Simply by being alive we encounter some level of risk to our lives, health, and financial condition. Some people are happy to accept high levels of risk, while others want to mitigate that risk as much as possible, and are willing to pay money to do so.
Consider buying a car; you might think that it's worthwhile to pay a bit extra for some safety features, or purchase a newer car with more advanced airbag system than a lower-priced used car without those safety features. Those safety features are there to mitigate the risk of injury or death in the event of a collision, and are worth money to some people.
Nobody buys a car with the intention of crashing it (well, almost nobody). Most people would consider the risk of getting into a serious collision to be rather small, or they wouldn't drive at all. Still, we consider it worthwhile to pay for safety features just in case we are unlucky. Therefore, risk mitigation has a definite financial value.
In other words, nobody ever thinks "That was really stupid of me to pay for the side-impact airbag since I never had an accident in that car," or "I was so wrong to wear a life-preserver on my boat, I never fell off once."
Likewise, buying insurance is a way to mitigate the risk of an unlikely catastrophe. Insurance does this by spreading the cost of an unlikely event among a group of people, with the assumption that a small minority of them will need the money.
Here's where the math comes in. Assume I have 1000 people who find the costs of being struck by lightning unacceptable, and would like to share the burden of that risk among themselves. Also assume that these people's chances of getting struck by lightning is equal at 1 in 1000, so that in a given year, one of those people is probably going to get struck by lightning. Finally, assume that the medical costs associated with recovering from a lightning strike are $20,000.
To cover these people annually would cost $20,000 divided among 1000 people, or $20 a person. However, someone is going to have to collect the payments and spend the time handling the claims and doing research into the probability of a lightning strike, so there is overhead involved. Assuming these 1000 people designate a single person to handle their lightning insurance and agree to pay him $1 each for his trouble, and to cover the cost of mailing them a bill. Total cost per year in that case is $21,000 divided evenly, or $21 per person.
These 1000 people find this cost acceptable because even if they were to live 100 years, the total they would pay for this insurance is $2100. If they do not enter into the insurance agreement, it's possible they will end up responsible for a $20,000 bill they may be unable to pay, so they're willing to pay $21 a year to eliminate that risk.
And that's how insurance works, in a nutshell. Now, let's change the scenario a bit, and assume that a few of those 1000 people have jobs installing flag poles and antennas on rooftops, and are fifty times as likely to get struck by lightning as the others. The man handling the insurance realizes this and calculates that the overall cost of annual payment will be higher.
How much higher? Well, with a 1/1000 probability summed over 1000 people, the annual probability of a lightning strike is 1, with a cost of $20,000. [1] When there are five people with a 50/1000 chance of a strike, and 995 with a 1/1000 chance, the probability of one strike is still nearly certain, with the probability of two strikes increased. The average annual payout is as follows:
1 50
( ---- * 995 + ---- * 5 ) * $20,000 = $24,900
1000 1000
The increased probability of a lighting strike will, on average, cost the group $4900 a year. This money has to come from somewhere. The group gets together and decides that it's only fair for the people who are at increased risk for lightning strikes to foot the bill, so these five people will now pay $981.
The other option would be for these at risk people to form their own insurance group, however, since they aren't sharing the risks among as many people, their rates would be even higher.
"But wait!" you say. "This means that the larger the group, the lower the premium for everyone!" Although this can be true on a small scale, on a large scale the difference is minor or non-existent as long as the risk is the same. Consider another 1000 people with the same probability of getting struck enters into the agreement; the annual cost would double, but the incidents of lightning strike would double similarly.
We also are neglecting that in the real world, calculation of risk is an inexact science. Realize that the incentive for the flagpole installers is to downplay the risk of their own lightning strike, such that the insurance man cannot accurately calculate how much his annual payout will be. He will likely come up short, and the result will be a larger premium for everyone next year to cover the cost.
Also, in a very small group, the odds of a flagpole installer being in the group at all become much lower. Let's assume that a lot of people are not fully disclosing their flag installing tendencies, driving up costs for everyone. A group of 800 people may split off and decide that they will not just raise premiums for the flagpole installers, but will exclude them entirely from the group, keeping costs low and providing nearly the same risk mitigation.
Now that that's out of the way, let's examine what would happen if the risks assumed by the insurance group increased for the entire original group. Let's say that the climate changes and there are twice as many thunderstorms as before, so everyone is twice as likely to be struck. Obviously, costs would double, and premiums would now be $40 each plus overhead. The cost of handling twice as many claims may be more, but probably not double, so let's say the total premium would be $41.50 each, or there will not be enough money to pay the medical costs for everyone.
So, as the risk of paying expenses goes up, so do the costs, and it's a nearly linear relationship. What happens if the lightning gets so bad that everyone is almost guaranteed to be struck once during a year? The insurance man now is handling claims as a full-time job, so the overhead would be at least $30,000. The annual cost to provide this would now be:
1000 people * $20,000 + overhead = $20,030,000
Divided among 1000 people, the annual premium is $20,030.
What we've shown is that as the probability of the "risky" event approaches certainty, the cost of providing insurance becomes greater than if each person paid for their own expenses directly. There is essentially no reason to have insurance for an event that is certain to happen, and it is in fact an extremely inefficient way to pay for things.
In fact, as the probability of the costly event becomes more certain, the smart financial move is to NOT buy insurance. If I have a $20,000 premium and the cost of the medical care is $20,000, I am better off without insurance because on the off-chance I don't get struck by lightning, I've paid nothing and am $20,000 richer.
The overhead in the above example was kept small to make the math easy, but consider what the actual cost of providing insurance to 1000 people each year would be, and you'd see it would be much greater than $30,000. You'd average 2-3 claims a day, would have to verify and support each of those claims, detect fraud, do extensive paperwork and keep accurate records, etc. That's probably more work than one person could do alone.
How does this affect our current health care situation? As it exists right now, many insurance companies are required by law to pay for things that aren't risky at all, in fact a large part of them are routine. This is an abuse of the purpose and notion of insurance, and it guarantees increased costs, because there is little risk of not experiencing routine medical costs like annual checkups.
When insurance is required to act as an intermediary between a doctor and a patient instead of managing risk, higher costs and higher prices overall result.
The conclusion is: it is mathematical fact that in order for insurance to provide value, the services it covers have to be unlikely among a given population.
The irony is that people with "good health insurance" are probably very happy that their plan covers "almost everything," when in reality, they are indirectly paying through the nose for something that would be cheaper if they paid for it directly. And when people willingly pay for insurance plans that include coverage for routine care, insurance companies have little incentive not to provide these services.
In fact, if I were an unscrupulous insurer and the government tried to force insurance companies to cover certain routine procedures, I may be quite happy that they just gave me a license to make a profit on something that's not in my customers' best interest to buy. The only drawback for me would be that some of my customers would no longer be able to afford the premiums and would drop coverage entirely. Notice that neither case benefits the customer.
- The probabilities discussed here are simplified and would only be true averaged over a long time. If the probability of getting struck by lightning is 1/1000, the chance of a single lightning strike in a year among 1000 people is closer to 37%. The chance of no strike at all is also about 37%. However, the probability of two strikes is about 18%, three about 6%, and so forth. Taken together, over many years, you'd average about 1 strike per year.
No comments:
Post a Comment