Arrow ‘63

Jacob Keegan
7 min readJan 16, 2021


Today, I’ll be summarizing the classic “Uncertainty and the Welfare Economics of Medical Care” by Kenneth Arrow. I think it provides a powerful and commonsense explanation of why medical care is different from most other goods and services. My personal notes will be in brackets [like this].

I. Introduction, Scope and Method

First, it should be noted that we’re focusing on medical care specifically here, rather than health in general. Many things affect health beyond just medical care. We’ll be comparing it to the norm in economics of a product sold under perfect competition, where firms don’t have the individual power to set prices, there are no restrictions on supply or demand or transaction costs, and markets are complete (meaning you can buy and sell anything that exists in the market, and can make bets on all possible future states of the world). Under these conditions, the so-called welfare theorems apply. The first welfare theorem shows that such a market will be Pareto stable, meaning no one could be made better off without making someone else worse off (this is also misleadingly called Pareto efficient or Pareto optimal). But this isn’t all that useful, because lots of things can be Pareto stable, even highly unequal societies. So we will prefer some Pareto stable allocations to others. This is where the second theorem comes in: it says that every Pareto stable state corresponds to some initial distribution of wealth with this model.

In some ways, this is a strong result. It basically says that if these conditions hold, governments need not concern themselves with interfering with markets at all: they just have to redistribute, and markets will get to an optimal state. In another way, this is also a weak result, because these conditions are far from reality. There are a limited number of products you can buy, and often high transaction costs for example. The farther this model is from the real world, the more intervention is justified. So the question is, how well does medical care fit this model? To answer that, let’s examine three crucial assumptions underlying the welfare theorems: the existence of competitive equilibrium, the marketability of all relevant goods, and non-increasing returns.

First off, there’s an obvious example where marketability fails: spreadable disease. For example, if I go outside without a mask or ignore social distancing, I put others at risk for my own benefit. I could get them sick and leave them with crushing medical debt, while I get no symptoms. In other words, I’m imposing a cost I don’t have to pay for. Second, there’s the fact that illness in general is unpredictable. You could be in perfect health for 30 years, and suddenly get cancer and rack up medical bills. So, it’s best to have insurance, to pay smaller amounts every year rather than a big amount at once. Thus the existence of health insurance. But health insurance lumps in a bunch of different risks, for everything from broken bones to lupus. Any glance at the real world will show you cannot buy insurance for every single one of these possible risks you face. So, not all relevant things are marketable.

There is an additional, more subtle problem. Illness is not just a known risk, it’s often unpredictable (take the example of cancer before). So, information that can lower that unpredictability becomes worth something to people. Of course, this in turn means that this information will concentrate among those who can make money from it. Yet the exact value of this information is hard to know. Take a concrete example. Say you have a pain in your lungs, and you’re worried about it. Naturally, you go to see a doctor. In that appointment, you’re basically paying them for information, about what’s wrong with your lungs specifically. Maybe the doctor will have no idea what’s wrong. Maybe they catch something that could have cost you tens of thousands of dollars, or even your life. But you have no way of knowing, AND no way of knowing how likely each outcome is, because the doctor is the one with that information. In other words, the very fact that you were paying the doctor for this information implies you don’t know the value of that information, which is obviously an issue if you want to ensure you’re paying the correct price for it. So, the competitive equilibrium does not necessarily exist.

Lastly, we turn to medical research. The free market naturally under invests in research, because its benefits accrue to more than just the firm who discovers it, and medical research is no exception. Beyond that, once you discover something through research, it’s incredibly easy to reproduce. This means there are increasing returns to scale.

So, these conditions needed for the market to be efficient do not hold. As we will examine more below, society in some way recognizes and tries to correct for this. “Society” here doesn’t just mean the government, but also licensing in the medical care industry for example. Yet those corrections often introduce other problems.

II. A Survey of the Special Characteristics of the Medical Care Market

As noted before, illness can be very costly. But not just in terms of direct medical costs: serious illness can also reduce future income, either by dropping you out of the labor force for a while or disabling you in some way (not to mention dying, of course). Combined this fact with the unpredictable demand for healthcare, and a customer cannot really test medical care to see if they like it. You can’t simply test out chemotherapy, or try different treatment centers for different prices. To be clear, the problem isn’t that you don’t know how a certain procedure or treatment works: That’s normal for commodities, you generally don’t know how stuff is made. The problem is there is inequality in the information about the consequences of a purchase. It’s a simple fact that the medical practitioner will know much more than you, and this simply can’t be overcome. So while you may expect your landlord or utility company to act in their self-interest, that’s not seen as acceptable for medical workers. After all, acting in their self interest could make your life hell for years, or even kill you, and you wouldn’t know. This means you have to trust them, which normal markets don’t require. Several things result from this. First, it’s common for hospitals to label themselves as non-profits. Second, there’s medical licensing, which in a literal sense delineates which practitioners you should and shouldn’t trust, as getting a license requires years and years of education. Lastly, you’ll expect to stick with the same doctor you trust, instead of always looking for better options like you do with other goods.

This unintentionally leads to several problems. First off, medical licensing restricts the supply of doctors, and such restrictions are inefficient in the normal market model. This is especially a problem because of the high cost of getting a medical education. Licensing also restricts the range of different medical products that can be sold. For example, you don’t need the person giving you a shot to have the same medical experience as someone giving you brain surgery or even therapy. Licensing reduces this to a binary.

III. Comparison with the Competitive Model under Certainty

Usually, people don’t go out of their way to support the consumption of others. It’s not like you’d be particularly moved by someone not getting a computer they wanted, for example. But individuals seem to want to help the health of others. Additionally, there are increasing returns to medical care. Think of how many more things a large hospital can have than a small one, including many things that aren’t divisible, like specialists or medical equipment. This is especially an issue in low-density areas with few, smaller hospitals.

IV. Comparison with the Ideal Competitive Market under Uncertainty

Even if they were insurance policies for all conceivable risks, medical care would still face issues. Since people are risk averse, they will prefer a guaranteed income of X over a non-guaranteed income with an average payout of X. This is, at its core, where insurance companies can make their money: by charging more than X for premiums. It should be noted that there are significant economies of scale here. Administrative costs as a percent of total spending will decrease as the insurer gets bigger. Plus, when the risk pool of customers is larger, there are more people to spread risk around to, so they can offer a lower price.

In the real life insurance market, you get insured against stuff you control, which could lead to you acting in riskier ways with regard to your health (since you know it will be covered). A physician should act as a check on this, ensuring any medical care given is actually needed. Of course, in the real world, often the exact opposite happens. In normal insurance markets, you pay more if you face a higher risk (like paying more in flood insurance if your area is often hit by hurricanes). Yet for health insurance, that would mean people with pre-existing conditions paying more [which we have already found unacceptable and banned under Obamacare].

As touched on earlier, you can’t really pay for medical care based on the results. Thus, there’s social pressure to make sure physicians are treating patients well. People “replace direct observation by generalized belief in the ability of the physician”. So a big part of what you’re buying is this obligation, this trust that they will treat you well. But if they instead were looking for their own profit, as normal workers would, this would certainly weaken trust. The freedom of choice of care is given to the doctor, who is expected to tell you the best treatment, regardless of cost.


Lastly, a note: Society will naturally create institutions to correct severe market failures. This applies to everything from physician licencing to unions. So we should be careful to decry things for interfering with the free market: they may exist to fix certain problems in the market. But of course, whatever ad hoc way society has of dealing with such problems is not necessarily the best way.



Jacob Keegan

Economics and welfare knower.