Healthcare Econ 101: Why tax the uninsured?

My mother is a microeconomics professor at the University of Utah. I’ve learned a lot from her about game theory through osmosis, and in my last visit she taught me a lot of the basics of healthcare economics which I’ll try to explain over the course of several posts. Specifically about policy changes coming about because of the Affordable Care Act or “Obamacare”.

Remember throughout all of this that this model of the world is the microeconomics model, meaning that it is a very mathematical and theoretical view of the world. However, I think having a theoretical understanding of a large system can help you understand the impact of large policy changes.

Imagine that I, as a patient, fully know the probability of what my healthcare costs are. That is, if I’m a healthy 20-year old, I might know that I have a 90% chance of costing $0 and a 10% chance of costing $400.

This means that on average, I would cost $40. This is where insurance comes in. If someone offered me a deal where I could pay a fixed amount and they would cover all of my healthcare costs, how much would I value it at? Since humans are naturally risk-averse (Take a look at the Bernoulli Utility Function), they’re actually willing to pay more for this good. Let’s assume everyone has the same risk aversion curve and would be willing to pay 1.25x their expected cost. That is, the healthy 20-year old would be willing to pay $50 for full-coverage.

This is where insurance comes in as an economic tool. Insurance capitalizes on the difference between our valuation of full coverage versus the actual healthcare cost. Insurance companies can be far more risk-loving than individual patients, because they can distribute the risk amongst all of their patients! That means they can value full-coverage for this 20-year old at $40. I think it’s pretty damn cool that a behavioral instinct in humans, risk-averseness, is what allows for insurance to exist as an economic tool.

Now let’s imagine a world where patients are evenly distributed between $0 - $600 dollars of how much value full healthcare coverage.

If we were to design an insurance provider for this patient population that ran at zero profits, what would the price of full coverage be? This is assuming that patients are perfectly logical and buy insurance only if the price is lower than what they value it at.

You can set up some quick algebraic equations, but as it turns out, insurance is priced $400. This means everyone who values insurance from $400 - $600 will pay for it. Given the even distribution, that means the average patient values the insurance at $500. But in our system, the actual healthcare cost is $400. Thus, our insurance system perfectly breaks even! This system isn’t great since it only covers the high risk population and the price is high!

Now let’s go and implement some Obamacare policies on our simple system. Imagine everyone who doesn’t buy insurance faces a fine of $200 if they are not insured. What happens to the price of insurance?

The price of insurance drops to $266.67. Because of the fine, everyone who values insurance at more than $66.67 buys it. That means the average amount a patient values the health insurance is $333.33 (That’s ($600 + $66.67)/2), which means the actual healthcare cost is $266.67. Thus, again our health insurance breaks even.

So, our new insurance is priced far lower and almost covers the entire patient population! Our insurance systems rely on encouraging the lower cost patients to sign up in order to keep prices low and now you understand how Obamacare is trying to fix it… theoretically at least!


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