by the number of people who use the road. Many are sure that in the latter case, people would have no incentive to change their behavior – they get the money back, on average, after all. When I explain that the marginal addition to the check they get at the end of the year when they get on the road is the toll/N, where N is a big number, and so is negligible, they don’t budge. But here’s the thing, if people are like my students, and we did institute such a congestion tax with a rebate, THEY WOULDN’T CHANGE THEIR BEHAVIOR and the policy would fail!
“Strenghten” actually makes sense through the health care channel. If public health care is inefficient, say it costs the public $1 net to offset the damage and that’s what happens given the law, the social cost is increased.
But that violates the assumption that the non-monetary cost is $0.50, which is not lifted in Q5; Q5 is only about the incidence.
I guess there’s no non-behavioral/non-paternalistic way out.
Kevin: “send everyone a check at the end of the year equal to the total toll revenues divided by the number of people who use the road”
There’s something wrong here. So I just have to use the road once to get an equal share of the congestion tax? Surely the harm is roughly both inflicted and borne in proportion to how much someone uses the road. So no tax required. Or maybe non-users bear an indirect cost in which case the revenues should be distributed to everyone. But I can’t see a case for equally among drivers.
Fran , I admire your willingness to subject an examination question to outside scrutiny; I’m not sure I would have the courage to do so! Interesting experiment, though, demonstrating just how difficult it is to create questions that work in confining students to the words on the paper.
Kevin – would you mind posting that question? I’m trying to think of a simple way of modelling the fact that that toll revenues are maximized by charging a fee equal to the Pigouvian tax.
I have one that’s a bit similar with carbon taxes, drivers and cyclists, revenue going back to drivers and/or cyclists, and a political equilibrium. I love the question, but it’s very complicated, and takes a long time to go through.
Franz, yeah, but people tend to forget the assumptions stated at the beginning by the time they get to Q5.
Linda – well, having scrutinized someone else’s question just a few weeks ago, it only seemed fair to subject mine to the same treatment. I’m glad to see, though, that WCI readers are mostly answering ‘weaken’, suggesting the question wasn’t too bad.
Frances: sure.
There is a highway that goes from point A to point B directly. There are many circuitous local routes between A and B that take 45 minutes and never get congested. On the highway a trip takes 15 + (1/60)T minutes, where T is the number of trips being taken, so one more trip adds one second to the trip time of all the other drivers. What is the Time saved by using the highway as a function of T? (30- (1/60)T
Graph this function of T. How many people will use the road if there is no charge? (30-(1/60)T* = 0, so T*=1800.) What is the marginal external cost of a trip as a function of T? ((1/60)T). Graph it on the same diagram. What is the optimal number of trips? (MB=MC where 30-(1/60)T** = (1/60)T**, so T**=900.) As Benjamin Franklin knew, Time=Money. To make things simple, let’s say all drivers are alike and value time at $1/ minute. So your diagram now tells you the dollar value of a trip on the highway as well as the dollar value of the external cost. Suppose you own the road. How many trips will be taken if you charge a $30 toll. (O) If you charge nothing (1800). If you charge $15? (900). Can you see that the dollar value of a trip function is the(inverse) demand function for trips?
Suppose that your costs are all fixed costs, so you maximize profits by maximizing revenues. Remember how to maximize revenues with a linear demand curve? What toll would you charge to maximize revenues and how many trips will be taken? ($15,900).
Kevin, thanks, nice question.
Damn, I left off the punchline:
What is the Pigouvian tax that will correct this externality? (At the optimal T=900, the marginal trip imposes a cost of 1 second on each of 900 drivers, for a total of 15 minutes. With our assumption about the value of time, then, the Pigouvian tax is $15, just what the greedy road-owner would charge to maximize profits!)
Kevin, would you expect students to work this out on their own? At what level? I mean it’s easy enough see that people use the highway until the time saved from doing so equals zero once you think about it, but can students work that out without you going through an example first?
Kevin quinn: “But here’s the thing, if people are like my students, and we did institute such a congestion tax with a rebate, THEY WOULDN’T CHANGE THEIR BEHAVIOR and the policy would fail!”
That reminds me of a story that one of my professors at UofT used to tell from his early days of teaching in the 1970’s. The big issue of the day was rising gas prices, and he’d have a big discussion with his class about the need (or not) to subsidize or otherwise regulate gas prices. In his early days, say, 1973, he’d make the case that rising gas prices wasn’t the end of the world, that people would change their behaviour (i.e., drive less, drive smaller cars, take public transit, etc.) and that there was no need to subsidize or regulate the price of gas (and that it might be inefficient to do so) – and his students would go nut: “people need to drive”, “it’s an essential good”, “it’s a neccesity”, “what about the poor? Won’t anyone think of the children?”. And so it went for a couple of years.
Then, one year, he got up and made the same argument, that there was no need to regulate or subsidize the price of gas, people would adjust their behaviour, yada, yada, yada, expecting the usual objections. But no, his students just looked at him like he was a moron: “Well, duh, sir, everyone knows that!”. While his intuition might have eluded his earlier classes, in the intervening years, his new crop of students had lived that intuition such that it was a self-evident truth.
I wonder how many of your students would change their answer after a couple of years of paying road tolls.