Costs and Percentages

Last week, I talked about the percentages and perceptions. This week I want to be little more concrete in my example.

Let’s take a hypothetical situation, and say that 1 million US citizens suffer from something we’ll call Dihydrogen Oxide poisoning.   Let’s also say that an analysis of the situation says that for every 100 million dollars we spend, we can solve this problem for 90% of those still suffering from this affliction. That’s not a bad assessment, up front that sounds like that’s $100 per person, or not a terribly bad investment.

Except for one little thing. That 100 million dollar investment only covers 90%.  So after the first 100 Million is spent, we’ve only solved the problem for 900,000 people, leaving 100,000 people still affected.

To get that remaining 100,000 people, we have to spend another 100 million dollars, but again, we’ll only solve it for 90% of them. So another 100 million spent, and we end up with a total of 990,000 people covered, and 10,000 people still left affected.

200 million spent, 990,000 people covered works out to an investment of a little over $202 per person. But we still have 10,000 people left affected - it will take another 100 million to cover 90% of those remaining.

300 million, 999,000 people covered works out to an investment of a little over $300 per person, but you still have 1,000 people left affected. But it’s not truly an investment of $300 per person - the investment was actually $111.12 per person for the first 900,000 people, and $1,111.12 per person for the next 90,000 people and $11,111.12 per person for the next 9,000 people.  It only averages out to a little over $300 per person when you consider them all - and that’s reaching 99.9% of the people affected.

Are you willing to spend $111,111.12 each for the next 900 people?  Or over a million dollars each for the 90 after that? Or over 11 million each for the 9 people after that? How much are you willing to spend to get that last person?

There is a point of diminishing returns, and you have to consider that when considering any policy. It might only cost a little bit over $600 a person to cover 999,999 people affected by Dihydrogen Oxide poisoning, but it might actually be better to only spend $300 per person to cover 999,000 of them, and spend that other $300 million somewhere else, to provide relief for another problem.

Most public policy situations like this aren’t quite this linear, but they almost always have the same situation of a point of diminishing returns, which, unfortunately, is often difficult to tell where it is.   Also unfortunate is the mindset in government and public perception that we have to always try and cover 100% of the problem instead of recognizing the point of diminishing returns, and investing those resources elsewhere.  This is is unfortunate, because it is almost always the taxpayer who ultimately ends up funding bigger and bigger bureaucracies that ultimately cannot solve the problems at hand to 100% satisfaction. In fact, there often comes a point in which the size of the bureaucracy creates more problems than it solves. And yet, we continue to think that more is better, that we can solve it, when in fact, the better answer may be to recognize when we’re doing the best we can for now, and that further investment could be more effective elsewhere.

It may be distressing to think about it that way, particularly when children are involved.  But would you sacrifice 100 people to save 1 child? And then do that time after time after time, even after it’s been found that most of the time you still don’t end up saving the child? Most logical people would say “Of course not,” yet many of our public policies have reached the point they work just that way.

It makes no sense.   

Think about it...