Health Care

Health Savings Accounts Will Solve Our Health Care Spending Woes

HSAs solve a problem, but not the problem.

Republicans are enthusiastic! From many of them I’ve heard about Health Saving Accounts. It’s not that hard to control health care costs, they say. Just reconnect health care consumers to their spending. Most recently, Dr. Ben Carson weighed in, even suggesting that the government simply fund people’s HSA to the tune of $2000 per person. I’m told that support for HSAs is an important plank in the (possibly mythical) “Republican healthcare plan.”

What’s an HSA?

An HSA is a pre-tax account into which you and/or your employer can put money reserved exclusively for health care costs. It might work like this: In lieu of traditional health insurance for minor medical expenses, your employer might provide you with an HSA to which she contributes. You could also put money into your account yourself. The first health care costs incurred that year would be paid out of your HSA. Once the HSA is exhausted, you, the employee, are responsible for paying medical bills directly. An HSA is usually coupled with a major medical insurance plan with a high deductible so that beyond several thousand dollars in medical bills, a traditional insurance plan kicks in.

How an HSA worksAn employer once offered this to my family. We paid a portion of our premium and got $2000 at the beginning of each year added to our HSA. From this account, we paid the full cost of all our medical expenses–doctor visits, medications, etc.. No copays or cost-sharing. Your HSA pays it all. If expenses got high enough, this account would run dry. After that point, we would pay all expenses out of pocket. To protect us on the high side, the plan included a major medical policy which would begin to cover expenses beyond about $4500, just like a standard insurance policy with a high deductible. You might think this was some scheme by my ruthless employer to cheat us out of health care, but my engineer co-workers and I all agreed. There was no scenario in which this plan would cost employees more than the old plan. If you go to the doctor once for $250, you pay less than the old plan. If you get cancer and rack up $600,000 in bills, you still pay less than the old plan. And for every point in between those two, the new plan was still less expensive for employees.

Market-based savings

So why did my employer make this change? The idea is that employees will pay attention to the cost of their health care and that alone will reduce costs. And it worked, at least on a personal level. We started asking, “How much does that cost?” and “Could we give it another day before seeing the doctor?” We didn’t have any major expenses while under that plan, but if we did, I think I would have asked “Is that the cheapest MRI, or just the closest?” This is where the GOP puts their faith. Unsurprisingly, they count on shrewd consumers in the free market and the responses of equally clever suppliers to bring prices down and quality up. So, is your blowhard Republican roommate right?

But not where we need it most

Unfortunately not. HSAs are effective at controlling costs for small medical bills, but America’s problem is at the other end. We’re spending over half of our health care dollars on just 5% of patients. Those people have long exhausted any reasonable HSA. Meanwhile, the bottom 50% of spenders, those still spending money out of their HSA, account for just 3% of all health care spending. Probably HSAs will affect almost none of the top 20% of health care spenders which account for 80% of health care spending. This graph, borrowed from NIH, shows this effect quite clearly. On the lower axis is the percentile rank according to health care spending. The vertical axis is the  fraction of health care dollars spent on everyone below that percentile rank. So, when we see that the 40th percentile has the value of 1.4%, we know we spend 1.4% of our health care dollars on the healthiest 40% of patients. The steepness of this curve indicates that the spending addressed by HSAs is a very small portion of total spending.

Most of our health care dollars treat just a few patients.

Health care is classically, almost pathologically, unsuited to a free market. Demand is inelastic. Information is asymmetric. And the numbers are so far beyond people’s experience, that we have great trouble assessing risk and valuing the different health care products. This problem just gets worse for more expensive treatments and, as shown in the graph above, that’s where the problem is. Even if HSAs dramatically reduced costs for the 80% of us whose costs fall under their major medical deductible, we’d still go bankrupt unless we find a way to control costs for that top 20% who’ve exhausted their HSA and have no personal incentive to control costs.

So, even without asking whether convincing people to postpone their colonoscopy or shop for the cheapest throat culture is really a net savings, we can conclude that HSAs are ignoring most of the problem. That doesn’t mean HSAs are a bad idea, but they are, at best, window dressing for anything aspiring to be called a “health care plan.”

#BecauseMath Economics Health Care

The Market Will Set the Right Price for Health Care

I don’t suppose the interweb needs another discussion of the failings of market forces in health care markets. And yet the idea persists that setting the price of health care should be left to the unregulated market and that this will lead to maximum efficiency. The omnipotence of the market is a comforting concept.

Demand-side troubles

But the market for anti-retroviral drugs bears little resemblance to golf clubs or top sirloin. At risk of sounding condescending, a typical demand curve looks like this


As the price of a good or service rises, the quantity demanded shrinks. Lots of people will buy a pair of basketball shoes for $6. A few would pay $140.

But this doesn’t often work for medical services. I recently had my appendix removed. I’m told a typical appendectomy costs $25,000–a lot of money no matter who you are. But whether it had cost $100 or $100,000, I still would have bought exactly one appendectomy. The demand curve for appendectomies looks more like this:

Quantity demanded is unaffected by price
Quantity demanded is unaffected by price

There is, perhaps, some fall in demand. A 96-year-old might decline a quarter million dollar appendectomy. In some cases, there may be more than one treatment for an ailment so that one good or service may be substituted for another. But, in general, demand for health care services, especially the very expensive, life-saving treatments, tends to be highly inelastic. The quantity demanded is affected very little by the price. So, can providers of health care charge whatever they like?

Supply-side salvation?

Not necessarily. There may be some help on the supply side of this market. But, one reason markets are so effective and robust is the interplay of supply and demand. Without both working properly, the market can misallocate. When the supply side of the equation breaks down, for example in the case of a monopoly, we know that even with a healthy demand side, we’ll run into inefficiencies. So, we already have cause to worry. A truly effective market needs both a healthy demand side and supply side.

Switching to the supply side of things, if the price of a good is very high, more people will be willing to supply it. A supplier that overcharges will find herself undercut by a competitor willing to supply the good at a lower price. So, even with highly inelastic demand curves, there’s an equilibrium price at the point where the supply and demand curves meet.

The market sets the price where the supply and deamnd curves meet.
The market sets the price where the supply and deamnd curves meet.

So, it all might work out just fine, as long as actors can’t manipulate the supply curve. Unfortunately, two of the easiest ways to do that are both, of necessity, highly active in health care markets. The first is patents. A patent grants a single company the exclusive right to produce a product for a certain period. A supplier with a patent cannot be undercut by a cheaper competitor. When you are the only supplier of a lifesaving procedure, the market will not place any limit on the price (although public opinion or your own morality might). For this reason, it’s more useful to think about the supply curve for health care research than for particular treatments. If the payout for developing a new drug is very high, more people will be willing to do research toward that end. So, even where patents are applied, there is a functioning supply side curve at work. But in such a market, price signals can take longer to move through the market. When I need medication today, it’s slim comfort to know that the exorbitant price I pay for patent-protected drugs is providing the impetus for a robust market for drug research.

Another common way to move a supply curve is through licensing. Most people who treat you in the hospital are licensed, some of them very licensed, which is wonderful. It comforts me immensely that the person holding the scalpel has undergone years of training and scrutiny. But, the effect of this is to reduce the supply of doctors, nurses and other medical professionals. The FDA’s approval processes provide the same type of scrutiny for medications, equipment and treatments, with the same effect.

I wouldn’t have it any other way, of course, but the effect of this licensing is to shift the supply curve downward, increasing the price of goods. The further the supply is reduced, the higher the price. The inelasticity of the demand curve (and also the supply curve) multiplies this effect.

As the supply is reduced, the price increases.
As the supply is reduced, the price increases.

You can see how influence of these licensing processes could be very lucrative for suppliers. Doctors, for the most part, do important work for sincerely good reasons, but putting the AMA in charge of licensing doctors is a lot like asking the fox to guard the hen house. The tendency of almost everyone is to highly value their own work and the incentive for doctors is to limit the supply of doctors, raising their own salaries. Similarly, if pharmaceutical or medical supply companies can delay or scuttle approval for competing drugs and equipment, they also stand to make lots of money.

I’m not for a minute suggesting we do away with licensing of doctors or patents for drugs. Health care markets can’t be effective without these things. But, perhaps it’s a good idea to think hard about the markets for health care rather than blithely assuming the miraculous market will allocate everything just right. Without some advocates for consumers of health care, rising, inelastic demand will push prices out of reach and make life-saving care an unaffordable luxury.

Health Care Media

Obamacare is killing this pastor

Sometimes these posts write themselves. Since I started this blog, I’ve been exposing myself to more right wing news sources. Occasionally, it really feels like cheating. Today, Fox News tweeted this


This Iowa pastor has cancer. His old insurance plan refused to cover his treatments due to a pre-existing condition. As a result, he has $50,000 in medical debt. He went to and found a “gold” plan that would cover he and his wife for $800 per month. But, because he signed up on the 18th of February instead of the 15th, his coverage doesn’t start until April 1. Now, who in their right mind thinks this is an Obamacare horror story? Fox. Oh, wait…

Faith Foreign Policy Obama

Leadership…it’s all about posture!

A special midweek stupidity update. I’m aware that not everyone reading this post is a Christian. But, a solid majority of people tweeting and retweeting this graphic are's about posture’s about posture

As a Christian myself, I’ll admit to being quite pleased with ThisWeekInStupid’s response below:

I think you may be right
I think you may be right


Have a good week and don’t forget to follow ThisWeekInStupid on twitter.

Foreign Policy Obama

The President’s failure to act has made troubles worse

Mitt Romney, bolstered by the recent praise from the Right on his prescience in identifying Russia as “our primary geo-politcal foe,” thought he’d weigh in on, well, everything. He did it in the Wall Street Journal here. As someone interested in Ukraine before it was cool and as self-appointed liberal liason to the Right, I’ve read a lot of conservative commentary on Ukraine. And this is not the dumbest, but it’s up there. Mitt, to his credit, doesn’t spend a lot of time, as others have, extolling Putin’s acumen in out-maneuvering Obama. This is an ignorant point of view. In fact, what Russia has done is further de-legitimized the UN Security Council–one of the last remnants of a world in which Russia could diplomatically influence other nations. What’s more, there are legitimate legal challenges to Russia’s permanent membership on the council. I’m neither an international law nor diplomacy wonk, but the idea of a formal challenge to Russia’s permanent membership would have more sticking power now than at any time. Those with a sense of irony, might propose that the permanent seat of the dissolved USSR (which seat Russia now occupies) should be rotated among the former Soviet Republics–Ukraine, Georgia and the Baltic states, for example. There’s a certain delicious parallel between this and Putin’s abandonment of the Budapest memorandum on the grounds that it was signed by a different Ukrainian government.
Further, if 4 of the 5 nations on the Security Council (the US, Britain, China and Russia) feel justified in waging wars over the objections of the majority of the security council membership, then a diplomatically and economically isolated Russia can do very little for its allies out of the immediate reach of it’s tanks and bombs.
And we haven’t even begun to discuss the economic costs to Russia, estimated at $400bn this year. That’s 20% of GDP or $2800 from every Russian (whose average salaries are just $800/month). And that’s before figuring losses due to any sanctions. I’m with (gulp) Ted Cruz on the idea of expanding natural gas shipments to Europe to increase these costs. Contrary to popular belief, Putin is no king. He has political rivals and has a parliament to wrangle. Anyone paying attention understands that this is a big tragedy for Vladimir Putin at home and abroad. Last November, he had an ally on his huge southern border and some semblance of legitimacy in the world.
But we were talking about Mitt Romney. His piece did have one thing in common with the rest of the neo-con idiocy out there. Mitt asks the question
Why are America’s hands so tied?
which ought to be rhetorical to anyone not in a coma last decade, and yet Mitt weaves some yarn about how, if we’d just been more willing to arm Middle Eastern freedom fighters, things would have been fine.
The 80’s called, Mitt. They want their foreign policy back.

Economics Morality

Selfishness is Good

For our first real post, we’ll turn to a deeply entrenched conservative belief. You might expect this on a site called ThisCentury(and Last)InStupid. It’s the idea that selfishness isn’t so bad after all. In fact, we could use more of it.

Occasionally, someone comes out and states this explicitly, but not usually.  More often its the implied justification of cruel policy. Or it appears as an allegory as in Paul Ryan’s favorite ode to greed, Atlas Shrugged. As will be familiar to many, Atlas Shrugged is a novel by uber-capitalist and self-professed narcissist Ayn Rand about a fictional America in which all the captains of industry tire of being disrespected, regulated, demonized and (most egregiously) taxed and decide to flee society to a secret mountain enclave and live together in capitalist utopia. The rest of the country, bereft of its “engine” grinds to a halt. Poverty and violence ensue.

This vision is the engine behind Republican policies that, sometimes quite overtly, enrich


the wealthy at the expense of everyone else. One fine recent example is the refusal of Republican Governors across the country to expand Medicaid in their states. Although it would cost their governments very little, and benefit the poor quite a lot, the principle of giving as little to the poor as you can get away with is so ingrained that they’d rather leave the poor without health care and let them be treated in emergency rooms and the cost of their unpaid care absorbed into the premiums of the rest of the state.

Or there’s the fact that we can’t close the “carried interest” loophole by which the income of hedge fund managers is taxed as if it were long-term capital gains or dividends (on assets they don’t own!). No matter how you feel about lower rates on capital gains, these are clearly income. So, you have people paying 15% on their multi-million dollar income. The people emptying their trash pay a higher rate. There are efforts at very high levels to fix this, but none very successful.

Agitation against sensible policies to alleviate poverty are often accompanied by mumbled pseudo-economic arguments about how discouraging the money-making activities of the wealthy will harm us all or how giveaways to the poor create dependency. But, simmering beneath the surface of these attempts to make economics support fiscal austerity is an audacious Republican hope–one buoyed by this Randian vision. The wish at the heart of modern conservatism is that selfishness, in the end, will turn out to be altruism—that, when the score is all tallied, the best thing we can do for the poor is to stick it to them just as hard as we can. Thus conservative guilt is swept away by one swift stroke of Milton Friedman’s pen.  This miraculous moral alchemy whereby, if two wrongs don’t make a right, nonetheless, two million do, is unchallenged on the Right since Adam Smith despite its manifest stupidity. This is partly because it’s unstated but also because it’s so damned useful. It was useful during the Cold War marriage of what today are called social and fiscal conservatism by severing the link between Christian charity and social welfare. It continues to be useful in justifying the neglect or animosity toward the social contract by the upper and middle classes today. It makes conservatism easier on the soul.

Now, some conservatives will try to separate personal and public morality saying that while public welfare programs harm the poor, private programs are another matter altogether. Of course, the original source of the charity can’t likely save the poor from the dependency-producing effects of free stuff. This view is likely more closely related to another pervasive dose of stupid up for discussion in a later post : “The government can’t do anything right.”

So, you heard it here first: Selfishness isn’t good. It isn’t noble or necessary or even inevitable. It wrecks communities and nations and, in a cosmically ironic twist, makes it’s practitioners the most miserable of all.

Appendix Economics

Appendix: Galt-ifying public goods

See how deep the rabbit hole goes…

In our first appendix, we wandered a little into the math behind public goods. That post has less algebra and more graphs. If what you read here is moving too fast, that might be a good place to start.

Public goods, in brief, are goods which you don’t have to own to enjoy. These are things like public parks, an army, or your neighbor’s front lawn. In that post, we assumed a particular form for a utility function for public goods.

[latex] \mbox{Utility} = \sqrt{\alpha S_0 + \sum\beta S_i}[/latex]

where $latex S_0$ is the amount I spend on the good, $latex S_i$ are my neighbors’ spending. The parameters, $latex \alpha$ and $latex \beta$ determine how much benefit I get from my own spending and my neighbors’ spending, respectively. There’s more on why this specific functional form was chosen here. Other forms are certainly valid.

In this model, the profit is the utility minus my expenditure, $latex S_0$

[latex] \mbox{Profit} = \sqrt{\alpha S_0 + \sum\beta S_i} – S_0[/latex].

If an overbearing government (or home owners association, or business) enforced the same spending on public goods by all beneficiaries, we can determine the optimal spending by equating $latex S_0$ and $latex S_i$ and taking the derivative of profit with respect to this single variable:

[latex] \frac{dP}{dS} = \frac{\alpha+(n-1)\beta}{2\sqrt{S(\alpha+(n-1)\beta)}} – 1[/latex]

Here we’ve introduced n, the total number of participants. Equating this derivative to zero, we find that the optimum level of spending is

[latex] S = \frac{\alpha + (n-1)\beta}{4} [/latex]

for a profit of

[latex] P = \frac{\alpha+(n-1)\beta}{4} [/latex].

per person.

If, on the other hand, we leave it up to each individual to contribute what she thinks is best for herself, we differentiate the profit equation with respect to changes in $latex S_0$ alone.

[latex] \frac{\partial P}{\partial S_0} = \frac{\alpha}{2\sqrt{\alpha S_0+\beta \sum S_i}} – 1[/latex]

Then, since all the participants are assumed to be 100% rational (and will therefore make the same decision), we equate $latex S_0$ and $latex S_i$, set the derivative equal to zero and discover that spending becomes

[latex] \frac{\alpha^2}{4(\alpha + (n-1)\beta)}[/latex]

and profit is

[latex] \frac{\alpha}{2}-\frac{\alpha^2}{4(\alpha+(n-1)\beta)}[/latex].

In the other post on public goods,we reported that, for our simple model of paving the street leading to a cul-de-sac with 5 houses, our homeowners would only be willing, on their own, to spend $2 on paving rather than the ideal $50, which reduced their profit from $50 to $18 each.

Now, let’s introduce a “Galt factor,” G, representing the increased productivity of workers in John Galt’s mountain enclave due to the absence of moochers. How high would the Galt factor have to be for the Galt society to have more efficient lawn care than us regular shmoes?  Both $latex S_0$ and $latex S_i$ should be multiplied by G since the labor and other input in the Galt society is that much more potent. So, we multiply all $latex S_0$ and $latex S_i$ by G in the profit for the non-cooperative profit and equate that to the (unmodified) profit for the cooperative system.

[latex] \frac{G\alpha}{2} – \frac{G\alpha^2}{4(\alpha+(n-1)\beta)} = \frac{\alpha+(n-1)\beta}{4} [/latex]

Solving for G, we find that the Galt factor necessary for the Galt society to operate more efficiently than a “moocher” society which recognizes and subsidizes the public good in question is


Here are some sample results using numbers from the beekeeping and road paving examples in the last post. In the gardening example, most of the benefit of keeping up my lawn goes to me. Only a little goes to my neighbors which is why $latex \alpha$ is greater than $latex \beta$ in the first two rows. The final 3 rows are based on a good that’s completely public–everyone benefits equally no matter who paid. Last post we used the example of paving the road that leads to the cul-de-sac. Since everyone enjoys the benefits of the spending equally, $latex \alpha=\beta$.

$latex \alpha$                $latex \beta$                $latex n$                     $latex G$

80                 10              5                  1.17

80                 10              100              7.0

40                 40              5                  3.27

40                 40              20               10.7

40                 40              100             50.7

We could even simplify the above expression by constructing the “public-ness” of a good, P.

[latex] P = \frac{(n-1)\beta}{\alpha+(n-1)\beta} [/latex]

Public-ness ($latex P$) is the fraction of the total benefit that goes to the community as whole. The Galt factor in terms of $latex P$ is

[latex] G= \frac{1}{1-P^2}[/latex]

Now, if we had any reason to believe our model this would be a very useful formula. Should a particular service be left to the market or paid for with public funds? Just figure P, make a guess as to how much more efficient your private market would be and compare. For goods that are completely shared, P is just $latex 1- 1/n$ with $latex n$ being the size of the community. For a cul-de-sac of 5, the Galt factor must be 25/9 = 2.78. For a small town of 10,000, P = .9999 and G = 100,000,000. So, for this adorably naive model the Galt society could likely manage to outdo us in gardening, as long as their cul-de-sacs didn’t get much bigger than 5 houses, but when it comes to truly public goods consumed by hundreds of people (like a public park or a security guard at your apartment complex) they’ll be hard pressed to accomplish in one hour what takes the rest of us a full work week. For goods shared by hundreds of thousands of people, the Galters might as well not try.

In many cases, at least some of the benefit can be secured exclusively for the benefit of the producer and her customers. For example, a road can be built with toll booths or the radio station can interrupt your music with commercials. These actions are effectively changing $latex \alpha$ and $latex \beta$. These efforts almost always lead to a reduction in both (i.e. it’s less useful to everyone), but also reduces $latex P$ making the private option more attractive and enticing people to invest in production. If we assume that private systems are more efficient than public ones, we can even reach the conclusion that adding obstacles (like commercials, patents and toll booths) can boost efficiency.

It’s fair to say that a model this crude isn’t likely to be accurate to any degree, but it gives an idea of some of the qualitative factors that effect evaluation of public goods. Too often our political discussion never gets past pithy platitudes. When we say, “private markets are more efficient,” it’s important to specify, even with a crude estimate, just how much more efficient. Liberals should not pretend the Galt factor is 1, but conservatives should not pretend it’s infinite. And, we should recognize that neither private nor public production is the right solution for all good in all markets. Math matters.

Do you have corrections or comments? How would you improve the model? Can you think of some goods for which the utility functions could be measured? Send me an email.