An Invisible Inequality

     Yesterday I wrote and posted an essay about why the economics of bulk discounts provides some justification for progressive income tax rates, and a friend asked about how this seems to be the very opposite of the traditional justification cited, namely that it's less of a burden for a rich person to pay a 10% tax than it is for a poor person to pay 10%. The traditional argument is that a dollar is worth less to a rich person than to a poor person, and so we should prefer our government to take more of its tax dollars out of the pockets of rich people than the poor. So how can my argument, which is that marginal dollars are worth more to the rich, be consistent with this?
     It is confusing, to be sure, so confusing that I felt it necessary to write a whole new blog post to answer it, instead of simply replying to the original comment.

     The source of the confusion, though, is this: Although we naturally treat money and wealth as essentially interchangeable (because, hey, that's what money is for: to exchange for wealth), they are fundamentally different things. Money is ultimately a fiction, or to put it less subversively, a convention. It stands for value, but isn't itself intrinsically valuable; when you get a dollar in exchange for something, what you're really accepting is a promise to be able to exchange that dollar for something else of value later on. And that something of value, whatever it is, is what actual wealth is all about. To put it another way, money is potential wealth, not actual wealth.

     Now, let's look at the traditional argument for progressive income tax my friend was talking about. You can see that it is really about wealth, because it works just as well if we substitute, say, bread for money. For someone with a loaf of bread to give up half a loaf is much more of a burden than for someone with ten loaves to give up five loaves, because of the condition they're in afterwards. The first person will be pretty hungry with only half a loaf to eat, while the guy with five loaves will suffer only for a lack of variety.
     The argument still works pretty well if we talk about dollars instead of bread, because on an every day scale, we tend to think of prices as constant: 1 dollar buys one loaf, 5 dollars buys five loaves. And so on a practical level, this has been a pretty good argument for why progressive income tax is fairer than a flat tax. The error of equating money with wealth here does not create any immediate confusion, and so it goes unnoticed. But it is still an error, and it leads us into trouble when we move too far beyond the everyday scale, to consider the workings of the economy as a whole, which is what we have to do when we talk about tax policy.

     Remember what I said about money being a fiction? That becomes clearer when you look at the bigger picture. Money is a placeholder for credit/debt, a hydraulic fluid for trade. You trade your labour for food, clothing, shelter, entertainment, etc., but money lets you do it indirectly. So what's really happening in an economy is people making stuff (wealth) and trading it with each other. The wonderful thing about the free market is that, by allowing people to make their own decisions about what to buy and sell based on the prices that emerge from voluntary negotiations, we can collectively come up with extremely efficient allocations of resources, much more efficient than we could produce with some super-smart person deciding and directing everyone's efforts. If there isn't enough of some good being produced, the price will rise, and more people will start producing it. If there's too much, the price will drop.
     In theory,  you don't need money for a free market. In a barter economy, people would still be able to see that there's lots of demand for this and very little demand for that, and so people who chose to make something valuable would accumulate more wealth than those who didn't. Money just speeds up the process and makes it much easier to see where the demand lies. But it does something else, too: it introduces some dangerous distortions to the process.

     Thought experiment time. Imagine you have two identical workers, equally skilled and equally productive, and both commanding the same hourly rate for their work. The only difference is that one has worked very little this year, and the other has already earned a hundred thousand dollars. You need to hire one for an hour's work, and since you'll pay the same rate and get the same result whichever one you choose, you should be indifferent as to whom you hire. And that's sensible. Except remember my previous post on the economy of scale and bulk discounts. If you happen to hire the guy who's already earned a lot of money, you won't be paying any more, but he'll be getting a lot more buying power out of the dollars you give him. So, from a society-wide view, all of us collectively will be allocating more chocolate bars, more piano lessons, more whatever, to the already-rich guy than we would be if you gave the same money for the same work to the other guy.  In other words, they may be getting the same amount of money, but the richer worker will receive more wealth.
     Think about that for a moment. I mean, there's only so much wealth to go around at any given time, and as a society, we do want to make sure it's used efficiently. That's why we have a free market system, because it generally encourages people to invest resources in things that create more wealth rather than less. But here, in the thought experiment, the two workers are exactly equal in the amount of wealth they produce for the money they are paid, and yet they receive unequal distributions of wealth when they go to spend that money. That's inefficient, and it's an inefficiency that results entirely from our mistakenly equating money with wealth.

     Now, you as an employer cannot be expected to distinguish between the two workers here, and it's not your responsibility to decide what's best for society; you just need someone to do the work, and you'll pay whatever you are willing to pay whoever is willing to accept that price. You're in no position to figure out what real wealth that pay will buy for each of your prospective job applicants. And yet society does have a legitimate concern here; we want an efficient allocation of resources.
     A properly calibrated progressive income tax, however, can fix this. If we impose a tax that keeps the buying power of each earned dollar constant, then the dollars earned by rich and poor alike will be a more accurate reflection of the wealth that the market should allocate them for whatever it is they contribute.

     In other words, I'm proposing that free market capitalism can be made more efficient at producing wealth if we use taxes to correct for the distortions that money introduces into the system.

Bulk Discounts and Progressive Income Tax

     I've written before in defence of the idea of progressive income tax, and I'll probably be writing more on it in the future. Today I want to advance an argument based on the buying power of money, and how it changes in a non-linear way with the total amount of money you have. In particular, I'm going to make the counterintuitive claim that the millionth dollar you earn is, in a very real way, worth more than the first dollar you earn.

     I realize that sounds crazy. After all, one of the fundamental features of money is that its units are complete fungible: one dollar is exactly equal to every other dollar. If I borrow a twenty from you today, and pay you back with two tens tomorrow, it simply makes no sense to say I didn't pay you back the same dollars; dollars have no independent identity. (Note that I'm talking about the twenty as money, not as a distinct artifact. You can distinguish one twenty dollar bill from another, but you cannot distinguish the dollars they represent.) But bear with me here.

     And I also realize that my claim will sound odd because it seems to be the exact opposite of another argument frequently used to justify progressive income tax, the idea that to a poor person, a 10% tax might be an unbearable burden while it would be scarcely noticeable to a millionaire. A single dollar is more valuable to a person with little money than it is to a millionaire, not less. So what gives?

     Neither of these two points is actually inconsistent with the argument I'll be making here. Yes, one dollar is exactly interchangeable with every other dollar. And yes, one dollar is a much more significant sum to someone with few dollar than it is to someone with many. But my claim is that the buying power per dollar increases the more dollars you have.

     Consider the idea of the volume discount. Say you can buy a chocolate bar for a dollar at the convenience store. If you're just buying one at a time, the price is the same for the rich person as it is for the poor person, and yes, $1 = $1. But if you go to a supermarket, you can probably buy a family-pak of 8 for $6, and if you go to a wholesale club, you can get two dozen for $12. When you buy in bulk, your per-unit price drops, and reciprocally, the number of chocolate bars per dollar spent goes up.

     This doesn't only hold for chocolate bars. It applies to almost all commodities, and even most services, thanks to economies of scale. And even for unique items like rare antiques or works of art or real estate, it is usually cheaper to obtain them if you have a lot of money than if you have just barely enough, because of financing costs; service charges are often waived on bank accounts if you keep above a certain minimum balance.

     Note that whatever the good or service in question, the price of a volume discounted item is always measured in dollars. Carrots become individually less valuable in dollars, the more of them you have, and so do chickens and cell phones and gallons of gasoline. They may do so at different rates, so if you're trading chickens for trucks, you might have to offer more chickens for the second truck than you did for the first. But dollars, as purely a unit of exchange with no intrinsic value, aren't subject to economies of scale and volume discounts, because they're what those volume discounted are measured in.

     So what does this mean for progressive income tax? What I want to suggest here is that in principle, it should be possible to come up with a good estimate of just how much more each marginal dollar of income can buy, and then to set a progressive income tax rate such that the after tax buying power of every dollar earned is equal.

     For example (and I’m just making these numbers up for illustration purposes), suppose one chocolate bar costs $1, 10 chocolate bars cost $9, 100 chocolate bars cost $75, and 1000 chocolate bars cost $500. That means that the average price for a chocolate bar is $1 if you buy one, 90 cents if you buy 10, 75 cents if you buy 100, and 50 cents if you buy a thousand. So, we would set the progressive tax brackets at 10% for income over $8, 25% for income over $74, and 50% for income above $499. Each additional dollar you earn, on this model, is approximately equivalent to one more chocolate bar you can buy.

     Now, in the real world, there are hundreds and hundreds of different things you might need to buy with your income, and the volume discounts for each come in at wildly different rates, so accurately measuring how much your overall buying power increases with income would be fiendishly difficult. I’m certainly not prepared to do the math here, but I hope I have shown that the actual, practical power of a dollar is not a constant; it depends on how many other dollars you have available to use with it, and the more dollars you have, the more powerful each of those dollars is. In practical terms, individual dollars are worth more en masse than they are alone, and I argue that this justifies taxing them at progressively higher rates as income rises.