Tax Rate Lottery

Here's a plan ventured by blogger, Stephen Gandel, at the Curious Capitalist:

"Let's say that all income below $500K was subject to taxation as it currently is, and that income above that level was subject to a tax rate lottery, held after the income is declared. Some of it gets taxed at, say, 75%, and some is not taxed at all. The goal is to increase revenue from this segment by, say, 10%. Quite a few $B. Maybe the "losers" are exempted from next year's lottery; they'll be taxed at the current rate."

The idea is that higher tax rates make people work less which is bad for tax revenues and, although the author never mentions it, bad for production. So how about we trick the rich into thinking they might not pay any taxes? That way, they keep working which means we could increase tax revenue.

The possibility that they only pay 15% in taxes would encourage them to work more increasing tax revenues! Gotcha Richie Rich!

Not only does this misunderstand the where US tax rates fall on the Laffer Curve, it also misunderstands how people react to uncertainty.

The whole plan is so stupid that I wonder if this isn't some sort of modern Modest Proposal. Allow me to dismantle this idea.

A Hypothetical Example:

Suppose, Richie has as trust fund which pays him $500,000 every year no matter how much or how little he works. Let's also suppose that Richie increases his total yearly earnings by $100 for every hour he works.

If the tax rate is 15% then he gets to keep $85 per hour. Let's say at that rate, he decides to work 50 hours a week for 50 weeks of the year bringing him in a pre-tax earning of $250,000 and $212,500 in after tax earning.

If the tax rate gets hiked to 75%, then Richie gets to keep only $25. This is a 70% reduction in Richie's hourly wage. According to a study done by Emmanuel Saez and Jonathan Gruber (who Gandel quotes in the article), that would reduce the amount Richie would want to work by 28%. That means he'll only work 1,800 hours and earn a pretax amount of $180,000 and keep an after tax amount of $45,000.

Under the first situation, the government gets a tax revenue of $37,500, but under the higher tax situation, the government pulls in $135,000. The numbers in this example are calibrated to be what Saez and Gruber predict people to do. So Gandel is wrong in assuming that increasing taxes will decrease tax revenues. For economists, we are not on the downward sloping portion of the Laffer curve.

So there goes the first part of his argument. If you need more tax revenues, don't do something bizarre like create a lottery. Just raise taxes.

The Lottery:
Suppose the government spins a wheel to determine Richie's tax rate. Half the slots are for a 15% tax rate and half are for a 75% tax rate.

Suppose Richie says, "I stand a good chance of getting a low tax rate so I'll work as if I'm going to face a 15% rate." If he did, he'd work the 2,500 hours and get to keep $212,500 if he lucks out and gets the low rate, but if he doesn't he earn works 2,500 hours to only get $62,500. Compare that to what he would have worked under the 75% tax and you see that he works a 700 hours only to earn $17,500.

It is pretty foolish to assume Richie won't act any differently in a situation where he has a low tax rate and a situation where he could be hit with a high tax rate. Richie will probably split the difference. He might work harder than he would in a high tax world but not as hard as he would in a low tax world.

Here's the kicker. People like two things, they like leisure and they like consumption. To get more consumption, they have to give up leisure. The lottery makes the returns to work uncertain, but doesn't change the certainty of how much you like leisure. The lottery has effectively reduced the incentive to work beyond even what a tax rate of 45% (the average tax rate Richie faces).

Instead of a lottery that on average has a 45% tax rate, we could have simply made taxes 45% and we'd get a higher tax revenue. Not only is a tax on people's earnings a drag on the economy, but the tax lottery actually makes it even more of a drag on the economy without getting anything in return!

The moral of the story is if you want to increase tax revenues then just raise taxes. Creating a tax rate lottery will do more damage to the economy just to raise the same amount of money. Plus the government wouldn't even get more money from the lottery than the old way of taxing.

There are further contradictions in the tax rate lottery which almost don't warrant comment, but here is a list:
1) The author realizes that if Bill Gates gets lucky and only pays a 15% tax rate, then the US government loses ton of money. More money than we can make up by charging a 75% rate on a bunch of people who earn $500,000. But the author also says, if you lose the lottery and get the high rate one year, you'll be exempt the next. This would just encourage people to work little, wait until they lose, then when they're exempt the next year, increase their work thereby avoiding the tax.

2) He claims that people will enjoy talking about how they won the tax rate lottery and they'll similarly enjoy losing the tax rate lottery because they can gripe about it. This is just crazy! If you get caught by the tax, then you'll have given up time with your family for no reason. You think people are going to be cool with that?

3) He claims that the fact that the tax rate lottery makes planning your life harder isn't a real problem for the rich since many of them already deal with uncertainty in their incomes. Many CEO's get 80% of their compensation in variable end of the year bonuses. But how much variation is there? Is it a 50% chance that you get nothing and a 50% chance you get $100 million? Probably not. Whatever variation there is, they probably are fairly certain about what they're getting. Also, it doesn't follow that because they deal with some variation, they should be able to deal with a lot more. That would be like saying, the guy on the tightrope deals with the rope wobbling some, so he won't mind if we start shaking it more.

Oil Spill Revisited

If you had to guess how many birds were killed by the oil spill, what would you guess? A hundred thousand? A million?

According to this government report: 2,188.

BP is apparently charged $50,000 per endangered animal killed by the spill. Which means that BP owes $109 million.

But is that the cost of all the lost birds? Is the value of a pelican really $50,000?

Planet Money has an interesting podcast on this subject. They find estimates that range from $30 to $45,000 per day. Basically, the whole valuation process of goods that have no market is difficult. The result (spoiler alert) is that a pelican is worth a pelican. Which means, that the value of a pelican is the cost of raising a replacement pelican.

So what does it cost to raise a pelican?

I found some info on a Florida bird sanctuary called Pelican Man's Bird Sanctuary. According to this article, the sanctuary was forced to close due to lack of budget and facing a $200,000 deficit. The sanctuary saved somewhere between 4,000 to 7,000 animals yearly. So if it's operating budget was $200,000 per year* and saves around 5,000 birds per year then the cost of saving a bird is $40 per bird.

According to that estimate, then BP truly owes around $87,500, not the aforementioned $109 million. Even if the government report above represents only a small faction of the true numbers of birds killed. BP could open a wildlife preserve for relatively little and replace the animals lost. You could even charge BP an interest rate on the lost animals and say BP has to replace all the dead animals and an additional 5%.

Forcing BP to pay for what it did is a good idea, wejust have to make sure it's the right amount.


*There were no reports I could find that told the cost of the sanctuary above what it made in revenues from visitors. Which means that $200,000 per year could be a wild overestimate. Just the way I like.

BP Oil Update

In my last post, I made some guesses about the costs the BP oil spill was imposing on the environment and Gulf tourism and fishing. I assumed that BP would be able to cap the leak and clean up would proceed from there. However, that is not the case, and I thought I ought to go back and look at some of my numbers and how they hold up in the face of new potentially higher costs.

My original estimate was $98 billion. So far it has cost BP around $3 billion and they have a total of $7 billion in escrow for future payouts.

President Obama made a speech that BP was going to "pay every dime for the oil spill." If this is true then the $10 billion cost to BP must also be the total cost of all damages. This would mean my estimate of damages done was $88 billion too high.

My conclusion in the previous post was that a tax of $3 per barrel would earn enough to fully pay for this spill. Given that the true costs are likely to be far lower than I estimated, the cost (and thus tax) per barrel of offshore oil would be much lower. Perhaps, somewhere around $1.

Can we afford to spill?

A friend of mine, Harrison, posted this graphic about the BP Deepwater oil spill. The caption reads, "Can we afford to spill any oil?" Um, no I guess not. The graphic shows the damages done by spilling, and I guess how much we need the oil. So, the graphic says, spilling is bad. Ok, sure, but how bad? Bad enough to shut down Obama's proposed offshore drilling? Bad enough to shut down all offshore drilling around the US?

The graphic doesn't have enough information to answer that, so I decided to do some digging, here is what I found:

Based of some numbers I got off a government website, the average amount of oil pumped out of US offshore oil rigs is around 2 billion barrels per year. Suppose that 2010 is peak oil for US offshore rigs and that every year after 2010, the supply dwindles to nothing by 2030. Under these stringent assumptions, that would be 32.6 billion barrels of oil pumped from 2000 to 2030.

There are three main costs that the spill has created, loss of fishing, loss of tourism and damage to wildlife. This website reveals that Louisiana fishing yeilds $2 billion annually. Suppose the spill completely shuts down the LA seafood industry this year and the industry only recovers a little bit each year until after 10 years, it is back to it's $2 billion status.

This EPA website says that the tourism industry for the Gulf Coast is worth $20 billion anually. Suppose the tourism for the Gulf completely shuts down this year and slowly recovers a little each year until 2020 when it get back to $20 billion.

Finally, there was damage to wildlife. This website estimates Exxon-Valdez spill cost $7 billion dollars. So let's assume the same amount of damage from this spill. So in 2010, we lose $7 billion worth of marine life and it takes 20 years to recover fully from the spill.

Using a little present value discounting, the total cost of the the oil spill would be $98 billion.

With that dollar amount in mind, we can find the cost per barrel pumped from offshore oil over the course of 2000 to 2030. So it's $98 billion divided by 32.6 billion barrels which gives us a cost of: $3.02 per barrel.

Spilling really doesn't appear to be much of a cost. Can we afford to spill? No, that's waste, clearly we'd rather not. But does it cost that much? Eh, not really. Should we shut down offshore drilling? No, but we should tax off shore drilling at about $3 per barrel. Why not even make it $4? Even if I undestimated the costs, we'd still be covered*.

*Really love wildlife? Make the cost to wildlife $100 million and the costs per barrel rise to $16. That would still be only about 22% of a $70 barrel of oil.

Cadillac Health Plan Tax

My friend, Justin, posted this radio interview with economist, Jonathon Gruber, on why the Cadillac Health Care Tax is a good idea. Allow me to summarize his points:

1. People with insurance that has a low-deductible (like people who have Cadillac plans) overuse medical treatments. For instance, I get a headache and go get an MRI to find out it's just a headache. I do this because I don't pay for the MRI directly (in general I'd only pay a small fraction.
2. Wages will rise after the Cadillac Tax is passed.

I agree with arugment 1. People do probably overuse health services since they don't pay for them. If people have to pay for them, then they'll use less. This can be good and bad. Let's say that the MRI revealed something and my life is saved at a realatively low cost. Paying for the MRI discourages my use and thus increases costs later.

His whole point is that on net, this will be cheaper for the economy. We save more medical resources by doing less useless medical spending than we lose by having that later spending.

Argument 2 works for me...mostly. Wages and fringe benefits are substitutes for employees. Probably perfect substitutes. If my employer pays an additional dollar of my health insurance, that is one less dollar that they have to pay me in wages.

His argument, is that by taxing Cadillac plans, people switch to cheaper plans which means (under competition) wages rise.

My concern is this: if people switch out of the Cadillac plans into high-deductible plans then the premiums on those high-deductible plans ought to start rising (according to economic logic on substitutes). This will have a downward pressure on the wages of the people who were previously not on the Cadillac plans.

I'm not sure how this all would play out. It seems like it depends on how many people opt to pay the fine for not having insurance.

Economics Of Thanksgiving

My darling wife found this article on the average cost of a meal at Thanksgiving and requested my analysis of the economics of Thanksgiving. Since I hate to deny her anything she wants, here are my thoughts:

As an economist, I wondered why people don't go out to eat on Thanksgiving and instead eat a large meal they prepare at home.

The article quotes a study that finds that a meal for 10 people costs $44.61 or about $4.50 per person which on the face of it seems pretty cheap. A good reason for eating in, as you can't get that quality of a meal at that price from a restaurant.

However, the study doesn't take into account the value of people's time. One recipe site recommends beginning your preparations at 10:45 am in order to eat at 5:30 pm. There are at least 2 hours of breaks in their cooking schedule but also, we need to add the time spent shopping for the specific Thanksgiving foods and clean up, which I'll estimate at 1 hour and 1 hour respectively. The total time for Thanksgiving cooking: 5 hours and 45 minutes.

Here are where some assumptions are going to be important. The less people enjoy cooking, the higher their time cost is going to be. Typically, the assumption is that people value their time at their wage rate (that being the opportunity cost). Below are some assumptions of people's value of time and their effect on the per person cost of the meal.



According to the Bureau of Labor Statistics, the average production worker earns just under $19 per hour. Earning $50,000 per year leads to an hourly wage of $25 per hour (working 40 hours a week, 50 weeks per year).

My guess is that to buy a comparable meal from a restaurant you'd have to pay at least $20 plus tip. These estimates seem to indicate that people who earn more $40 per hour (salary of $80,000 per year) would be made worse off by having to stay home and cook their own meals!

This clearly isn't the whole picture. People value time with the family and the special taste of their family recipes. Thanksgiving isn't inefficient for the rich because they enjoy the family time too. However, if Lincoln had added a second and a third Thanksgiving in March and July and I bet you'd see more people eating out.

Illegal Music

Here’s the headline and subtitle of an article about British music priracy:
“Illegal downloaders 'spend the most on music', says poll
Crackdown on music piracy could further harm ailing industry”

The author of this article is making a critical error. She assumes that the correlation between amount of money spent on music and downloading is causal when based on this study, it is just correlation. Consider two people: Al, a music-lover, has a high willingness to pay for music and Bill, who is indifferent to music, and has a low willingness to pay.

If there is no possibility that they could download music illegally, Al would still spend more on music than Bill. If all music was free on the internet and could be downloaded without fear of punishment, Al would again consume more music than Bill.

Since the legal music competes with illegal music, the price of one affects the demand for the other. An increase in the price of legal music may drive Al to download more illegally. In fact, since Al can get music illegally, it makes him less willing to pay for the legal music.

The effect would be the same for Bill. Low music expenditures would be correlated to low illegal downloads because that person doesn’t like music! This correlation does not imply that shutting down music piracy would be bad for the music industry. Shutting down piracy would drive Al and Bill back to legal music downloads (since the price of illegal music would become infinite). This would be good for record companies.

When the author claims that a crackdown could harm the music industry, she is assuming that legal music and illegal music are complements. That perhaps if you can hear it an album first, you’re more likely to pony up money for it.

My point is that the study doesn’t tell you whether legal and illegal music are substitutes or complements. You’d need a study that looks at how changes in the price of legal music affect the amount of illegal music downloads or a study that looked at how restricted access to illegal music affects legal music purchases.

Based on what the recording industry says, I’d bet they are substitutes. It’s their profits that are being impacted, so I’d give them the benefits of the doubt on this one. If illegal music is really a complement, they wouldn’t be so avid to shut it down, they'd be running free music stations themselves.