> Agricultural subsidies exist primarily due to lobbying,

That's mostly true, but it's also true that we don't want to starve. There are 330 million hungry mouths in the US and we've got to keep production way above that level or it becomes a big political problem real quick.

If we just let the market set prices, in years where farms are all producing bumper crops, oversupply would push profits way down. This would force many producers to sell their farms (most likely to corporate-scale farmers) and leave the sector. Subsidies keep a nonzero number of producers producing independently. Granted, the corporate-scale farmers (who also accumulate funds via subsidies) can buy out producers who want to sell, but with subsidies, more producers can afford to say no and stay independent.