The Mirage of a Growing Fuel Supply
Mathematically, drilling more oil is a losing game.

When I discussed the exponential function in the calculus classes I taught, I used consumption of a non-renewable natural resource as an example; since there is a national debate about energy policy, it may be useful to talk about the mathematics involved in making rational decisions about resource use.

Here’s the hypothetical situation: we have a 100 year supply of oil—that is, oil that would last 100 years if consumed at its current rate. But the oil is consumed at a rate that grows by 5% each year. How long will it last under these circumstances? It’s an easy calculation, about 36 years.

But let’s say we underestimated the supply, and we actually have a 1,000 year supply. At the same annual growth rate of 5%, how long will that last? The answer is about 79 years. Then let’s say we make a striking discovery of more oil—a bonanza—and now we have a 10,000 year supply. At the same rate of our growing use, how long would it last? Answer: 125 years. Estimates vary for how long currently known oil reserves will last, but all are considerably less than 100 years. But the point of this analysis is that it really doesn’t matter what the estimates are; there is no way that a supply-side attack on America’s energy problem can work.

Calculations also show that if consumption of an energy resource is allowed to grow at a steady 5% annual rate, a full doubling of the available supply will not be as effective as reducing that growth by half – to 2.5%. Doubling the size of the oil reserve will add at most 14 years to the life expectancy of the resource if we continue to use it at the currently increasing rate. On the other hand, halving the growth of consumption will almost double the life expectancy of the supply, no matter what it is. This math reality seems to have escaped the politicians pushing to solve the energy problem by simply increasing supply.

Building more power plants and drilling for more oil is exactly the wrong thing to do, because it will encourage more use. To avoid dire consequences, we need to find the political smarts and will to reduce the growth in energy consumption to zero—or even begin to consume less. I must emphasize that reducing the growth rate is not what most people are talking about when they advocate conservation; the steps they recommend are just Band-Aids. If we increase the gas mileage of our vehicles and then drive more miles, for example, that will not reduce the growth rate. Reducing the growth of consumption means living closer to where we work or play. It means telecommuting. It means controlling population growth. It means basic conservation techniques that work. It means shifting to renewable energy sources. It is not, perhaps, necessary to cut our use of oil, but it is essential we cut the rate of increase at which we consume it. To do otherwise is to leave our descendants in an impoverished world.

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