A thesis I've been hearing a lot about recently goes something like the following. It doesn't speak directly to subsidising food production costs, but is related to the same idea - what is wrong with cheap and plentiful food?
Here is the thesis:
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Ongoing food and clothing donations to countries in need cause more harm than good.
While short term donations are able to help bridge emergency situations, such as after a natural disaster, ongoing donations lead to dependence.
Local producers of food and clothes are unable to compete with free, donated goods, and so switch their production to other goods or stop producing altogether.
If and when the supply of donated goods runs out, the country has already lost their ability to provide for themselves.
Thus, when supplying aid to countries in need, it is essential to promote local independence in addition to filling their immediate need, taking care to avoid the creation of a dependency.
It's basically just the same problem as with the predatory pricing strategy called "dumping". You price your product below your cost to produce it to make your competition go out of business, then you can raise prices to exploit your monopoly position.
In kind food aid is essentially unintentional predatory pricing.
I think the big difference is that people, intending wholeheartedly to do good and help these countries, instead cause significant damage.
Things like this are one of the reasons I find the Gates Foundation's way of working so interesting. They spend a lot of time and effort, supported by a lot of money, to help entire societies to improve. Things like enabling women to take control of their own reproduction, which has a huge stabilising effect on an economy. Moving the needle on that issue takes a significant amount of work, and is much harder than simply sending aid.
The problem with this is of course, that it is expensive and takes time.
Often countries really do need aid, and fast. If people remain willing to send aid, it's a hard sell to say "actually, we don't want that free food, thanks", not least of all because they might need more aid in the future!
Ah, so that's sort of like what I've always heard about using bird feeders -- that the birds will get dependant on it, and if you stop filling them, a lot of birds will die off.
Food subsidies are a transfer payment to the people buying food. But the theory is that subsidies create waste - resources are diverted to creating food that wouldn't be if it were unsubsidesed.
The economically honest change would be to cut the subsidy, give out a welfare payment of a similar amount, and then let the market sort itself out. Nobody is a net loser, but the economy can reallocate resources out of farming if it wants. In this case, presumably foreigners would pick up food production and the Americans would go build infrastructure or something instead of farm.
I dunno how feasible the politics is, but that is the basic "everyone wins" case. Arguably the farmers might be worse off because they have to find something else to do.