First, I'm against all farm subsidies and tariffs on food products and ethanol.
Looking a little more closely, I think that it would be difficult to predict how removal of government involvement would effect retail prices but it seems that it would most likely raise the price of corn and lower that of sugar. If nothing else, we might be able to enjoy Coke sweetened with cane sugar again, as our neighbors in Mexico (and during Passover).
With respect to the public health consequences of subsidies and taxation, I don't think that those are clear at all. One might argue increasing the price of corn would be good, because then high fructose corn sugar would be more expensive. But, it would also raise the price of meat, and there are plenty of people who would argue on public health grounds that people should be eating more meat and less corn, flour and rice. What I think is the fallacy is that the government's involvement in subsidies is impairing good policies which can be crafted on an unambiguous body of public health research on nutrition. As stated in the most recent issue of the Atlantic:
When a five-year study of 10,000 people finds that those who take more vitamin X are less likely to get cancer Y, you’d think you have pretty good reason to take more vitamin X, and physicians routinely pass these recommendations on to patients. But these studies often sharply conflict with one another. Studies have gone back and forth on the cancer-preventing powers of vitamins A, D, and E; on the heart-health benefits of eating fat and carbs; and even on the question of whether being overweight is more likely to extend or shorten your life. How should we choose among these dueling, high-profile nutritional findings? Ioannidis suggests a simple approach: ignore them all.
I don't blame Coke for selling Diet Coke any more than I blame Kawasaki for selling motorcycles that go 140 mph. Lots of people get hurt riding motorcycles and lots of obese and lean people drink Diet Coke or Coke. What I am blaming, pre-emptorally, is if the government (whether state or federal) taxes Coke thus creating a price differential between Coke and Diet Coke, juices, and other similar beverages, it will be based on public health reasoning that reducing Coke consumption will create better public health outcomes. What the most likely outcomes are an increase in the consumption of Diet Coke and juices or 500 calorie frappucinos (how much would you have to tax those $5-6 drinks to get a decrease in consumption?), and there's no reason to believe that either of those will contribute to a decrease in obesity.