That "cheap wheat, corn, and rice grown in more agriculturally productive regions" is cheap because its production is heavily subsidized. When economists talk about removing agricultural subsidies (pretty much the only thing almost all macroeconomists agree on, for what little that's worth), they're generally talking about removing trade barriers and removing agricultural subsidies in the form of payments to farmers. I suppose it's true that if you fixed tariffs without fixing the other side, you'd still have a problem.
There are lots of other reasons why farmers in developed countries can grow food cheaper than those in developing countries:
- access to capital. A modern family farm has several million dollars worth of land and several million dollars worth of machinery. Farmers don't buy $500,000 combine harvesters for no reason -- in the long run they're cheaper than the alternatives.
- security. A modern farmer just leaves millions of dollars worth of machinery in his yard, usually unlocked.
- information. In developed chemicals the government & universities put out lots of information about techniques, seed varieties, chemicals, machinery, timing, weather forecasting, et cetera
The interesting thing is, agribusiness can take its technology to the developing world and do the same work there that it does here (with less security but also with fewer environmental and labor related restrictions and costs). Right now there are just very strong disincentives to do so in many cases.
I can't speak to the state of information and knowledge of agriculture in the various countries we'd consider "developing," and how it compares to universities and government here, but I bet it varies quite widely. That's a good point, though - it matters a lot.
Iowa is number one in corn because it has the best soils in the world for corn. There is no third world country that can compete with the native soils of Iowa. You can solve all the other issues (many of which are real) and they still lost the location lottery and cannot compete. (some regions can grow two crops a year though which might make them better than iowa despite not as good of soils)
That would be the nice thing about an open market: different areas could stay focused on what they're particularly good at. Iowa would definitely stay involved in corn.
But as you sort of alluded to, in a free market some areas could put downward price pressure on corn even if they're not as efficient as Iowa. If they've got land that isn't very well suited for anything else, and it's a choice between making a little money on corn and little or no money at all with their arable land, they'll probably go for it...
