The thing everyone always forgets about food production in armchair analysis is that it is not constant. Some years we produce more, some years we produce less. We can smooth across space and time to keep short-term or regional shortfalls from becoming a famine, and we do so most of the time, most places.
In any year, in any place where there is not a famine, we are, by definition, producing more food than anyone wants to consume, in aggregate at least if not for individuals. Whenever you are producing an excess of something, the price will fall.
Famine, if it happens, won't happen as a slow decline of food production, until at a predictable time we cross from producing 100.0000001% of the food the world needs to producing 99.9999999%. It will happen as a slow decline reducing our safety margin until some sort of three-sigma weather event makes for a really bad year -- flooding in some regions kill production here, drought in other regions kills production there, a blight on crops in otherwise fair weather, and the production for the next N months falls below the level of the stockpiles to last.
That is the point at which the market will react and food prices will go crazy. It won't do anything to help production -- some things take time, not money. It will just be the world playing musical chairs to see who gets left without enough food to eat.