Vox.com’s Sarah Kliff has been mounting an excellent campaign to make hospital emergency room charges more transparent. One example making the rounds is several accounts of short ambulance rides being billed in the vicinity of $2000. I have yet to see a good discussion of this rate level presented as the very basic math problem that is the “Fixed-cost Dilemma.” So, let’s take a look at that.

In short, the Fixed-cost Dilemma demonstrates that there is no “correct” price that a business should charge for goods or services that have a very high fixed cost but a relatively-low variable cost, a situation that occurs both in ambulance rides and in the development of prescription drugs. This is normally seen as an economic or accounting problem, but when it comes to healthcare, this becomes a critical social problem as well, and the two perspectives may suggest very different solutions.

I will use a very simplified drug development cost problem to illustrate the mathematics, and then bring it back to ambulance rides. Let’s assume that we are a pharmaceutical firm and we have a great new drug in the final stages of development. Before we sell the first pill, we will have spent $10 million in development costs, but once we get into production, the variable cost will only be one dollar for each pill manufactured. The problem is that we have no idea if this pill will be accepted in the market at all, let alone know how many units it will sell over its life.

If we ignore any profit we want to make, the chart below shows what we will need to charge per pill in order to recover our development and production costs.

So, if you are in charge of setting a price, which cell on the chart will you select? Unless you are an infallible marketing prophet, there really is no economic answer. The usual practical answer, one which often arouses the ire of the public, is to price as high as you can get away with, and hope for a lot more sales to both recoup your costs and make a substantial profit.

Ambulance services have a similar problem. No matter how many request-for-service calls you expect, you need to staff up both the equipment and personnel to cover 24-hour services. These are effectively fixed costs. And one ambulance will likely not be enough. Rather than following some nice “normal” statistical distribution of emergency calls, ambulance requests are more likely to follow a Poisson probability distribution, which means that for significant periods there will be zero calls, yet with interspersed sequences of frequent, and even near-simultaneous calls. If you are in charge of the health and safety of your community, how many ambulances and staffers will you put in place?

We have moved in many places from “community service” ambulance systems to “free market” systems. In other words, that $2000 ambulance ride you were just charged for includes the fixed cost of guaranteeing me an ambulance ride at some unknown point in the future. You have just been charged a lot of money to deliver a community-benefit “public good” to the rest of us, that public good being a 24/7 ambulance service ready to roll, and “free” to me unless I use it.

This financial model would be akin to having the local fire department bill you for a $20,000 call-out charge to put out a small trash can fire, in order to “fully absorb” the fixed costs of the department. The upside: the rest of us citizens would pay nothing to have the department at the ready (at least until our own trash cans are on fire).

Let me suggest that there is no good “free market” answer when it comes to high-fixed-cost issues of public health and safety. Note that we typically do not do this kind of analysis in funding our military, which is also a public good. We don’t require a “military security trust fund” or “military services insurance” or “user pays” system be set up. In recent years, neither political party even worries much about deficit spending when it comes to funding the military. We simply decide it is in the public good and we ante up the cost (or borrow the money).

If we were to decide that certain pharmaceutical advances (e.g., achievable cancer treatments) and medical services (e.g., ambulances) are really public goods, then the analysis could alternatively be in how to best raise and spend the fixed costs in the most equitable way, providing for the greatest possible public good. But saving real lives via ambulance services has instead become, in many cities, a free-market, economic, “make today’s user pay for my future ambulance ride” problem. Can someone tell me why this is desirable?