The main question regarding non-renewable resources is whether our dependency is sustainable. The surprising answer is that we will not run out of fossil fuel within the foreseeable future.
But what do we do in the long run? Our present-day energy supply is based on coal and oil, created over millions of years. Many have pointed out the apparent problem that--to uphold our civilization--we consume millions of years' resources in just a few hundred years.
Rather, we should use our resources sustainably, such that our consumption does not prevent future generations from also making use of these resources. But even if this argument sounds quite reasonable, it is impossible to use isolated, non-renewable resources such that future generations can also be assured of their use (unless we also include a certain probability that the civilization dies out). Even if the world used just one barrel of oil a year this would still imply that some future generation would be left with no oil at all. ("One barrel" should be taken as a metaphor for a tiny fraction of the present-day oil consumption. Since oil is created on a million-year time scale, we can actually use a small amount each year--the oil that was created during that period--and still leave the coming generations with their own supply. A back-of-an-envelope calculation would seem to indicate that this amount is less than 50,000 barrels per year or what is equivalent to one minute of today's oil consumption.)
However, this way of framing the question is far too simple. According to the economics Nobel laureate Robert Solow, the question of how much we can allow ourselves to use of this or that resource is a "damagingly narrow way to pose the question" (see his "On the intergenerational allocation of natural resources," Scandinavian Journal of Economics 88 (1986), p. 142). The issue is not that we should secure all specific resources for all future generations--for this is indeed impossible--but that we should leave the future generations with knowledge and capital, such that they can obtain a quality of life at least as good as ours, all in all.
This is actually a surprisingly important insight. Let us look at it in connection with oil. Sooner or later it will no longer be profitable to use oil as the primary fuel for the world. The price of oil will eventually increase and/or the price the other energy sources will fall. But societies do not demand oil as such, only the energy this oil can supply. Consequently, the question is not whether we leave a society for the coming generations with more or less oil, but whether we leave a society in which energy can be produced cheaply or expensively.
Let us put this slightly more simplistically. If our society--while it has been using up the coal and oil--simultaneously has developed an amazing amount of technical goods, knowledge and capital, such that this society now can use other energy sources more cheaply, then this is a better society than if it had left the fossil fuel in the ground but also neglected to develop the society.
Asking whether we will run out of oil in the long run is actually a strange question. Of course, in the long run we will undoubtedly rely on other energy sources. The reason why the question nevertheless makes us shudder is because it conjures images of energy crises and economic depression. However, there are sufficient resources for the long future and there are good reasons to expect that when the transition happens it will happen because it actually makes us even better off.
As Sheik Yamani, Saudi Arabia's former oil minister and a founding architect of OPEC, has pointed out: "the Stone Age came to an end not for a lack of stones, and the oil age will end, but not for a lack of oil" (cited in W. Greider, "Oil on political waters," Nation, 10/23/2000, 271(12), pp. 5-6, although, as with all popular phrases, more people seem to claim ownership). We stopped using stone because bronze and iron were superior materials, and likewise we will stop using oil, when other energy technologies will provide superior benefits. (Likewise, when The Economist asked in early 2001: "Will The Oil Run Out?" their answer was: "Eventually, yes; but by then it might no longer matter.")