The case is simplest for such renewable natural resources as second-growth forests. Essentially, woodland is one crop that may be grown on the land, and if the land is best suited for woodland, its rent will be based on its value in growing timber. The productivity of land in this sort of use will also depend on the cost of extraction. If the land is very hilly or swampy, then it may be difficult to use machinery, or more costly machinery may be needed -- raising the cost of harvesting the timber. With natural resources in general, cost of extraction is inversely related to productivity and therefore rent.
For mineral resources such as petroleum and gold (and old-growth forests), no renewal is possible in an economically meaningful time frame. Nevertheless, the supply-and-demand price of natural resources will include a component of differential rent. The cost of extraction of mineral resources will vary. For example, petroleum at great depth or under deep water will cost much more to drill and operate the well than shallow, dry-land oil deposits. Thus the shallow, dry-land deposits with lower costs of extraction are more productive. In general the cheaper deposits will be extracted first. But oil or minerals from costly deposits must sell for the same as those from deposits that are cheap to extract, so the ones from deposits with low costs of extraction will be sold at over their cost, the difference being differential rent.
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