Seems to me, just like The Limits to Growth cited (which, admittedly, I haven't read, so I'll go with Mr. Worstall's take), said Tim Worstall makes the same kind of error — when you limit either the information going in or the conclusions you'll allow, you're bound to come up with a crap conclusion. Here, we speak solely of energy and mineral resources (in the general sense). Without trying to make a detailed argument, factor this in:
In 1800, there was one city with a population of 1 million — Beijing. By 1900, the population of the world was about 1 billion, mostly agrarian, with at least ten cities exceeding that population (London the most populous with 6,480,000, followed by New York with 4,242,000). By 2000, the world population was nearing 7 billion, with many cities around 20 million (Tokyo the largest at 26,400,000, followed by Mexico City at 17,900,000. New York, only the fifth most populous had grown to 16,600,000 — approximately a four-fold increase in 100 years). If we are able to survive and maintain that world growth rate, by 2100, there will be 49 billion people on the planet.
Already, and for some time now, we have been having problems with our fisheries. According to Pew, about 10 years ago, 92% of large ocean fish were already extinct! Sure, we're doing fish farming (which is barely taking up the slack, if that, and we can switch to species that were hitherto distasteful, though history shows when we do that, we soon extinct them, too. Witness the Patagonian toothfish a.k.a. Chilean sea bass.
Fisheries are not the only place where we are seeing scarcity. With more and more people, and increasingly those wanting the American lifestyle, the writing is on the wall. (I've heard —but can neither prove nor demonstrate— that if the current population were to live that lifestyle, we'd need four Earths.) However much there is of any given resource, that number is finite. If we do not get off this planet in a big way and find more resources, then there will be consequences that all the economists —of whatever stripe— in the world cannot solve. Other than that, any solution will have to rely on natural systems, whether that means living within the carrying capacity of the Earth or Mathusianism, I cannot say.
I'm not altogether hopeful...