Dixie Cups, CAFE Standards, and Numeracy

The second use is more resource-saving than the third.

At my cottage in Canada, I have running water from a pump in the lake but not safe water. So in what we call the “bath hut” I have a bottle of clean water from which I pour a little into a Dixie cup when I brush my teeth. After I’ve finished brushing, I swirl the toothbrush around in the Dixie cup water and then empty the water.

I used to throw away the Dixie cup immediately after, but when I had a friend visiting last week, I noticed that he reused his. So I started doing the same.

What I found, though, is that the cup lost a lot of resilience after the second use. So I started throwing the cups away after the second use.

Then my numerate mind went to work. I realized that getting the second use was more important than getting the third use. Why?

Here’s why. Imagine that I’m at my cottage for 18 days, which is approximately right. If I use each Dixie cup once, I use 36 (one in the morning and one in the evening.) If I use each cup twice, I use 18 of them, saving 18 Dixie cups. If I use each cup 3 times, I use 12 of them, saving an additional 6.

So the saving in resources from a second use is triple the saving in resources from a third use.

The point generalizes. What if I went for a fourth use? Then I would use 9 cups. The saving from the fourth use would be only 3 cups. And so on.

What’s the point?

There are really two points.

The first is the power of thinking on the margin. The next use, in going from 2 to 3 uses, is less resource-saving than in going from 1 to 2 uses.

The second relates to an issue I worked on when I was the senior economist for energy with President Reagan’s Council of Economic Advisers: the CAFE mandate. CAFE is short for Corporate Average Fuel Economy. The mandate was part of the Energy Policy and Conservation Act, a law that President Ford signed in 1975. It was an indirect result of the price controls on gasoline, imposed by Nixon and kept by Ford. People were facing an artificially low price of gasoline and, OMG, were acting as if they were facing an artificially low price of gasoline. They weren’t switching to fuel-saving cars as quickly or extensively as many government energy planners thought they should.

So rather than get rid of the price controls, Congress and the president came up with a requirement that each auto manufacturer, for a given model year, reach an average fuel economy of x miles per gallon, where x steadily ratcheted up over the years.

I had 2 bosses at the CEA, chairman Martin Feldstein and member William Niskanen. Bill and I would have liked to repeal CAFE but that wasn’t going to happen. So we argued against further increases and in favor of relaxing the standards.

We were unsuccessful.

But here’s an argument that I didn’t emphasize but should have. The fuel economy saving from moving from a mandate of, say, 20 mpg to a mandate of 22 mpg is greater than the fuel economy saving of moving from 22 to 24. Imagine that in the United States, people drive their 100 million cars an average of 10,000 miles, for a total of 1 trillion miles. With an average mpg of 20, they use 50 billion gallons of gas. If the mandate is raised to 22, they use 45.5 billion gallons, for a saving of 4.5 billion gallons. But if the mandate is raised from 22 to 24, they use 41.7 billion gallons, for an extra saving of 3.8 billion gallons. If the mandate is raised from 24 to 26, they use 38.5 billion gallons, for an extra saving of 3.2 billion gallons. Notice that, just as with Dixie cups, each increment of required mph saves less gasoline than the previous increment.

I’m assuming away behavioral effects. The so-called rebound effect is that with higher mandate fuel economy, the price of an extra mile falls, and so people will drive more miles. But this assumption doesn’t hurt my reasoning because with each increment of mandate mpg, the rebound effect attenuates also.

So this is one of the things a microeconomist who studies regulation does on his vacation. Oops. I’m in Canada. Not vacation, but holiday.