A small percent of a big number

I have taken a little time to get around to this, but a couple of weeks ago the Productivity Commission released a report into waste management. The blaze of publicity centered around their conclusion that only 1 percent of all plastic bags used in Australia find their way into streams and such, potentially choking wildlife to death. The PC reached the conclusion that perhaps a blanket ban on plastic bags would be over-kill. This is the kind of conclusion that economists normally latch onto -- you know, policies should have a proper weighing of costs and benefits. See Harry Clarke for an example and The Age for a write-up.

Now I was curious about this one because all of the reports reported the 1 percent (a small number) and concluded that plastic bags were a small problem. But 1 percent isn't a number at all, but a ratio. So what is the number?

Well buried deep in the PC report is the total number of bags consumed by Australians per day: 8 million. So that means that 80,000 bags a day are going into streams and such. That translates to 3 million per year. Now that seems to me like a big number. In 2005, this number was 34 percent less than 2002 because of the campaigns against plastic bags; that is 1 million less. (According to other sites, the total might actually be many times higher perhaps of the order of 60 million).

The issue with regard to the 1 percent, therefore, is that it doesn't tell us whether plastic bags are a problem or not. The magnitude will tell us more about the cost. But it does tell us that policies designed to reduce overall plastic bag usage might be hitting at the wrong end of the problem. Instead, we likely need to spend money limiting the amount of plastic bags that enter into streams. That would directly hit upon the cost.

[Of course, it could all be because of a few offenders and not general practices. In this case, we need even better targetted policies. See this New Yorker article by Malcolm Gladwell for more].