With the Obama administration pushing a massive reform of our Health Care system, I figured I would share my opinion on the subject, for all of those interested. I firmly believe that if you want to solve a problem, the best approach is to come up with mathematical models for your problem, analyze them, and do what the models suggest. In this post, I will gradually build a mathematical model that describes health care, asking questions about the model and proposing policies reflecting the outcomes of the model. Let’s begin!
Model Version 1: There is a universe of N individuals with two states: healthy and sick. Let the variable t represent time, with t = 0 being some arbitrary date, say January 1, 2009. In this model, t is discrete – that is, it takes on the values -3,-2,-1,0,1,2… &c. In other words, there are no fractional times. At each time t , there is a certain probability p_sick that an individual will become sick. It costs c_cure dollars for a sick become healthy.
How much does Health Care cost in version 1 of the model? If we have N people, then at teach time tick, p_sick * N become sick, then the total cost of keeping everyone health is
c_total = N *p_sick *c_cure.
In this simple model, we have only one question to ask: who pays the cost of health care? Should the individual who becomes sick pay for his own cure, or should the government foot the bill? I contend that this this question is entirely a value judgment. Everyone has a different opinion on what’s fair or just. We could argue about constitutionality, but that wouldn’t get us anywhere either – everyone interprets the constitution differently and different people will just claim that the constitution backs their case. Thus, the first conclusion:
Conclusion 1: The question of “who should pay for health care” is entirely a personal value judgement.
Model Version 2: In version 2 of the model, we add in different diseases, and choices. Let D = {d_0, d_1, d_2….} be different diseases that people could acquire. Note that we could consider things like broken legs and concussions to be ‘diseases’ because people do suffer from them, and they do cost money to cure. For each d_i, there is a cost c_i to cure that disease. Note that for some i, c_i is infinite. In other words, for some ailments, there are no known cures. Additionally, let A = {a_o, a_1, …} be a set of actions that an individual could perform. The actions a person takes affect the probability that they catch certain diseases. For example, if you choose to drive a car to work, you increase the probability of getting any number of bodily ailments. If you eat a bag of Cheetos for lunch, you increase your probability of getting a heart attack. Let risk be a function that takes an action a_i and a disease d_j as input, and returns p_j. In other words, risk(a_i,d_j) is the probability that you will suffer from disease d_j if you perform action a_i.
How much does health care cost in this model? It’s almost impossible to answer. You’d have to know risk(a_i,d_j) for each possible combination of i and j. As the models get more and more complex, we see that we can’t really predict from logical principles how much health care is going to cost unless we can predict what kind of actions people are likely to take. What we can observe, though, is that the question of ‘who pays’ becomes more interesting. If the government pays for all health care, then people have no incentive to minimize the risks they take. If individuals pay for their healthcare, however, they have every incentive to minmize the risks that they take, reducing the total cost of healthcare. Model 2 suggests that the best solution is to have individuals pay for their own health care, so that they minimize the amount of risk that they take.
Suppose one of the actions is ‘going to the doctor for a routine checkup.’ Clearly, this action reduces the risk of many diseases. If individuals are forced to pay for their own health care, and rational individuals wish to minimize the cost they spend on health care, then rational individuals would go to doctors for routine checkups. In reality, this often doesn’t happen – so something is wrong with the model. Let’s expand it.
Model 3: Same as Model 2, except the concepts of “cost” and “cure” change. Now, instead of cost being associated only with disease, each action a_i has an associated cost given by cost(a_i) Sometimes the cost of an action is positive (going to the doctor, going to see a movie, buying gas) and sometimes the cost of an action is negative (i.e. selling a house, going to work.) For each disease d_i, there is an action that cures the disease. Let this action be called cure_i. Additionally, the function risk now takes a third argument as input: the state of the individual at time t. In other words, if you’ve currently got a cold, then your risk of sinus infection might go up.
How does Model 3 differ from Model 2? We have removed cures as some abstract thing that happens to people, and transformed them into actions that people take. As a result, the incentive structure of the system changes. When some diseases increase the risk of other diseases, rational people are more willing to pay to treat the first disease, in order to prevent themselves from getting the second. We can also explain why a lot of people people don’t go to the doctor under our current health care system - the cost of going to the doctor is positive, but the benefits are small, becuase insurance is more likely to cover catastrophic illnesses than it is to cover minor ones.
I could go on and continue to expand the model, but I won’t (although I’d find it very interesting to do so.) The conclusion I’ve drawn from the modelling process is that healthcare is really complex, invovling many value judgments. Answering questions such as ‘who should pay for what’ and ‘how much will it cost’ is not easy to do. In light of that conclusion, the question you should ask yourself is: “What is the best way of answering complex questions involving the value judgements of many individuals?” Economists have been studying this question for centuries, and, empirically, the answer is pretty clear – governments are notoriously bad at answering these questions satisfactorily. Markets, while far from perfect, are the best solution anyone has ever devised.
The primary problem with a Market-oriented solution to health care is that it excludes those who are unable to afford health care. I believe that the best way to handle those who are unable to afford health care is to supply them with vouchers that they can use to purchase health insurance of their own choice. This would create competition and reduce costs. The Obama administration seems to belive not only that the government is entitled to answer all of these questions for us, but the government is actually capable of doing so, in a fair and just manner. Believing that requires a hurculanean leap of faith in government. If you think the government is capable of solving the healthcare problem better than markets, you must certainly believe that the government can solve the question of ‘who should produce what, and who should consume what’ even better. Communism died for a reason: governments are not as efficient or responsive as markets. Listen to the empircal evidence of history, and make up your mind accordingly. I welcome your comments.
