Tax Cuts, Fairness and Pie

ZenTiger repeats the old story of the 10 men at the restaurant.

It’s a good story to illustrate the way we talk about tax. But I was thinking the other day, that it could be improved by the addition of some actual illustrations – graphs.

So here goes.


Every day, ten men went to a restaurant for dinner. They always ordered the same meals, and the bill for their food always came to exactly $100.00. They did this day after day, year after year, without variation.

They did not divide the cost of the bill up equally among them, however. Since some of the men were more wealthy than others, they all agreed that an equal split would be unfair to those with less money. So, the men decided to pay the bill in precisely the same way we all pay our income taxes.

The first four men paid nothing at all. They ate for free. The fifth man paid $1.00; the sixth paid $3.00; the seventh paid $7.00; the eighth paid $12.00; the ninth paid $18.00. And the tenth man, who was by far the richest of them, paid exactly $59.00, which was most of the $100.00 bill. He didn’t mind, however, since he could afford to pay that amount. All was well. The ten men were happy with this arrangement, and they continued to eat at the restaurant every single day, enjoying their time together.

So what does that look like?

From that chart, you can see exactly how most of the food is being paid for by the richest man – something that happens in progressive tax systems all over the world.

Then one day… the owner of the restaurant threw them a curve. As they stood at the counter to pay their bill, he announced that he would reduce the cost of the meals for them. “Since you are all such great customers, and I am so appreciative of your business,” he said, “I am going to reduce the total bill for your meals by $20.00. From now on, your ten dinners will cost you only $80.00.”

The men were pleased. But the situation did present a problem. How were they to divvy up the savings among them? Obviously, they could not simply credit $2.00 (one-tenth of the $20.00 savings) to each of the ten men, since that would mean that the first four men would actually be getting paid $2.00 to eat! No good. It only seemed fair that the first four men, who paid nothing to begin with, should likewise not get any of this $20.00 refund. But still, there was a problem. If they now divided the $20.00 savings among the remaining six men, that would be $3.33 per man. If that amount were subtracted from each man’s payment, then the fifth man and sixth man, who had been paying $1.00 and $3.00 respectively, would then be getting paid to eat. That wouldn’t work, either. No, the solution to this problem required some ingenuity.

Just then, the restaurant owner, who had been listening to the discussion, interrupted. He offered a solution. He suggested that the fairest way to settle this dilemma would be to reduce each man’s bill by the same proportion as he had been paying in the first place. The owner walked over to his calculator and figured out the amounts each man should pay. And so it was agreed.

The fifth man, instead of paying $1.00, now paid nothing, just like the first four men had always done. The sixth man paid $2.00 (reduced from $3.00); the seventh paid $5.00 (reduced from $7.00); the eighth paid $9.00 (reduced from $12.00); the ninth paid $12.00 (reduced from $18.00). This left the tenth man with a bill of $52.00, instead of his previous bill of $59.00. The men paid their bill according to this arrangement, and they left the restaurant, satisfied.

Again, here’s the graph.

So the bill looks the same, but with everyone getting a cut. The 5th man now gets his small bill reduced to zero.
Outside the restaurant, however, the men began to compare their savings. The sixth man started complaining. “I only got one dollar out of the $20.00 savings. That’s not much,” he said. He pointed to the tenth man and declared, “And he got $7.00. What gives? That’s not fair. He’s rich. He doesn’t need the money. Why did he get $7.00, when I only got $1.00?”

“Yeah, that’s right,” exclaimed the fifth man. “I only saved a dollar, too. It’s unfair that the rich guy got seven times more than I did! I surely have a much greater need for money the he does.”

“That’s true,” shouted the seventh man. “Why should he get back $7.00, when I got back only $2.00? That stinks! The wealthy get all the breaks. The rich just get richer.”

“Wait a minute!” yelled the first four men in unison. “We didn’t get anything at all. Not one stinking cent! The rich fellow, who drives here every day in a Lexus, got $7.00, and we all take public transit to this restaurant, and we got nothing at all. This system exploits the poor.” With that, the men became angry. “And I lost everything,” said one of the four. “My wife left me, my daughter is in the hospital, and I can’t get work. I could sure use a break. Instead, I got not one lousy penny of the $20.00, and I have to watch this guy who’s filthy rich take $7.00 of it! I won’t stand for it!”

The nine men surrounded the tenth. Their anger mounted as they continued to express their resentment at what they thought was a supreme injustice. Finally, they lost control of their senses. They beat up the tenth man. They left him bloody in the street, and they went home.

Here’s how those men were viewing the price reduction

They’re right – most of the price reduction went to the 10th man and 9th man. But notice that it’s a pie graph, talking about differences in the old and new proportions rather than the proportions themselves?

The next day, the tenth man did not show up for their regular dinner. The nine men sat down and ate without him. But when it came time to pay the bill, they discovered something: they were $52.00 short! Needless to say, that was the last time those men ever ate at that restaurant.

I wish I could say that these nine men learned a valuable lesson, that they came to understand the principle upon which a tax cut is based. But they didn’t. They were too stupid to understand.


Here’s the graphs that they missed.

Proportion of the old bill to each man.

Proportion of the new bill to each man.

See that? The 10th man is actually paying a larger percentage of the bill with the new arrangement!

So let’s get this straight.

  • The reduction lead to no one paying more
  • The reduction reduced the bill to all who were paying
  • The bills of all the poorer men reduced absolutely and in proportion
  • The reduction moved proportionally more of the bill onto the richest man

There’s only one way to claim that the price cut, and our recent tax changes “benefited the rich”. That’s to talk about the tax cut

  • as though it were handing out money, rather than reducing a bill
  • as though the cut was a pie (proportional arrangement) itself, ignoring that it is a change to an existing proportional arrangement
  • but most importantly, it talks about a proportional cut to a proportional system in non-proportional terms.

That’s grossly dishonest.

By phrasing tax cuts in these terms, Labour and the left force more and more burden onto the richest man. They also demonize him as getting “more money” when taxes are cut across the board.

As the story illustrates, that’s very dangerous. It runs the sever risk that those being attacked will quite rationally decide that paying so much money to be the whipping-boy of society is stupid, and they will leave.

When that happens, we all end up worse off.

Now, I’m not saying here that we should give the rich a small tax burden. I’m simply saying that we should stop looking for ways to bash them, and start acknowledging that the vast majority of us are getting far more from the government than we pay in taxes, and we are bashing the people who make that possible.


  1. Brilliant addition to the old story, well done.

    I mentioned it to some-one recently, and then thought maybe I could find the original story, and put it on the blog just for my own reference. So I did. Boy, am I pleased I did because as old as it is, many people still haven’t read this. Also, it’s inspired you to do the graphs and explain the pertinent wrinkle – the unfair terms of the critique.

    If I were to look for real criticism of this situation, it’s simply that the rich person can afford to be generous and the poorer ones cannot, and so rely on the richer person’s contribution and they forget the money, have a great conversation and companionship sharing a fine dinner. Perhaps the rich person has enough wealth that the cost of the meal is payment enough for the fine company.

    On the other hand, there was an undercurrent of greed and it didn’t take much for the friendship to be destroyed and the poorer ones ended up losing out in the short term because of their violence. What are the messages then? We can generate a pile of ideas to discuss further looking at this parable:

    * Pay your taxes or society will disintegrate?
    * Accept tax increases if you are rich or be beaten up.
    * If we remove the rich person, it allows a poorer person to earn more money (some people believe a bloody revolution clears the way for a new society), and then they will presumably be glad to pay the high taxes…actually, given they beat the rich person up, I doubt they will be the type that will become generous in their richness.
    * What were they doing spending money on a lavish dinner anyway? A simple dinner would have required less input from the rich person and the disparity would have therefore been less. Does that make the envy less? Are we prepared to cap the quality of restaurants instead of the cost of the meal and the resulting high taxes? The health system and tax expenditure on health might be the area to apply this thought… (and think on the recent changes in the USA)

    There’s a few other thoughts too, but dinner calls.

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