Handing off what you cannot absorb

Everything in this course so far has been about making a plan work: measuring, budgeting, clearing debt, growing what is left, and putting it in the right container. All of it assumes the ordinary case. This lesson is about the other case.

A car is written off. A pipe bursts. You are admitted to hospital. The thing these have in common is not that they are unlikely, because over a long enough life they are close to certain. It is that they are large and badly timed, and no budget survives them by being tidier.

Insurance is the tool for that, and it is widely misunderstood in both directions. Some people think it is a rip-off because the company expects to profit. Others think it is a good investment because they got more back than they put in. Both have the same misunderstanding underneath, and by the end of this lesson you should be able to say what it is.

Where this applies, and what this lesson is not. The vocabulary here is US health, car and home insurance, and the dollar figures are US ones. Pooling is the constant; who does the pooling is not, and in a tax-financed system the pool is the tax base rather than a book of customers, with the same arithmetic underneath. The question to take to your own system is the one this lesson answers: which risks should you hand off, and which should you carry yourself?

And the standing note, which matters more here than anywhere else in the course, because this lesson gives more direct answers than any other. This is education, not personalised advice. What follows is the arithmetic and the vocabulary, and the weighting depends on facts about your life no course can know. For anything binding, your state insurance department regulates these products, publishes consumer guides, and handles complaints.

What insurance is for, stated plainly

Insurance isn't an investment, and it isn't supposed to pay off on average. If it did, nobody could sell it.

What you are buying is a change in the shape of your risk. Without insurance, most years cost you nothing and a rare year costs you everything. With insurance, every year costs you a known premium and no year costs you everything. You have traded a small certain loss for the removal of a large uncertain one.

That trade is worth making when the large uncertain loss would break something. It isn't worth making when it would only annoy you.

One large exception, stated here so it does not quietly break the arithmetic later. All of this assumes you are paying the full price of the policy. Often you are not. In the US in 2025 the average employer health plan cost $9,325 a year for single cover and the worker paid $1,440 of it, so the employer paid roughly six sevenths, and that share is not taxed as your income.¹ A policy somebody else largely pays for is not a negative-expected-value trade at all; it is a transfer, and turning it down to save your share is usually a mistake on any reading. The reasoning in this lesson is about which policies to buy at their full price, not about whether to accept coverage that is being funded for you.

Pooling, and what the insurer's profit is buying you

Ten thousand people each face a 1% chance of a $50,000 loss in a year. For any one of them, the year is wild: almost certainly nothing, occasionally ruin. Across ten thousand of them, though, the total is dull and predictable: about a hundred losses, about $5 million, year after year, within a narrow range. That is the whole trick. Risk that is unbearable one at a time becomes forecastable in bulk, and an insurer is a machine for standing in the bulk position.

So the company can charge each person the $500 that the average loss costs, plus something for running the business and something for profit. Say $650. Every customer now pays $650 with certainty instead of facing a 1% chance of losing $50,000.

Do the expected value from the customer's side and it looks like a bad deal, because $650 is more than $500. It is a bad deal, in expected-value terms, and it is meant to be. The reason to buy it anyway is that you aren't an insurance company. You can't run the same year ten thousand times and collect the average. You run it once, and the version of you who has the $50,000 loss and no policy has lost the house.

That's why "they make a profit, so it's a rip-off" doesn't follow. The insurer's profit is the price of moving a risk from someone who cannot carry it to something built to carry it. What does follow, and it is the sharp end of the same reasoning, is that you should not pay that margin on losses you could carry yourself.

The rule, and the test that applies it

Insure the catastrophe, not the inconvenience.

The test that turns that into a decision is one question asked about a specific loss: if this happened tomorrow and nobody paid me a penny, what would I do?

• If the answer is "pay it from savings and be irritated", carry the risk yourself. Paying an insurer's margin to be spared an irritation is a poor trade, and over a lifetime of small policies it adds up to real money.
• If the answer is "borrow at 24%", "move", "not get the treatment", or "I do not know", hand it off. That is what insurance is for, and the premium is worth paying even though the expected value is against you.

Notice what this test depends on. Not on how likely the loss is, and not on how big it is in the abstract, but on how big it is compared with what you have. The same $2,000 risk is an inconvenience to one household and a catastrophe to another, so the same policy is a waste for one and essential for the other. This is lesson 2's cushion arriving in a new place: the cushion is self-insurance for small risks, and the more of it you have, the more risk you can sensibly carry yourself.

The vocabulary, which is small and does most of the work

Five words decide what a policy actually does. Learn them once and every policy you ever read is legible.

• Premium. What you pay to hold the policy, whether or not anything happens.
• Deductible. What you pay first, before the insurer pays anything.
• Coinsurance or copay. Your share after the deductible is met. Coinsurance is a percentage (20% is typical), a copay is a flat amount per visit.
• Out-of-pocket maximum. The ceiling on what the year can cost you. HealthCare.gov defines it in two sentences: "The most you have to pay for covered services in a plan year. After you spend this amount on deductibles, copayments, and coinsurance for in-network care and services, your health plan pays 100% of the costs of covered benefits." Federal law caps it, at $10,600 for an individual and $21,200 for a family for the 2026 plan year.
• Coverage limit and exclusions. The most the insurer will pay, and the list of things it will not pay for at all.

Read that definition again, because two phrases in it carry the risk that surprises people. It applies to covered services and to in-network care, and the glossary spells out what it therefore excludes: your premiums, anything the plan does not cover, out-of-network care, and charges above the amount your plan says a service is worth. A policy isn't a promise to make you whole. It's a promise about a defined list, and the exclusions aren't fine print in the sense of being unimportant. They are the product.

For scale, here is what US employer coverage looked like in 2025.¹ The average plan cost $9,325 a year for single coverage and $26,993 for a family, of which the worker paid $1,440 and $6,850. Of workers with single coverage, 88% had a general annual deductible, averaging $1,886; of all covered workers, 34% were in a plan with a deductible of $2,000 or more. The average copay was $27 for a primary care visit and $45 for a specialist, and average coinsurance was 19% for office visits and 20% for a hospital admission. Among workers with an out-of-pocket maximum for single coverage, 12% had a limit of $2,000 or less and 21% had one above $6,000.

Two of those numbers say something the averages hide. The average deductible is $2,631 at employers with 10 to 199 workers against $1,670 at larger ones, so how much of this you get to choose depends on where you work. And 61% of firms with ten or more workers offer health benefits at all, 97% of the largest against 59% of the smallest, so a good many readers are not choosing between two plans through work and are buying on the marketplace instead, where the same five words still decide what a policy does.

Two plans, a quiet year and a bad one

Priya is choosing between two plans through work. The numbers are made up and round, so you can watch the arithmetic move.

Plan B saves her $1,200 a year in premiums and asks her to carry $2,500 more before the insurer starts paying. Which is better depends entirely on a number she does not have, which is how much care she will need next year. So work all three cases.

A quiet year, no care at all. A costs $3,000. B costs $1,800. B wins by $1,200.

A middling year, $2,000 of covered care. Under A she pays the $1,000 deductible then 20% of the next $1,000, so $1,200, plus $3,000 of premium: $4,200. Under B the whole $2,000 sits below her deductible, so she pays all of it plus $1,800 of premium: $3,800. B still wins, by $400.

A bad year: a hospital stay, $60,000 of covered care. Both plans hit their ceiling. Under A she pays her $4,000 maximum plus $3,000 of premium: $7,000. Under B, $7,000 plus $1,800: $8,800. A wins by $1,800, and that $1,800 is what the extra premium bought.

The crossover is $2,500 of covered care in the year. Below it, B; above it, A. The picture below has the whole comparison in it, and it shows two things the three cases do not.

Two things this picture teaches that the three numbers alone do not.

The gap between the plans is never enormous. The worst case under either is a bad year, and the difference between them at their worst is $1,800. What the out-of-pocket maximum does is put a floor under how bad the decision can be, which is why it is the number to look at first and the one people never quote.

Below the deductible, a high-deductible plan buys her nothing she uses. For the first $3,500 of care, Priya under Plan B pays full price while also paying $1,800 a year in premium. The insurance is still there, and its value is the part of the picture past the crossing, but in an ordinary year she is paying for protection she does not touch. One fact worth knowing before you read your own plan: under the ACA, in-network preventive care is covered before the deductible, so a high-deductible plan isn't full price for literally everything.

And the case for the high deductible, which deserves stating in its own terms rather than as a trap. The deductible is not only a way of making a policy cheaper. It is there to put a price back in front of the patient, and the evidence that this changes behaviour is strong: the RAND Health Insurance Experiment ran from 1974 to 1981, randomly assigning about 5,800 people in 2,000 households across six sites to plans with different coinsurance rates, and people in the highest cost-sharing plan spent about 39% less on medical care over a year than people who got care free.² Most of that came from starting less care rather than from paying lower prices, and the effect on hospital spending, the serious end, was small. Supporters of high deductibles read that as waste being squeezed out, and pair the plan with a health savings account, which is lesson 7's tax wrapper attached to the money you are now expected to spend on the deductible. Critics read the same number as care being skipped, some of it needed. What that reduced use did to people's health is the genuinely disputed part, and I haven't opened the original RAND health-outcome papers, so this lesson reports the spending result, which was checked, and leaves the health question open rather than answering it from a source nobody read.

Which leads to the thing the arithmetic cannot tell her, and it is the point of the lesson. A $3,500 deductible is only a cheaper policy if you can produce $3,500.

Work it for someone who cannot. Suppose the same choice, and $300 in savings. A bad year arrives in March. Under Plan A she owes $4,000 at her maximum and can pay perhaps $300 of it. Under Plan B she owes $7,000. Whatever she cannot pay goes on a card at 24%, so Plan B leaves roughly $3,000 more on that card, and a year of carrying it costs about $720 in interest on the extra alone. So the $1,200 she saved in premiums is eaten by the middle of the second year, and that is only the interest: the $3,000 of extra principal was never a saving at all. Lesson 3 begins again on a larger balance. For someone with lesson 2's cushion in place, Plan B is a reasonable bet with a known worst case. For her it is not a cheaper plan; it is a larger uncovered gap with a monthly bill attached. The right deductible depends on your cushion, not on the plan.

What people actually choose, when you can watch fifty thousand of them

If you had to guess whether people over-insure or under-insure small risks, the evidence is unusually clean, and it comes from a study that got hold of the right data.

Justin Sydnor obtained a random sample of 50,000 home insurance policies from one large US insurer, where the basic contracts differed only in the deductible, chosen from $1,000, $500, $250 and $100. Because the dataset also recorded every claim, he could compare what people paid for extra coverage with what that coverage turned out to be worth.³

• 83% of them bought a lower deductible than the maximum, paying more to be covered for a smaller loss.
• The most common choice was $500, and that group paid on average $100 a year to bring the deductible down from $1,000.
• Their claim rate was under 5%, so the extra $500 of coverage was worth less than $25 a year in expectation.
• On average, they paid about five times more in premium than the extra insurance was worth to them.

To justify that choice with ordinary risk aversion, a customer would need to believe their chance of claiming was about 18%, several times the rate at which these customers actually claimed. The paper's own conclusion is that fitting these choices to a standard model gives "implausibly large" measures of risk aversion.

What the study settles and what it does not. The data are unusually clean and the choice pattern is not in doubt. What that pattern shows about the buyer is argued over: one line of work reads it as distorted probability, people systematically overweighting small chances rather than being extraordinarily averse to risk, which is a different diagnosis with a different remedy. And the lesson's own reasoning supplies a second alternative, because for a household that could not produce the deductible on the day, buying certainty about a bill is a sensible purchase rather than a mistake. Sydnor's customers were homeowners with a $1,000 maximum deductible, so that reading has limited room here, but it has some.

One sentence from the same paper that gets left out when this study is quoted, and should not be. Sydnor also found that the insurer did not appear to earn excess profit on low-deductible customers, because those customers claim more often, so the higher average premium is largely justified by their higher claim rate. The finding is that an individual is making a poor decision for themselves, not that a company is running a swindle. Those are different claims, and only the first one is supported.

Extended warranties, and what the numbers on them say

The purest case of getting this backwards is sold at every till.

An extended warranty on a $400 phone, or a $1,200 service contract on a car, is insurance against a loss you could absorb. It has to be priced above its expected cost or nobody would offer it, and the numbers give the scale. Consumer Reports' 2014 survey found the average car service contract cost $1,214 against a median of $837 of repairs used, and that 55% of buyers never used the contract for a repair. On laptops, 15% of buyers with a PC warranty used it for a repair, and 7% of Apple owners with extra coverage.⁴

Notice that the first comparison puts a mean against a median, and lesson 1 told you what to do about that: the median discards the tail, and the tail is the whole point of insurance, so the gap between $1,214 and $837 overstates the case a little. The argument survives anyway, and the reason is the one this lesson keeps returning to. On a car, the tail is a transmission; on a $400 phone the tail is $400, and a policy cannot protect you from more than the thing is worth. Where a service contract does pass this lesson's test is the case worth naming: a used vehicle with a plausible five-figure failure, owned by somebody who could not absorb one.

The point is not that the sellers are dishonest. The point is the one the St. Louis Fed's own teaching note makes: a warranty provider "must charge their buyers more than what they will likely need in coverage so that the provider makes a profit", which is true of every insurer and is fine when the risk is one you could not carry. What makes a warranty a poor deal isn't the margin but the size of the loss it covers, because a $400 phone is on the wrong side of the absorbability test before any pricing question arises.

The alternative is not "go without". It is to notice that you already have the mechanism. Lesson 2's cushion is a fund that pays for broken phones, and it charges you no margin.

Life insurance, and who actually needs it

Life insurance is for people whose income, or whose unpaid work, somebody else depends on. That is most of the needs test, and it explains the cases people get wrong in both directions: a single person with no dependants and no shared debts usually does not need it, and a stay-at-home parent whose work would have to be replaced at cost usually does, despite having no salary.

There are two shapes on the market and the difference matters. Term insurance covers a defined period, pays if you die within it, and builds no cash value; its premiums are lower in the early years. Cash-value policies (whole life and its cousins) pay a death benefit and also accumulate a balance, and cost more. Part of each premium buys the death benefit, part pays the expenses and charges, and what is left accumulates as the cash value, which is why a cash-value policy is a bundle of insurance and a savings product. That means lesson 5's question applies to the savings half: what does it cost, and how does it compare with buying term and putting the difference somewhere cheap? Sometimes the bundle is the right answer. What you should not do is compare a term premium against a cash-value premium and conclude that one is expensive, because they are not the same product. The state regulators' own buyer's guide gives the practical instruction: ask for an illustration showing future values and benefits, and check whether you could still afford the premium if it rose.⁵

How much, and for how long, is a question you can answer yourself, and it is the one the needs test turns into arithmetic. Term insures a specific obligation for a specific period, so total the obligation. Someone with a $180,000 mortgage balance, a partner who would need perhaps three years of their $40,000 income to reorganise, and a five-year-old means roughly $180,000 plus $120,000, and a term long enough to carry the child to independence, so twenty years rather than ten. That is a defined answer arrived at from their own facts, and it will be wrong in the details and right in the order of magnitude, which is the useful kind of wrong. Notice that the number falls every year as the mortgage shrinks and the child grows, which is why the sum is worth redoing rather than buying once and forgetting.

Two things the simple needs test misses, and a well-informed reader would raise both. Insurability is itself worth something, since a policy taken out while young and healthy locks in a price that a later diagnosis would raise or remove. And some obligations survive death: a co-signed private loan or a co-borrowed mortgage can land on the other signatory, which is a dependency even when nobody depended on the income.

What people get wrong

"Insurance is a rip-off because they profit." True that they profit and false that it follows. You are paying to move a risk you cannot carry to something that can, and the margin is the price of the move. The correct version of the complaint is narrower: do not pay that margin on losses you could absorb.

"I've paid in for years and never claimed, so it was wasted." The product was the protection, and you used all of it. This is only a real complaint when the risk was one you could have carried.

"A low deductible is better coverage." A low deductible is more coverage of the part you can most easily cover yourself, and the evidence says most people buy too much of it. What determines your right deductible is your cushion.

"Health insurance covers what I think it covers." It covers a defined list, in-network, up to defined limits. The out-of-pocket maximum is the number that bounds your bad year, and it does not bound out-of-network care, non-covered services or premiums.

"Life insurance is for everyone." It is for people whose income others depend on. That is a real answer rather than a sales answer, and it is why the question "who would be in trouble if I died tomorrow?" comes before any product.

"I'll deal with it if it happens." The whole point of the failure mode is that it arrives with no notice and no cash. That is not a plan, it is the absence of one, and it is the state insurance is designed to prevent.

What we know about what insurance does, and what is argued over

Two things here are worth separating, because the first is unusually well established and the second is not.

What one trial found insurance does. The Oregon Health Insurance Experiment is the closest thing to a randomised trial of health coverage in a modern US setting. Oregon had more applicants for a limited Medicaid expansion than places and chose a lottery as the fair way to ration them, which also produced a genuine control group. After two years, coverage increased the use of care and the amount spent on it, raised the detection and treatment of diabetes, improved self-reported health, cut the rate of screening positive for depression by about nine percentage points, and cut catastrophic out-of-pocket spending, defined as more than 30% of income, from 5.5% of people to 1.0%, a fall of more than 80%. It produced no statistically significant improvement in blood pressure, cholesterol or blood-sugar control.⁶

That last result is the one people quote, and it is the one most often over-read, so be precise about what it can carry. Few people in the study had the conditions those three measures track, so the confidence intervals were wide enough to contain improvements that would matter clinically. The finding is that the trial did not detect an effect on those measures in two years, which is not the same as finding there is none, and two years is short for cardiovascular outcomes.

What the trial did measure cleanly, and found large, is financial protection, which is what the pooling argument at the top of this lesson says insurance is for. Both sides of the policy argument have read the same results differently and neither reading is silly: the increase in use with no detected biomarker gain is the efficiency critique, and the near-elimination of catastrophic costs is the protection case. This course reports both and settles neither.

What is disputed. How often medical costs actually cause bankruptcy is genuinely contested, and the dispute is a first-rate exercise in reading a statistic, which is why it is here rather than left out.

Himmelstein, Warren, Thorne and Woolhandler surveyed people who had gone bankrupt and asked whether they had substantial medical bills or illness-related income loss, counting those who did. They found medical events involved in about 60% of personal bankruptcies.⁷ The strength of that design is its reach: it picks up every route by which illness arrives at a household's finances, including the ones no hospital record contains, and it asks the people it happened to.

Dobkin, Finkelstein, Kluender and Notowidigdo re-asked the question with a different design. They took hospital admissions in California and compared people's bankruptcy rates before and after their own admission, which separates the effect of the medical event from everything else in their lives.⁸ The strength of that design is that it can show causation. Their arithmetic is worth following, because you can check it. An admission raises the annual chance of bankruptcy over the next four years by 0.004. About 7.8% of that population is admitted in a year, so 0.004 multiplied by 0.078 gives 0.031% of the population going bankrupt each year because of an admission. The annual household bankruptcy rate among the non-elderly is 0.8%, and 0.031 divided by 0.8 is about 4%.

Their criticism of the survey method is worth learning as a general habit. About 20% of Americans have substantial medical debt, and under 1% file for bankruptcy in a year. So finding medical debt among people who went bankrupt does not by itself show that the debt caused it, any more than finding that most bankrupt people own a phone shows that phones cause bankruptcy. Something has to separate the two.

Himmelstein and Woolhandler's reply is as pointed, and it is the stronger half of it that matters. An admissions record is a narrow instrument: a household can be ruined by outpatient costs, by a chronic condition needing drugs that cost tens of thousands a year, or by months out of work, none of which involve an admission, and the design "is not designed to measure bankruptcy associated with a child's or spouse's illness". So the 4% is not an estimate of medical bankruptcy; it is an estimate of hospitalisation-caused bankruptcy, and everything outside that channel is unmeasured rather than shown to be zero. They add that "almost everyone we labeled 'medically bankrupt' explicitly told us that medical problems caused their bankruptcy", which is evidence of a kind, though of a kind that cannot settle a causal question on its own.⁹

Both are right about what they measured, and they measured different things. One counts every route by which illness can wreck a household's finances and cannot show causation. The other shows causation cleanly for one route and misses the others: outpatient costs, chronic conditions, a family member's illness, and lost income without an admission. The number you should carry out of this is neither 60% nor 4%; it is that the question "how many bankruptcies are medical?" is not answerable without saying what counts as caused by, which is the same discipline lesson 1 applied to the $400 factoid.

This course takes no position on US health policy. What it will say is the thing both camps agree on, which is that in a system where a hospital stay can generate a five-figure bill, the out-of-pocket maximum on your own policy is a number worth knowing by heart.

Practice

Connections

Lesson 2 built a cushion and called it an emergency fund. This lesson gives the more exact name: it is self-insurance, it is what lets you carry small risks without paying anyone a margin, and it is also the thing that decides what deductible you can afford.

Lesson 1's habit of asking what a statistic measures gets its hardest workout here. Two research groups produced 60% and 4% for what sounds like the same question, and both are defensible, because they counted different things.

Lesson 4's habit of asking what an average is actually an average of is what makes this lesson possible and also what it has to argue with. The average year says do not buy insurance; the shape of the risk says buy it for the losses you cannot absorb. Knowing when an average is the wrong tool is a harder skill than computing one.

Lesson 1's split between fixed and variable costs turns up here as something you can choose rather than something you inherit. A premium is a fixed cost you can put in a budget; a claim is a variable one you cannot. Part of what you buy when you insure is the conversion of the second into the first, which is exactly why lesson 2's budget survives a bad year better with insurance in it than with the same money saved.

Lesson 5's cost lens is what you point at a cash-value life policy, and lesson 7's distinction between a wrapper and what is inside it is the same distinction in a different costume.

Lesson 9 takes the largest financial decision most people make, which is housing, and one of its inputs is now on the table: homeowner's insurance is a line item in the cost of owning.

Go deeper

• KFF, Employer Health Benefits Survey, published every autumn and free. If you want to know whether your own plan is generous or thin, this is where to compare it.
• Justin Sydnor, "(Over)insuring Modest Risks", American Economic Journal: Applied Economics, 2010. Twenty pages, readable, and the rare piece of behavioural economics with a clean dataset behind it.
• NAIC Life Insurance Buyer's Guide. Written by the state regulators rather than by anyone selling a policy, which is exactly why to read it before you talk to anyone selling a policy. Your own state's insurance department also handles complaints.
• The Oregon Health Insurance Experiment. The project page links every paper, and the summaries are written for non-specialists.

Sources

[1] KFF, Employer Health Benefits 2025 Annual Survey, Summary of Findings; average annual premiums $9,325 single and $26,993 family, worker contributions $1,440 and $6,850, 88% of single-coverage workers with a general annual deductible averaging $1,886, the firm-size split ($2,631 at firms of 10 to 199 workers against $1,670 at larger firms), 34% of covered workers with a deductible of $2,000 or more, average copays of $27 and $45, average coinsurance 19% for office visits and 20% for a hospital admission, the out-of-pocket maximum distribution, and 61% of firms with 10 or more workers offering health benefits. https://files.kff.org/attachment/Employer-Health-Benefits-Survey-2025-Annual-Survey-Summary-of-Findings.pdf . The out-of-pocket maximum definition quoted in full, its exclusions, and the 2026 federal limits of $10,600 individual and $21,200 family are at https://www.healthcare.gov/glossary/out-of-pocket-maximum-limit/

[2] Aviva Aron-Dine, Liran Einav and Amy Finkelstein, "The RAND Health Insurance Experiment, Three Decades Later", Journal of Economic Perspectives 27(1), 2013 (free at NBER as working paper 18642); the experiment ran 1974 to 1981 with more than 5,800 individuals from about 2,000 households across six US locations, and comparing the 95% coinsurance plan with free care gives a 39% decline in average annual medical spending, with the effect on inpatient spending small and generally insignificant. https://www.nber.org/papers/w18642 . The health-outcome findings of the original RAND investigators are not cited here, because rand.org refuses automated retrieval and this course does not cite what it has not read. The lesson therefore reports the utilisation result and names the health question as unsettled.

[3] Justin Sydnor, "(Over)insuring Modest Risks", American Economic Journal: Applied Economics 2(4), October 2010, 177 to 199; 50,000 policies, 83% choosing a lower deductible, $100 average premium to move from $1,000 to $500, claim rates under 5%, coverage worth under $25, the $500-deductible group paying about five times more than the insurance was worth, the roughly 18% subjective claim rate needed to justify the choice, and the finding that the insurer does not appear to earn excess profit on those customers because their claim rates are higher. https://www.aeaweb.org/articles?id=10.1257%2Fapp.2.4.177 . The alternative reading of the same choice pattern, as probability distortion rather than extreme risk aversion, is Levon Barseghyan, Francesca Molinari, Ted O'Donoghue and Joshua Teitelbaum, "The nature of risk preferences: evidence from insurance choices", American Economic Review 103(6), 2013.

[4] Federal Reserve Bank of St. Louis, Page One Economics, "Do you want an extended warranty with that?", October 2021, quoting the sentence that a warranty provider "must charge their buyers more than what they will likely need in coverage so that the provider makes a profit", and citing Consumer Reports' 2014 survey: an average service contract of $1,214 against $837 of median repairs used, and 55% of buyers never using the contract for a repair. https://www.stlouisfed.org/publications/page-one-economics/2021/10/01/do-you-want-an-extended-warranty-with-that . The laptop figures are Consumer Reports' own survey of laptop coverage: https://www.consumerreports.org/extended-warranties/extended-warranty-for-laptop-should-you-buy/

[5] National Association of Insurance Commissioners, Life Insurance Buyer's Guide and consumer pages; term against cash value, the instruction to ask for an illustration showing future values and benefits, and the question of whether you could still afford the premium if it rose. https://content.naic.org/consumer/life-insurance.htm . State insurance departments, which regulate these products and handle complaints, are listed at https://content.naic.org/state-insurance-departments

[6] Katherine Baicker et al., "The Oregon Experiment: effects of Medicaid on clinical outcomes", New England Journal of Medicine 368, May 2013, and Amy Finkelstein et al., "The Oregon health insurance experiment: evidence from the first year", Quarterly Journal of Economics 127(3), 2012; the lottery design, the increases in use of care, in diabetes detection and treatment and in self-reported health, the 9.15 percentage point fall in screening positive for depression, catastrophic out-of-pocket spending falling from 5.5% to 1.0%, and no statistically significant effect on blood pressure, cholesterol or glycated haemoglobin. https://www.nejm.org/doi/full/10.1056/NEJMsa1212321

[7] David Himmelstein, Elizabeth Warren, Deborah Thorne and Steffie Woolhandler, "Illness and injury as contributors to bankruptcy", Health Affairs, 2005, and "Medical bankruptcy in the United States, 2007: results of a national study", American Journal of Medicine 122(8), 2009; the surveys of bankruptcy filers behind the roughly 60% figure. https://www.healthaffairs.org/doi/10.1377/hlthaff.w5.63 . That page sits behind a bot wall on some networks; the 2009 companion study is reachable at https://pubmed.ncbi.nlm.nih.gov/19501347/

[8] Carlos Dobkin, Amy Finkelstein, Raymond Kluender and Matthew Notowidigdo, "Myth and Measurement: the case of medical bankruptcies", New England Journal of Medicine 378, March 2018; hospitalisation raising the annual bankruptcy probability by 0.004 over four years, a 7.8% annual hospitalisation rate, a 0.8% nonelderly household bankruptcy rate, the resulting 4% estimate, and the base-rate argument that about 20% of Americans have substantial medical debt while under 1% file in a year. https://www.hbs.edu/ris/Publication%20Files/NEJM%20Medical%20Bankruptcies_73829c0b-2f87-4898-89d4-5398e23017d0.pdf

[9] David Himmelstein and Steffie Woolhandler's reply to Dobkin et al., published by Physicians for a National Health Program, an organisation that campaigns for single-payer health care; quoted here for the authors' own statement of their case. https://pnhp.org/news/again-medical-bankruptcy-is-not-a-myth/

All dollar figures in the worked examples are invented round numbers chosen to make the arithmetic visible. Premiums, deductibles and out-of-pocket limits change every year and vary by state and plan; the figures quoted from source [1] are for 2025 and the federal out-of-pocket limit is for the 2026 plan year.