Where Did the Other Dollar Go, Jeff?
三名游客来到一家旅馆，经理告诉他们，三人间的价格是30美元。游客每人掏出10美元，入住了房间。
第二天退房时，经理意识到，这间客房的定价应该是25美元，便要求服务员将多收的5美元退还给客人。服务员不诚实，仅向每位游客退还1美元，将剩下的2美元占为己有。
现在，三名游客每人实际花费了9美元，总计27美元。服务员保留了2美元，加在一起是29美元，请问剩下的1美元去了哪里？
There’s a brain teaser that shows up from time to time, in various forms. I first encountered it in a book of puzzles I read when I was a child. It’s called Where Did the Other Dollar Go? and it goes something like this:
Three tourists stop at a hotel, and the manager tells them that a shared room will cost $30. Finding the price agreeable, they pony up $10 each and retire to the room. Later that afternoon, the manager, who is honest, realizes that the room was meant to be priced at $25. The manager orders the bellhop to return the excess $5 to their guests. The bellhop, who is not honest, takes $5 from the register and return only $1 to each tourist, pocketing the remaining $2—the guests don’t have to fuss over uneven change that way.
Now, each of the three tourists has spent $9, for a total of $27. The bellhop has retained $2, which brings the total to $29. Where did the other dollar go?
The puzzle uses mathematical sleight of hand to put together an equation, 3 × 9 + 2 = 29, that appears to model the situation described, but really it does not. By juxtaposing dollars spent with dollars held, the equation manages to double-count some dollars while failing to represent others, leaving a total that is just slightly off what we would expect.
Most of us learned in school that it is an error to add measurements that have different units: ten meters and five minutes don’t add up to fifteen of anything. This puzzle teaches us that the inverse is not true: two measurements that have the same unit attached (dollars, in this case) may still sum to a value that represents nothing meaningful.
A couple of weeks ago, Jeff Bezos published an open letter to Amazon’s shareholders. Bezos, having recently announced his retirement as CEO of the retail and cloud services giant, is a little more sentimental than usual as he takes pride in the company’s achievements and envisions its future. The letter has already drawn a lot of criticism for its attitude towards Amazon’s treatment of employees, and I’m not going to retread that ground here. Instead, I want to take a closer look at the section titled “Create More Than You Consume”, in which Bezos attempts to summarize the value Amazon creates.
Bezos breaks down Amazon’s business dealings into a few categories, attaches a dollar figure to each one, and then adds them all up to arrive at the grandiose conclusion that Amazon created $301 billion in value just in 2020. In doing so, he plays the exact same game as the puzzle above: taking a list of mostly-orthogonal measurements that all happen to be expressed in dollars, adding them together, and applying an abstract enough label to the whole thing that it’s not immediately obvious what the problem is.
Before I go further, a personal note: throughout this article, I’m going to tacitly accept some of Bezos’ underlying assumptions—that “value” can meaningfully be expressed in terms of United States dollars, that it can be accurately determined by markets, etc. This should not be read as an endorsement of any ideology. I’m just meeting the claims on their own terms in the pursuit of that which I truly value, which is quibbling about math.
The most egregious misrepresentation of value creation in the letter is the $91 billion figure that Amazon has paid out in compensation to employees. This is patently ridiculous. Every single dollar of compensation paid out is done transactionally: it is used to purchase labor. In a typical transaction, no market value is created.[1] If I give you an apple and you give me an orange, the total amount of fruit in the economy remains constant. We can’t create fruit by bartering with it. We can only do so by foraging or cultivating an orchard.
Money and labor are both more abstract than fruit, so there is a little bit of leeway to interpret employment transactions as being non-zero-sum. One might argue that labor is more efficient when performed as part of a collective rather than as an individual, and so employment is inherently value-creating. Or one might consider that, taking the marginal utility of money into account, a dollar in the hands of an Amazon employee is in fact more valuable than the same dollar in the hands of an Amazon shareholder. Of course, that would lead us to ask whether Amazon on the whole contributes to inequality, a question I can’t begin to quantify here. But however you look at it, taking full credit for every single dollar of compensation as value creation—as if Amazon, and not the US Mint, created those dollars, and as if the many, many millions of hours of labor consumed by the company in return were valueless—is a ghastly overstatement.
Bezos claims that Amazon made $21 billion in net income for the year, and counts that as value created for shareholders. Of all the figures given in the letter, this is the only one that may actually be appropriate as a measure of value created, although he still gets the reason kind of wrong. If you spend $50 on art supplies and turn them into a painting worth $500, you have created $450 worth of value. And when you sell the painting, you end up with net $450 that you didn’t have before, because that’s the difference in values between what you consumed and what you produced. In this way, the amount of money you made is equal to the value you produced (we are assuming, like good little capitalists, that markets are efficient and that externalities don’t exist and all that). But the value you created isn’t the money. The money already existed and was floating around the economy long before you picked up the brush. The value you created was in the art, which is now in someone else’s hands. So while Amazon shareholders may be $21 billion richer than they were before, it’s not meaningful to say that value was created “for the shareholders”. It doesn’t matter whom value was created for—the shareholders would be the ones getting rich regardless.
Afterward, the letter looks at those whom Amazon enables to create value of their own, and then takes credit for that value. It estimates $25 billion in profits for Amazon’s third-party sellers, and then attributes that entire value towards Amazon’s total value created, as if none of those third parties would be doing anything at all in Amazon’s absence. It estimates the cost reduction AWS customers enjoy by not using traditional hosting, and adds it to the total. And it estimates the time saved by consumers who shopped at Amazon instead of brick-and-mortar stores, and—in a particularly bold move, considering that just a few paragraphs ago it ascribed no value whatsoever to the time of its own employees—attaches a dollar value to those hours and throws that on the pile as well.
These are three completely different measurements: one is profit, one is savings, and one is time. They cannot be added together to anything meaningful. But they all happen to be measured in dollars—or, well, two are measured in dollars and the third can be hastily converted—which we’re expected to believe is good enough.
Moreover, all this pays no mind to the actual provenance of the alleged value. If you run a business that happens to sell products on Amazon, or do hosting on AWS, and you’re calculating your own value created, you’re going to take that platform for granted, and you should. It was probably part of your business plan from the start, and if that technology wasn’t available you would have done something else. You’re certainly not going to chop some percentage off your total because the credit for that value belongs to Amazon—just like how Bezos didn’t make any adjustments to his $301 billion figure to account for how some of it was enabled by the construction companies that built Amazon’s data centers, and the power companies that keep them running, and the developers that wrote the open source software that underlies their systems, and the manufacturers that produce products for them to sell, and the farmers and educators and transit authorities and governing bodies and legal systems that all maintain a modern society capable of supporting specialized businesses and are funded or subsidized primarily through income taxes, which Amazon pays almost none of. But I digress.
The point is, when you purchase a service from Amazon, the future value created by your usage of the service belongs to you, not to Amazon. Even if it seems like Amazon should get some credit, there’s no reasonable way to measure such things, no scheme for attributing “value creation” fairly between the producers of every good and service you may have consumed on your way to running a business. Anyway, Amazon has already been credited for providing those services since they made money off the deal. Every business relying on Amazon contributes to that $21 billion in profit Amazon made.
And to be clear, using profit to measure value created is also fraught. It captures neither value created through charitable work, nor that destroyed through exploitation of the commons or other externalities. But if you want to measure those things, then measure those things. Don’t throw hundreds of billions of dollars’ worth of arbitrary statistics into a pile and expect us not to blink at the fourteen-fold inflation over the one provided statistic that’s actually relevant.
1. Edit 2021-04-28: Previously, this line simply said "no value is created", which several readers justifiably criticized. It is true that trade generally increases utility in ways that don’t get tracked by the market. The Amazon letter generally treats "value" and "market value" as equivalent for Amazon’s purposes, so my larger point stands, but it is not appropriate to generalize that equivalence to all trade. Mea culpa.