The problem is not resouces, but how they are held and distributed. When the rice crisis hit a few years ago, there was enough rice (although it would have meant in some cases dipping into reserves), but it was not evenly distibuted throughout the world, and most of it was held by corporations whose only interest was the bottom line. So what rice was released into the system from held stores came at a very high price. Many nations were forced to buy rice to distribute to their people because their populations could not have afforded the inflated prices caused by what is, essentially, an artificially generated shortage.
The biggest problem of the planet's carrying capacity is water. Not just potable water for people to drink and cook with, but water for agriculture, too--and the latter is the serious problem. China "mines" ground water in order to make crop land of marginal terrains. This is part of an obsessive attitude toward food production which impels them to reject the purchase of foreign grain (the Chinese rely primarily on wheat and rice, with millet consumption being negligible). In fact, their access to naturally available water is sufficiently limited, that their vacuuming up of ground water puts them in future water debt, and costs them far more than it would to just buy grain from foreign sources. China certainly has the foreign exchange reserves to buy that grain.
That would mean buying it from those who can produce a surplus. This would be Canada and the United States, and to a lesser extent Russia/the Ukraine (wheat) and southeast Asia (rice). Not only has China been obsessive about producing all their food within her own borders since 1949, but the leadership would have serious political objections to purchasing grain from the United States, Canada and Russia/the Ukraine. The rice available from southeast Asia is not sufficient to meet market demands in the world, let alone if China adopted a more sensible policy and bought imported grains. The United States produces about $2 billion worth of rice annually, slightly more than half of which is used for direct human consumption. The capacity for rice production in the United States is under-utilized, and rice production can be done in terrains which are otherwise agriculturally marginal. Rice production also has the lowest environental impact of any major cash crop. The rice produced in California, for example, is done in marginal terrains which are heavily used by migrating birds along the Pacific flyway, and the rice wetlands do no violence to the ecology of the flyway. So long, however, as China and Japan remain obsessed with producing their own rice (and China her own wheat), American rice production will remain an under-utilized agricultural resource.
In 1913, the Russian empire was the largest single producer of grain for export. The Great War, followed by the two Russian revolutions, and Stalin's manufactured "Kulak" crisis destroyed large-scale agricultural production in Russia. Most of the grain production in the old Russian empire was within what are now the borders of the Ukraine. Careful management of that resource (don't hold your breath) could make the Ukraine a major player in global grain production.
Potable water will likely be the first crisis area of a burgeoning human population. The Great Lakes hold just more than 20% of the world's surface fresh water, and neither the United States nor Canada need that resource to produce potable water for drinking and cooking. Lake Baikal in eastern Russia contains almost as much fresh water, or slightly more fresh water, depending upon whose estimates one refers to. Between them--the Great Lakes and the lake system of eastern Russia, nearly 45% of the world's unfrozen, surface fresh water is within the teritory of three nations--the United States, Canada and Russia.
Once again, none of these water problems are a product of insufficient resources--they are the product of the distribution of the resources, combined with the issue of by whom the resources are held. Politics enter into it, too. It's highly unlikely that the United States and Canada (who cooperate very well in the management of the Great Lakes as a resource) are going to be interested in selling off any significant proportion of the fresh water contained in the Lakes. In fact, it is unlikely that any export of water in North America will be, in the foreseeable future, an important global resource. As it stands now, about the only water sales of any financial importance is the sale of Canadian water to feed the voracious American bottled water market. Neither nation is selling water in any significant amount outside their borders, and i don't see it happening any time soon.
Political considerations and capitalism determine, more than any other factors, the carrying capacity of the planet as it now stands.