Popularizing Deadweight Loss

by on October 29, 2010 at 7:30 am in Economics, Education | Permalink

Indy requests a popularization of deadweight loss. Let's do the deadweight loss from a tax.

Imagine that you want to go to New York on a trip.  You value the trip at $50 and a bus ticket costs $40.  Do you take the trip? 

A. Yes.  The value ($50) of the trip exceeds the cost of the ticket ($40) so you travel to New York.   

How much consumer surplus (net value) do you get from the trip?

A. $10=$50-$40.

The government taxes bus tickets which raises the price of a bus ticket to $60.  Do you take the trip?

A. No. The value of the trip is now less than the price of the ticket.

What happened to the $10 consumer surplus which you used to get when there was no tax?

A. It's gone since no trip takes place.

Did the government get any tax revenue from you?

A. No.

Key idea: Consumers lose but the government does not gain from trips that are not taken.

Conclusion: Deadweight loss is the value of the trips (trades) which do not happen because of the tax.

1 josh October 29, 2010 at 4:05 am

Easy peasy. How about fixed costs vs. variable costs? Should be common knowledge, but I notice a lot of people have very confused assumptions about how businesses set prices.

Also, the concept of a price-taker is pretty important and little understood.

2 anon October 29, 2010 at 4:20 am

But there is something odd here. Let's say the price of fuel goes up and the company raises the price to 60 dollars. Is that a deadweight loss? IIRC the answer is no.

But, a government tax is also just an input cost – it's the cost of providing the public goods that the bus company requires to operate.

So why the special emphasis on the consumer surplus lost for that specific reason?

3 John Farragut October 29, 2010 at 4:47 am

"But, a government tax is also just an input cost – it's the cost of providing the public goods that the bus company requires to operate.

So why the special emphasis on the consumer surplus lost for that specific reason?"

If P = MC = 60 due to oil prices or whatever, then taking the trip would destroy value. So it is efficiently not taken. With the government tax, MC = 40, so the trip is worth more to the rider than it costs to offer. But the price P = 60 doesn't reflect the true cost, MC, so the trip is not taken. There is foregone value to society.

4 andy October 29, 2010 at 4:55 am

But you will use the $40 on something else, wouldn't you…?

5 spencer October 29, 2010 at 5:00 am

Wouldn't you use the $40 on whatever gives you $9.99 in consumer surplus?

6 biL. October 29, 2010 at 5:03 am

andy asks: But you will use the $40 on something else, wouldn't you…?

Yes, but you will get less than $10 of net value out of that expenditure.

(Otherwise you would have initially spent the $40 on "something else" instead of taking the bus trip.)

7 andy October 29, 2010 at 5:21 am

Tyler: Conclusion: Deadweight loss is the value of the trips (trades) which do not happen because of the tax.Conclusion: Deadweight loss is the value of the trips (trades) which do not happen because of the tax.

biL: Yes, but you will get less than $10 of net value out of that expenditure.

Seems to me that Tyler's conclusion and your conclusion are a little bit contradictory. Wouldn't the 'deadweight' loss be some difference between the course I have taken and I would have taken lest the government didn't tax me… but the course is always different and not all of it is deadweight loss…?

8 AL October 29, 2010 at 5:25 am

So lets say you wanted to buy product X at 1000$. your state charge tax rate y which raises the total cost to something more than you value the product to be. your neighboring state has a tax rate 0.5y, which brings the total cost below your value for the product.

You're still not maximizing your utility for the product, your state misses out on all that tax revenue so the only person that made out here was the neighboring state.

does that fit here?

9 Doc Merlin October 29, 2010 at 5:39 am

"Can you please give a (famous?) real life example of significant economic magnitude where a taxation counter-productively lead to dead weight loss and lower tax revenue."

When Regan's congress instituted a luxury tax in Yachts. People stopped buying them from the US, and Yacht makers had to lay off all their workers and go out of business .

10 Floccina October 29, 2010 at 5:47 am

I think a better example is a guy who would pay 20 after tax dollars to have his lawn mowed but will do it himself if he needs to pay more than $20. The lawn mowing service can mow his lawn with an hours worth of labor including capital and everything but it takes him 2 hours. His mowing his own lawn is not taxable but the lawn mowing service has to pay all kinds of taxes because of those taxes they charge more that $20 dollars and the man mows his lawn himself. He loses and the mower service loses.

11 figleaf October 29, 2010 at 6:04 am

Hmm… seems to me in Alex's simple illustration the situation couldn't remain in equilibrium anyway since the bus company's leaving $10 on the table for every trip.

So a more correct model would be that it's worth it for you to ride the bus to New York City for $50 the bus company will charge you $50. Now what happens when the government imposes a $10 tax? Yes, in Alex's example the tax would be $20, in which case there would indeed be deadweight loss… of $10. But up to a $10 tax you'd probably just see the bus company lower its price back to the original $40. In an efficient system under Alex's artificially simplified model, your long-term ticket price wouldn't change at all.

Or let's say we enter Alex's halcyon world where there's no government and no taxes. The bus company mistakenly charges $40 to get you there, even though it's worth up to $50 for you to go. Then some combination of private toll collectors, highway robbers, or infrastructure deterioration will combine to get your $10 anyway.

Oh right. One last model tweak to make the example even more Libertarian. Let's say it's been worth $50 for you to go to New York but the bus company has only needed to charge $40 because the government has been subsidizing bus company operations by providing right of way, road construction, oil production, and law enforcement through general tax revenue. Matt Yglesias gets into office and with a stroke of his pen eliminates all such general subsidies, lowering the income tax on the other 250 million Americans including you and the bus-company owner by about (calculating…) $0.00000008. The combined, subsidized cost of going to New York turns out to have been $60, thus the $20 tax increase the government imposes brings the cost of a trip to its actual true cost. If it's still only worth $50 for you to go to New York then neither you nor the bus company should have been doing business in the first place.

What do you plan to spend your $0.00000008 refund on?


12 anon October 29, 2010 at 6:25 am

Actually it is unclear the 1990 yacht tax case is a clear cutexample of deadweight loss. According to Bernanke the problem was that the tax was not applied to imported yachts, causing consumers to buy those in detriment of the one's built here.

13 ben October 29, 2010 at 6:44 am

I teach economics, and deadweight loss is one of those things where it's very tricky to explain the intuition- most books don't even try. I like your example, but the problem is (as others have pointed out) that you will spend the $40 on something else that the government taxes and that provides consumer surplus.

I think you can do it if you get a bit more convoluted- say, you're trying to decide how many hours of overtime to work to pay for your weekend trip. The effect of the tax is that instead of buying a more expensive ticket to NY you buy a cheaper one to less appealing Philadelphia. So, because of the tax you work fewer hours, your firm produces less, the government forgoes the tax revenue they could have gotten for you would have produced, etc., and you can show everyone loses.

14 Jim October 29, 2010 at 6:50 am

Speaking of yachts, John Kerry (MA Senator) decided to dock his yacht in Rhode Island in order to dodge the MA sales tax, which had recently gone up from 5% to 6.25%. The deadweight loss to Massachusetts was over $400,000. Before he was caught, of course.

Who knows how low the rate would have to be to get Kerry to follow the law, but it's safe to say that a lower rate would result in a greater likelihood of income for the state of Massachusetts.

15 J Thomas October 29, 2010 at 7:03 am

You want to go to New York. You spend $40 on a bus ticket.

In New York, you spend $20 on famous New York pizza, made with special imported cheese. Then you spend $10 for some famous New York cheesecake, also with special imported ingredients. You spend $100 on a lebanese prostitute who sends much of her income home to her aged mother in Beirut. Much more exotic than plain old Dolores, who regularly gets your $35 and sends some home to her mother in Nebraska. You find a duty-free shop and buy some booze, for $200.

On the bus ride home you notice that your feet hurt, your stomach hurts, your head hurts and you're beginning to get that little burn that says you might be getting the clap again. You know that just like last time you'll drink up the booze quick with your "friends" and the result will be longer and harder hangovers, you probably won't even remember how good it felt. As you think about it all, with the afternoon's whiskey starting to fade away, you think that next time for $10 you'd just stay home.

Then the bus company raises their price by $20.

OK, that's enough, it isn't worth it. Next time you eat pizza from Mr. Gatti, cheesecake from Safeway, you spend some time with Dolores, and $20 in booze locally. Your total savings:

$40-60 not spent on the bus,
$15 not spent on pizza,
$ 5 not spent on cheesecake,
$65 not spent on women,
$180 not spent on booze.

180 minutes not spent on the bus,
80 minutes not spent on the subway,
90 minutes not spent walking.

Your stomach hurts, your head hurts, and you have that little twinge that you may have given Dolores the clap and she'll be ready to give it back to you soon. But your feet don't hurt and you don't smell like a bus.

The bus trip used to have a $5 tax and now it has a $25 tax. The government is out $5 because you didn't go to New York. But it gets that back on taxes on your $20 booze, plus over $100 of your money would have gone straight out of the country and contributed to the balance of trade deficit.

You think it over. "That was OK but really nothing special. For $10 or maybe $20 I'd go back into New York again and splurge."

16 Yancey Ward October 29, 2010 at 8:04 am

Wow. Alex, you will have to try again, it appears from the comments.

17 libert October 29, 2010 at 9:18 am

Alex & Doc Merlin both use the example of the yacht tax. It may be a good example, but both posts make a all-too-common mistake.

They both count the "bunch of workers out of work" as a cost of the policy. On the contrary, any good economist will tell you that this is a benefit. Remember: labor is a cost of production. The fact that workers got laid off actually helps reduce the deadweight loss. Imagine if they had kept their jobs, making yachts that no one wanted to buy; that would have been a wasteful consumption of labor and capital resources.

18 Jens Fiederer October 29, 2010 at 10:26 am

I think one problem is politics: people knowing and disagreeing with Tabarrok's politics simplify this example to "Taxes are bad" and launch into their refutation.

I don't think this was meant that way, though. Nobody said you were the bus company's ONLY customer. Some customers's undoubtedly had a consumer surplus of $30 originally, found the surplus reduced but still worthwhile, and splurged. In those cases, the taxes DID raise money — yay (assuming the tax money is being spent wisely)!

The point would be more that the deadweight loss is something to consider in the big picture, which is not an issue in this example. Whether the tax is good or bad depends on how many people were deterred and by the deadweight and, for those not deterred, the utility of the tax money collected compared to what the utility that extra money would have been in our dude's pocket.

19 Roger G. Jolley October 29, 2010 at 11:25 am

<<They both count the "bunch of workers out of work" as a cost of the policy. On the contrary, any good economist will tell you that this is a benefit.>>Posted by: libert>>>

This is an unfortunate way to explain things, especially if its true its a benefit somehow…""bunch of workers out of work" as a cost of the policy….any good economist will tell you that this is a benefit.""

The American people are wildly scrambling to keep on without jobs. Economist reminding each other that a bunch or workers out of work is a benefit just sounds bad.

Besides, whatever money is saved by not having a labor force anymore is of no benefit because there is also no customer and thus…no profit. Where's the benefit in that?

20 JR October 29, 2010 at 12:05 pm

In this example, is deadweight loss $10, $40, or $50?

21 JR October 29, 2010 at 12:09 pm

In this example, is the deadweight loss $10, $40, or $50?

@spencer, I believe the standard answer is that a tax on employment has a similar deadweight loss from jobs that a consumption tax on bus tickets has from bus ticket sales.

22 mulp October 29, 2010 at 12:58 pm

The value of the trip is $50.
The cost to the bus company is $40.
The cost to taxpayers for military middle east policy to keep oil price down, plus the cost of the depreciating bridges built 50 years ago, plus the cost of failing to invest in expanding tunnel capacity into NYC to support population growth causing longer travel times, etc totals $20.

The trip to NYC gets a $20 subsidy paid for by the unborn in military debt and unfunded anticipated bridge failure from use, plus inefficiency spread among all travelers to NYC in wasted time from congestion.

If the ticket price reflected more accurately the costs, fewer trips would be taken reducing the demand for capacity reducing the wasted travel time and unmet demand for added capacity, and funded replacement for depreciating productive assets, and less need to fight wars around the world to keep oil prices lower.

We might also consider the price of that bus trip in 1979 and in 1999, with the price starting at $50 (real, $15 nominal) falling to $30 as a consequence of deregulation of transportation and increased regulation of vehicle design – in the former case, bus travelers substituted plane travel, driving down the quality of bus travel (fewer choices, less convenience, less access) and air travel (lower status, bus like crowding, less comfort) while the CAFE standards drastically shifted the oil demand curve resulting in declining real fuel prices. The low fuel prices and lack of maintaining CAFE pressure plus rise of Asia drove up fuel prices and the price of the ticket to $40 even as the military intervention funded-by-debt costs skyrocketed.

In the two decades after deregulation, both the bus companies and airlines reduced service quality while losing money consistently and ending up in total bankruptcy. What do we call the transfer of shareholder value to passengers? Are the passengers a dead-weight loss to shareholders?

We might also consider the driving alternative which depends on lots of subsidies, especially in the wasted time of the passenger working for free as the pilot/driver/navigator, something we know they don't want to do giving the number of auto drivers trying to read, hold meetings, write memos, be hair dressers and manicurists, while driving. If in a horse drawn cart, you would be able to delegate the driving to the horse and use really low cost roads, but cars force you to pay attention to driving while demanding government build high quality roads right to your house.

23 Rahul October 29, 2010 at 5:41 pm

The whole argument seems very elegant. But I scarcely know of "real" people that make decisions in terms of "consumer surplus". When I decide on spending $50 on a bus-trip instead of a Kobe-steak did I really do it on the basis of the fact that the bus trip provided me with a greater consumer-surplus?

Think about the last 5 most expensive items you bought today. Now try to write down the consumers-surplus you got out of them. If I ask you the same question tomorrow would you have answered the same? Did you really take those decisions on the basis of a "consumer-surplus"?

I just feel that people making decisions are not so rational and uni-dimensional as economists sometimes pretend.

The whole dead-weight-loss model is very elegant. But the realism of it's axioms makes me question how valid and useful this is.

24 Rahul October 29, 2010 at 5:45 pm

Are dead-weight losses specific to taxation? Or can they be used in other contexts?

25 J Thomas October 29, 2010 at 8:28 pm

"Hey, man, you run a lumber company, right?"
"Why, yes I do."
"Well, I read that anytime you clearcut a square mile you plant trees in the whole thing afterward. Right?"
"Yes, we do."
"And when you pay to do that, you pass the costs on to your customers, don't you?"
"If our costs didn't get paid by our customers we couldn't stay in business."
"And how long does it take those new trees to grow up so you can cut them down?"
"Sixteen years, usually. Sometimes seventeen."
"Well, I'm a building contractor, man. And I buy the lumber made from the trees you cut down. I pay you to plant trees, and that doesn't do me any good at all. Somebody else sixteen years from now will get those trees, not me."
"Yeah, man. The money you spend planting tress is a dead weight loss to me. i could afford to buy more lumber if you didn't charge me for that."
"But if we didn't plant trees, where would the trees come from that you will need in 16 years?"
"Don't worry about that! As long as the government stays out of it, supply and demand will make sure we have the right number of trees. Free markets at work. It never fails. But right now you oughta stop charging me for you to plant trees. It's a dead weight loss, man. I don't get anything at all from it and I'd buy more lumber if you cut the price."

26 Gil October 29, 2010 at 9:06 pm

Just as a follow-up:

"Think about the last 5 most expensive items you bought today. Now try to write down the consumers-surplus you got out of them. If I ask you the same question tomorrow would you have answered the same? Did you really take those decisions on the basis of a "consumer-surplus"?"

You don't have to precisely calculate consumer surplus to point out that an increase in price, whether by tax or regulation or imperfect competition will price x number of consumers out of the market. The sellers who would have sold to those buyers at the lower price don't make the sales. Part of the problem with putting a number on that is determining what the equilibrium price would have been without the intervention/imperfection, but that doesn't detract from the general point of the concept.

27 Steve Roth October 30, 2010 at 8:31 am

Deadweight loss is a useful concept/thought experiment, but it's overemphasized, perhaps because of its inflammatory title. It should probably get less attention than it does, because the price/supply/demand/quantity diagram/model, by its very nature, doesn't incorporate exogenous effects of the thing causing the deadweight loss.

Impose taxes on a good, the PSQD diagram shows quite clearly that there's a deadweight loss.

But there are innumerable effects of that taxation (or other influence) that are exogenous to the diagram — and those effects themselves actually feed back to affect the diagram. i.e. if the taxes are well spent and the economy grows, that will result in increased supply and demand for the good (not necessarily equally).

So again: a useful thought experiment, but not at all useful all on its lonesome.

This is why we have macro in addition to micro. Because micro arguments are necessary but not nearly sufficient to explain the effects of things like taxation.

28 a October 30, 2010 at 11:40 pm

Thanks Doc Merlin, Alex, Sean P for real life examples of dead weight losses related to taxation and thank Dan H for the example of Pigouvian taxes reducing dead weight losses.

29 J Thomas November 9, 2010 at 6:54 am

"I get the point of the example, but it always amazes me that the assumption is a net loss, because that means the $40 never gets spent and thus no tax is had from it. Does anyone believe that the money is never spent?"

Sure, but the immediate result is a net loss. It's a net loss to the particular tax. If they increased the tax hoping to get more money from that tax, they failed.

On the other hand if they were to increase the tax on tobacco products hoping to reduce the amount of legal tobacco used, and use went down enough that tax revenues went down, that would be a plus. And sure, the money would get spent some other way and probably taxed some, so it wouldn't be a net loss to society.

I don't understand which times it's appropriate to think about the alternative effects and which times it is not. Compare dead-weight loss, where we don't consider that the money will be spent anyway, to industrial automation where we do imagine that the lost jobs will be replaced by other jobs.

In the one case, alternate uses for the money are not considered.

In the other case, it's completely obvious that when automation replaces human workers with machines, the jobs are lost. But the assumption is that the market will prevent a net loss of jobs, so it's as if no jobs are lost.

Two different approaches. Which approach is better for which situation?

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