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> By definition, insurance is literally not intended to save the insured person money, in expectation.

You fundamentally misunderstand the concept of insurance. Group insurance is, by definition, a way to spread the cost of rare catastrophes around the group so that the affected individuals don't bear the full brunt. There is the full expectation that in the event of a major medical event you will save money.

Try reworking your example around major medical events (e.g. a $500K hospitalization) rather than preventive care (the function of which is to reduce the risk of certain controllable medical events).

> What will be the co-pay for the annual physical for an insured patient?

> The answer is that it will be $100 - there is absolutely no risk involved in this situation, so the expected payouts of the insurance company will be $100, and therefore they will incorporate that into their price.

No. Even pre-ACA, insurance companies offered low co-pays. How did they do that? Because your monthly fees will over the course of a year add up to far more than the cost of an annual physical. The purpose of insurance is to protect yourself against rare, but catastrophic events: you will probably not experience a wide variety of expensive medical ailments, but if you do they will likely leave you in financial ruin if you're uninsured, so you pay an insurance company money to protect yourself against that risk.

(Or, alternatively, your employer pays a health insurance company money to protect you against that risk, and offers that benefit to you as part of your total compensation package. Which is essentially the same as you paying for it, with some amount of risk differences and thus potentially lower costs due to the pooled employee health insurance policies, but that's outside of the scope of this discussion. TL;DR: it's still regular market economics.)

You might wonder why insurance companies offered low co-pays at all — was it just some marketing gimmick? But no, you can explain that with regular economics too: insurance companies are incentivized to make annual physicals affordable and attractive, because they can catch potentially-expensive medical issues when they're still much less expensive, thus lowering costs for the insurance company.

> The purpose of insurance is to protect yourself against rare, but catastrophic events: you will probably not experience a wide variety of expensive medical ailments, but if you do they will likely leave you in financial ruin if you're uninsured, so you pay an insurance company money to protect yourself against that risk.

Yes, this is what I am saying. However, that has nothing to do with the price of co-pays for routine care, which is by definition predictable.

> But no, you can explain that with regular economics too: insurance companies are incentivized to make annual physicals affordable and attractive, because they can catch potentially-expensive medical issues when they're still much less expensive, thus lowering costs for the insurance company.

See, this is another pervasive myth. For healthy individuals, the annual physical is not cost-effective - it is very unlikely to result in long-term benefits to the patient, and it is far more likely to result in unnecessary care (such as follow-up tests and differential diagnoses for false positives): https://sciencebasedmedicine.org/re-thinking-the-annual-phys...

Also, I don't know why you're drawing a dichotomy between what I'm saying and "regular market economics". Everything I have said is standard, textbook economic theory. There's nothing obscure or even controversial about it about economists.

Insurance companies are for-profit institutions, and there's no law compelling them to offer co-payments for preventative care. Do you believe that insurance companies are giving out charity?

> Everything I have said is standard, textbook economic theory. There's nothing obscure or even controversial about it about economists.

Claiming that "health insurance isn't really insurance, except in name - we talk about it as insurance, but in reality, it's a wealth redistribution program tacked onto a risk smoothing product" is definitely non-mainstream. An insurance company takes in payments to insure you against high-risk events, and that's exactly what a health insurance company does: you pay them a monthly fee regardless of whether you need medical care (or your employer pays them for you as part of your compensation package), and when you do need expensive medical care, they pay for it. In fact, many plans explicitly only pay for expensive medical care: anything under your deductible, aka inexpensive medical care, you're required to pay for. You might be able to make some sort of weaker claim about wealth redistribution post-ACA, but — co-payments existed pre-ACA.

> Insurance companies are for-profit institutions

Actually, some of the largest insurance companies and the vast majority of risk-bearing providers (hospitals that act as insurers) are non-profits. Though I never said that their pricing was based on charity; I said it was based on the fact that the product they offer is not really insurance (and that it exists in a marketplace in which prices are incredibly distorted by the existence of other factors, which would have been too long to explain in that simple example).

> Claiming that "health insurance isn't really insurance, except in name"... is definitely non-mainstream

On the contrary, that's the overwhelming consensus among economists. Which isn't surprising, because the economics of insurance are generally covered even at the undergraduate level, and the ways in which health insurance differs from a true insurance program are pretty glaring.

The five largest health insurance providers in the U.S. by market share are UnitedHealthGroup, Kaiser, Anthem, Aetna, and Humana. Of those five, all but Kaiser are strictly for-profit, and Kaiser is a consortium of for-profit and non-profit entities.

Equating risk-bearing providers and health insurance companies for the purposes of arguing that health insurance isn't insurance might as well be tautological. Sure, blueberry pancakes aren't really pancakes if you include blueberry muffins in the category of blueberry pancakes, but who cares?

I don't follow, unless you regard 'health insurance subsidies' as a part and parcel of 'health insurance'. Means-tested health insurance subsidies are absolutely a form of wealth redistribution, no doubt, just like housing subsidies are wealth redistributive - but that doesn't mean that the home rental market is wealth redistribution in disguise.

This only holds true if the physical only identifies disease that have downside risk. More realistically, most early identification situations can greatly reduce the cost of future care, eg the overweight 40 y.o. who intervenes to avoid being the obese 60 yo.

It also ignores a number of other selection criteria and behavioral issues, which you are honest enough to note in your pretend for a moment intros.

However, people who proactively care for their health carry "upside risk" as well as downside, which your scenario does not account for.