Next, to a puzzle! Try to solve it. If you can't, don't worry: Adam Smith couldn't either!

This puzzle will help you understand the world, economics, and the solution to the kidney problem. It concerns itself with what makes something valuable, and thereby, what sets prices. When the first set of pioneering economists wanted to figure out value and price, they had a number of competing ideas: maybe it is how useful something is? Maybe it's how rare something is?

But they ran into a problem. Nothing is more useful than water; almost nothing you own matters more to staying alive. Yet water is nearly free. A diamond is useless — you cannot drink it, eat it, or shelter under it — yet it costs a fortune. How can the most valuable thing on earth be cheap, and a useless bauble dear? Smith called it the difference between value in use and value in exchange, and he could describe the gap but not explain it. For nearly a century it sat there, unsolved — the diamond–water paradox.

We assume the price of water should reflect the worth of having any water at all— all of it, the whole life-giving category. But nobody ever buys "all the water." You buy the next glass, having already had your fill today. And the next glass, when you aren't thirsty, is worth almost nothing — a cent, maybe less. That last, barely-wanted glass is what sets the price, because in a world awash in water, the next unit is all that's ever in question. Diamonds run the other way: you own none, so the next one is rare and craved, and its worth — its value at the margin — is enormous.

If diamonds were as common as water, would they have the same price?

The paradox collapses once we separate total usefulness with worth at the margin. Water wins on total usefulness by a mile and loses at the margin, because we already have so much. Diamonds are completely useless, but they are rare at the margin. You would give your life for access to kidneys in general, but you would happily be compensated to give up just one kidney.

Price tracks the margin, not the total — and value, it turns out, lives in the last unit.

This was the insight of the 1870s, and it was so far-reaching it earned the name the marginal revolution. Moving value from the whole to the margin solved Smith's puzzle: people make decisions on the basis of the next unit of consumption.

Utility is the satisfaction, well-being, or value a person gets from a choice — and economists give it a playful unit, the util. A cold soda on a hot day might be worth 10 utils to you; a warm one, 4.

Here's the thing: Utils are bunkum. They're totally made up.

Here is the awkward truth: satisfaction cannot really be measured by utils. There is no happiness thermometer. We can't open your head and read off "27.3 utils." Worse, we can't compare across people at all — my 10 utils and your 10 utils aren't the same thing in any literal sense. This is the measurement problem, and for a while it looked like it might sink the whole idea of economics.

Fortunately, "utils" are a lot like models: imperfect, but useful. Pretending satisfaction is countable makes the logic visible, even if we can't use them to measure.

How can we measure? How can we make that precise enough to compute? By using revealed preferences. I don't know how many utils you got from your soda, but I know that you got more utility per dollar from your soda than from any of the other options on the menu or you would have bought them instead!

Picture a consumer in a delightfully simple world with only two goods to choose between — hot dogs and soda. They want to maximize total utility, and they decide one unit at a time, on the margin, always asking: "what gives me more right now — the next hot dog, or the next soda?" The answer shifts with every purchase, because of diminishing marginal utility: the more hot dogs you've eaten, the less the next one appeals.

A simple two-good model is easy to understand: a consumer will make choices that maximize their marginal utility.

But what of real life? What of an infinite-good universe?

Before we move on, make sure you are fluent in calculating marginal utility from total utility. Get that subtraction fluent and the next step is a breeze; fumble it and it will trip you every time.

Comparing raw utils across goods is like comparing two trips when one distance is in miles and the other in kilometers. It's tricky to model infinite goods, so instead we make every market into a three good model: good x, good y, and price. By using prices we get a common unit. In real life you don't weigh one good in isolation; you walk in with a single wallet and face dozens of competing price tags. A price is the meta-incentive: the universal scale that translates a $4 burrito, a $12 movie ticket, and a $50 pair of shoes into the very same denominator — dollars.

Note that price is an incentive for buyers who want to minimize what they pay, and sellers who want to maximize what they receive in a sale. As Milton Friedman once pointed out, we do not want the price to go up, nor do we want the price to go down. We want the price of things we buy to go down, and the price of things we sell (like our labor) to go up.

To be rational is just to optimize against that scale, stretching a limited budget for the most satisfaction it can buy. You've run this calculation in your head a thousand times; you call it hunting for the best bang for your buck.

So you don't chase the highest raw marginal utility. A trip to space has enormous marginal utility, but it costs a fortune per unit of happiness. You chase the most satisfaction per dollar: divide each good's marginal utility by its price, and spend your next dollar wherever that ratio is highest. Moreover, you might spend money if it's a good deal, but you also might save your money if that brings you more utility!

As you spend money, notice something interesting: decreasing marginal utility sets in, and the amount of marginal utility per dollar drops. You continue consuming until the marginal utility drops below that of another consumption choice, and you purchase that. As you continue to make consumption decisions, your marginal utility per dollar will begin to equalize.

That equalizing is the quiet signature of diminishing marginal utility, and you feel it far beyond snack stands. At a buffet you don't load your plate with only the single best dish; after a few bites its marginal utility drops below the next dish, so you spread across the table until each forkful is about equally worth taking. Studying for five classes, you don't pour every hour into one; as the marginal payoff of the next hour falls, you shift to another, until the last hour in each subject gives roughly the same boost. The optimum always has the same shape — move money or effort from wherever it is worth less to wherever it is worth more, and you arrive, inevitably, with the margins balanced.

Diminishing marginal utility also says something quietly human: we crave variety. Love hot dogs all you like — by the fourth, its marginal utility has fallen so far that a cold soda, or almost anything else, easily beats a fifth. That is why almost no one pours an entire budget into a single good: each good argues itself out of your wallet as you pile it up, handing the next dollar to something else. It is also the first hint of why certain goods travel in pairs — the hot dog that makes you reach for a soda — a thread we will pick up later on when we discuss complementary goods.

When prices and income change

Now that we've solved one bundle, at one set of prices, under a single budget constraint (four hot dogs and three sodas at $15), it's time to get a little more like real life. See, the interesting questions are about change — what happens to that bundle when some variable moves, say price or income? We call these kinds of questions comparative statics: how does your outcome change when a variable changes? This is where the marginal apparatus starts to earn its keep.

Changes in price. Suppose the stand raises the price of a hot dog from $3 to $4; soda and your $15 budget are unchanged. Every hot dog's marginal utility per dollar now falls — you are dividing the same MU by a bigger number — so the old bundle is no longer balanced. Its first four MU/$ figures drop to 7.5, 6, 4.5, 3, and that last 3 is now beaten by a soda. Re-solve and you land on three hot dogs and three sodas (3 × $4 + 3 × $1 = $15). The price went up; the number of hot dogs you buy went down, from four to three.

That is not a coincidence — it is the whole point. Price is the denominator of MU/P, so when a good's price rises, its MU/P falls below the balanced level and you buy less; when a good's price falls, its MU/P rises above the balanced level and you buy more, until diminishing marginal utility pulls MU/P back into balance.

Let's state it simply: when price rises, you'll buy less. When price goes down, you'll buy more. And, importantly, when the price of the goods you purchase goes down, you'll get more utility. Remember this, because we're going to come back to it.

The same logic covers a free good. If a good's price is zero, there is no denominator to hold you back: the rule says keep consuming until its marginal utility itself falls to zero — you stop only when one more unit would start to make you worse off.

Foreshadowing the demand curve. Run the same experiment at a few prices and read off how many hot dogs the rule selects: at $3 you buy 4, at $4 you buy 3, at $5 you buy 2. Plot price against quantity and you have drawn a downward-sloping curve of how much you would be willing to buy at a variety of prices. Cool! This is a very simplified version of a demand curve, which we'll discuss in the next chapter. All we had to do to get it was assume a rational shopper maximizing utility under a budget. Lower price → larger quantity demanded is a pretty important conclusion, and we'll come back to it soon!

Changes in Income. Now hold prices where they started ($3 and $1) but raise the budget from $15 to $19. Nothing about the rule changes — with prices fixed, the balanced MU/P you are aiming for is the same — you simply have more to spend. Re-solve and you buy more of both: five hot dogs and four sodas (5 × $3 + 4 × $1 = $19). More income, spent by the same rule, buys a bigger bundle — no new machinery required.

We now have the vocabulary to name what just happened. A normal good is one you buy more of when you get more money. Most goods function this way, and that is why they are called normal — our hot dogs and sodas both rose with the bigger budget, so for this shopper both are normal goods. Some goods have the opposite relationship: you buy fewer of them as your income increases. These are inferior goods, and the name is about the relationship with income, not the quality of the good. Bus tickets are the classic case: when money is tight you ride the bus, but as your income climbs you buy a car and ride less — so your demand for bus tickets falls even though nothing about the bus itself changed.

Now that you understand how marginal utility works, you can make a more informed decision about kidney markets.

Hold two people side by side. A healthy donor has two kidneys and needs one; the marginal utility of their second kidney is low — its job is mostly redundant, and they will live a normal life without it. A patient in renal failure has zero working kidneys; the marginal utility of a single kidney to them is almost beyond measure — it is the difference between dialysis-bound and free, between dying and living. Diminishing marginal utility says these two numbers are wildly far apart. Whenever marginal values sit that far apart, a trade can make both people better off. The kidney ban doesn't prevent a bad trade; it forbids an extraordinary one.

Notice the sleight of hand the word "donor" performs. "Giving up on having kidneys" sounds like a catastrophe — and it would be. But that's not the trade. The trade is "willing to give up a single, spare kidney" — a much smaller sacrifice, with the donor's own health carefully protected.

The entire reason why kidney markets could work is because there is a difference in value for the marginal kidney!

Agreement and Disagreement

None of this is to say that the objections to kidney markets are unimportant.

Here's the part skeptics miss: those objections are not dead ends. They're design constraints — and people have already designed around them.

Roth himself built an elegant answer. Rather than cash, he engineered a kidney exchange: when a willing donor isn't a medical match for their intended patient, a clearinghouse links them into chains — your donor gives to a stranger, that stranger's donor gives to you — so incompatible pairs become compatible. No money changes hands, repugnance is avoided, and thousands of transplants have happened that otherwise couldn't. It's a market in matches, not in organs, and it helped earn Roth the 2012 Nobel Prize. The objection produced the solution.

The United States has also quietly built a clever middle path — not payment, but the removal of disincentives. It is currently illegal to pay for an organ, yet a federal program (the National Living Donor Assistance Center) reimburses a living donor's travel, lost wages, and dependent-care costs, and a private program (the National Kidney Registry's Donor Shield) covers up to roughly $30,000 in lost wages and expenses. The careful framing is that these funds are not a reward for donating — only a guarantee that donating won't leave you worse off financially. It's genuinely cool: it makes a heroic act cost-neutral without ever putting a price on the kidney itself.

But — and this is where care matters — that middle path stops exactly short of the people who could most benefit from going further. It's worth resisting the comfortable thought that the middle path is "close enough." While we sell plasma, blood banks experience persistent shortages. Not-paying has not "solved" blood.

Reimbursing costs makes donation free; it doesn't make it worth it for someone whose six weeks of recovery is a financial catastrophe even after wages are covered. There are good, generous people of modest means who would gladly give a kidney to a stranger if doing so also lifted their own family — and right now the law tells them that the one thing they cannot receive is the very thing that would let them say yes. We protect them from being exploited by a market; we do not protect them from the quieter loss of a trade that would have helped them and saved a stranger's life.