I don't think we had a famine in the last half century that was caused purely by production. The beauty of a working free market is that starving people are willing to pay quite a lot for cheap food, and so it's virtually impossible to starve just by being poor. The problem was always that the food couldn't get to them. I'd bet on a half-half mix of regulatory issues and fighting.

But yeah, production issues can increase price, which will create a whole lot of issues downstream - for example even if people won't literally starve, some of them won't be able to both eat and make rent. Which will predictably piss them off, and this is how you get Arab Spring as a consequence of corn ethanol.