The other fallacy of Malthusianism is that people (like other life forms) breed faster when there's surplus, and slower when there's not. Thus, as the population approaches the resource limit, it grows more slowly.
See, for example, Verhulst's mathematical description of population growth [0], written in response to Malthus. You can chart the data and see a very clear divergence from Malthus' expectations [1].
