# The Economics of Insurance: Simple Examples Explained

Insurance has been in the news quite a bit recently.

Obamacare premiums are increasing. Trump wants to repeal the ACA and let free markets and competition drive prices down.

Everyone thinks they have a good intuition for this stuff because of their high school economics classes.

But is that how it really works?

This is going to be a long post building simple models of insurance to show that insurance is not a good that behaves like other economic goods. You can’t just apply “common sense” economics to insurance and expect to get the right answers.

It’s a very strange product.

## Economics of Insurance Basic Model

• We have a single insurance company and 1000 people in our world, all of Low Risk.
• We’ll assume this means they have a 1% chance of needing a doctor’s visit in the next year.
• In this world, the visit will universally cost \$200 without insurance.
• The insurance plan covers the whole visit.

All right.

This is really easy to figure out.

How much should the insurance company charge to make money (to continue existing)?

Well, they expect 10 people to need the visit, which costs them \$2000 for the year. This means they break even if they charge \$2 to each person for the year.

They need to make money to pay for operating costs, so let’s say they charge a freakishly low price of \$3 a year.

Now we run the model.

Since we’re using standard economic assumptions, we assume all people behave rationally.

Do the Low Risk people buy the insurance? If they do, their expected health cost for the year is \$3 (the cost of the insurance plus nothing else since the insurance company pays for the visit).

If they don’t buy it, their expected cost for the year is (.01)(200) = \$2.

Woops.

None of our rational actors are going to buy the insurance, and the company collapses from no business.

Fiddle with this.

Add in a .001% chance of a freak accident costing \$10,000 in surgery. Try to add in things that make it more realistic, like using a copay to lower cost instead of a yearly fee.

You’ll find that no matter how you fiddle with it, it will never be rational for Low-Risk people to buy insurance. It’s just a fact about insurance companies charging enough to make money. Note that adding in higher-risk people will only raise the price.

### Conclusion

Low-Risk people don’t buy insurance without something forcing them to, like an individual mandate.

Small Caveat: People aren’t rational, and this is good. They realize that even though they lose money by buying insurance, they are paying for something that can’t be quantified: security.

The monthly fee is worth the peace of mind that a freak accident won’t bankrupt them and completely ruin their life.

## Basic Model Tweaked

I’ll breeze through this because these are the exact same calculations with Medium-Risk and High-Risk pools of people.

If everyone has a Medium Risk of 50%, then the insurance plan must cost \$1000 a year per person to break even.

Woops.

We don’t have to go further. The policy costs more than paying full price for the doctor. Likewise for High Risk at 90%.

Conclusion 2: Insurance doesn’t work unless there are Low-Risk people in the pool to decrease the cost.

Conclusion 3: The more Low-Risk people in the pool, the lower the cost can be for everyone.

## Insurance Simple Economic Model Combined

Let’s combine the different risk types into one model, but the price of insurance is uniform across all risk.

This is obviously closer to reality.

We’ll assume that most are Low Risk, and as risk increases, the number of people in that category decreases. To do this properly we should probably use a distribution, etc, but let’s keep it really simple:

• Low risk: 900 people
• Medium risk: 95 people
• High risk: 5 people

The insurance company expects to pay [(900)(.01) + (95)(.5) + (5)(.9)] (200) = \$12,200 for the year.

They can break even by charging \$12.20 per person for a year of coverage. Let’s suppose they charge \$13.

The first conclusion still applies, meaning the Low-Risk people don’t buy it.

Assuming we force Low-Risk people to get the insurance, Medium-Risk people expect to pay (.5)(200) = \$100 for the year without insurance, but only \$13 with insurance.

Our rational Medium-Risk and High-Risk people willingly buy insurance in this case as long as enough Low-Risk people stay in the pool.

It is worth reiterating that under ideal assumptions and no mandate to buy insurance (and no subsidies), none of the Low-Risk people buy insurance, and the costs shift to Medium-Risk people.

It is no longer rational for them, so they don’t buy. The risk shifts to High-Risk people, they don’t buy, and the company collapses.

### Conclusion

Without forcing Low-Risk people to buy insurance, insurance companies will still collapse with a mixed pool of risk and uniform prices.

If Low-Risk people are forced to buy insurance, it becomes rational for higher risk people to buy insurance even with the company making money.

Since this is secretly a post digging into rhetoric from Trump, and he plans to repeal the ACA, it seems the mandate will be repealed. Take from this post what you will regarding this conclusion.

Caveat 2: In real life, people suck at determining their risk. Lots of Low-Risk people will think they are Medium, so under this delusion they rationally buy insurance.

But likewise, lots of Medium-Risk people think they are low risk. This makes it rational for them to not buy insurance.

If we assume the delusions are random and not skewed, the price will be slightly lower, but not enough to invalidate the Conclusion.

This is massively offset by the fact that High-Risk people (i.e. those with “preexisting conditions”) tend to need procedures that cost a lot more.

## Variable Price Simple Model

Let’s introduce variable prices for different risk.

Is it possible for the company to price policies to make money and yet be rational for everyone to buy it?

These are the exact same calculations we’ve been doing, but we don’t even have to do calculations to see this is impossible if we understand expected value/costs.

Independent of risk, it is only rational to buy insurance if your expected cost with insurance is less than your expected cost without insurance.

The insurance company only makes money on you if the price they charge is more than the expected cost.

Thus, to make it rational for everyone, they must set a price to lose money.

### Conclusions

Even with variable prices for different risk levels, insurance companies can never price policies to be rational for everyone to buy.

Even under ideal economic assumptions, if there is only one insurance company, it will always fail without a mandate to increase Low-Risk buyers or some form of subsidies to lower prices.

Let’s take a quick breather here.

Hopefully, if you’ve never thought about this carefully, you’re starting to see why applying “common sense” economics from your high school class might not get you to the right conclusions.

Insurance is super weird as a commodity. But things are about to get weirder.

Caveat: One could probably write a 500-page textbook just introducing appropriate complexities to the single insurance company model.

I am under no delusion that the above analysis bears any resemblance to the “real world.” These are supposed to be overly simple models to challenge people’s intuition.

## Insurance Economics with Competition

Competition!

Now let’s assume there are 2 insurance companies. They compete with each other for selling policies.

There’s already something weird here because unlike standard market economics, a sale is not a sale.

If there are two apple vendors, the vendor doesn’t care who they sell the apple to. A sale is a sale. They make the same money no matter who buys it.

The Medium- and High-Risk people cost the insurance company money, whereas the Low-Risk people make the company money.

So what’s rational for the company in this case?

They want to separate prices. They want policies for Low-Risk people to be lower than the competition, but they want policies for higher-risk people to be higher than the competition so they go to their competitor. This way their competitor loses money!

They aren’t in competition for the people who most need insurance. For those people, competition increases the price of insurance.

I’ll reiterate this again as a conclusion.

### Conclusion

For the people who most need insurance, competition increases the price of insurance.

For the people who don’t need insurance, in a perfectly free market under ideal assumptions, they aren’t buying it anyway, so who cares what their price is?

Yeah.

Insurance isn’t quite so intuitive, is it?

I’ll end by reminding you of the fundamental difference between selling goods and insurance.

If a company decreases the price of a good to steal customers from a competitor, they make up the loss from lowering the price by selling more.

This is why competition lowers prices.

More sales of insurance doesn’t necessarily lead to more profit.

Thus, if an insurance company lowers prices, they don’t necessarily make up the loss due to price by selling more.

We didn’t even scratch the surface here, but this post has gone on longer than most of you will read.

I wanted to get to scenarios like government regulating uniform prices across risk together with competition and variable policies.

(Hint: competition could lead to an increase in trash policies which cover practically nothing so lowering prices guarantees more profit but defeats the whole purpose of insurance).

Maybe next time.