Sunday, December 20, 2009

On the marginal costs of health care reform

A few weeks ago a federal advisory panel created an uproar when it recommended women put off regular mammograms until age 50. The network news led with the story for a few days. Congressional representatives took to the floor to decry the "rationing of health care." One congresswoman (I don't recall who) stated something like "We will not ration health care on the basis scientific of research!" which I think is the dumbest statement ever spoken in Washington.

Richard Thaler, whose unrelated book I just bought, wrote on this touchy subject for the Economic View column of the NY Times yesterday. He's simply trying to explain to people about what happens when the costs outweigh the benefits.

What the advisory panel was saying was that the marginal cost of a mammogram for a woman under 50 outweighed the marginal benefit, partly due to the number of false positives. It costs a lot of money to screen people and the number of lives saved didn't make it worth it. Thaler does a great job of showing a math example, click the graphic on the left. In his example using the real fact that 10% of mammograms for women in their 40s produce false positive results, only 9 out of 1008 women who tested positive would have cancer. So, while 1008 would test positive and receive expensive treatments, you're only potentially helping 9 women (and creating other stress and problems for the rest). We could eliminate all 1008 of the mammograms and save millions of dollars. The 9 with cancer would likely detect it some other way or later. Maybe some would die, but is saving those few lives worth all the millions of dollars spent testing everyone? How about when it's taxpayer money? Thaler also looks at some different aspects, so read him first.

My sister-in-law posted in a comment a while back "How can anyone measure the value of a human life?" Insurance companies and the government do this every day. What's the optimal amount to spend on prevention? You spend until the marginal cost is equal to the marginal benefit. We cover this in the Insurance and Risk Management class I taught for the first time this semester. Observe the following exam question:

XYZ Railroad transports toxic chemicals long distances. If a derailment and spill occurs, the estimated damages to the environment and cleanup cost is $10 million. The chart below shows the possible safety expenditures for XYZ and the probability of a derailment and spill for each level of safety expenditure.


Calculate the optimal level of safety spending for XYZ railroad.

Note that the railroad company can NEVER eliminate the chance of a loss. Similarly, we could spend trillions and there would still be a few uninsured people out there. We can never eliminate the uninsured completely. Rational people think at the margin, so you have to think "How much does it cost to get that next uninsured person insured and what would be the dollar amound of benefit generated?" The CBO does that with every bill written.

Unfortunately, politicians aren't always rational. We also see this in church where a congregation has spent a lot of money on a program and will say "If just one person gets saved, it's all been worth it!" The problem is that ignores opportunity costs-- that money could have been used much more effectively some other way.

The correct answer to the problem above is $100,000. If the company spends nothing on prevention then its expected loss is $300,000 ($10 million x .03). By spending $100,000 on prevention (the marginal cost) the expected loss falls to $200,000--ie: the marginal benefit is $100,000. The optimal amount of spending is where marginal cost = marginal benefit.

What if the company spent an additional $50,000? Its expected loss would be reduced by only $40,000. The cost outweighs the benefit, so this is not a wise decision for a firm.

The problem is that if XYZ has a train wreck causing $10 million in damages people in Congress will subpoena the CEO and ask "Why didn't you spend more on safety??" If he answers that he was behaving rationally he'll be excoriated by Congress and the national media.

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