What is a subsidy?
A subsidy is a payment made by a group (usually the state) to individuals or corporations in order to shift the balance if the rational economic decision for the individual would be detrimental to the group as a whole otherwise. For example, if there are different quality kinds of crops that can be planted, for example a GM maize that brings in high yields but can only be processed to High Fructose Corn Syrup or a naturally bred corn that brings lower yields but tastes well enough for direct consumption, then if demand for both exceeds supply, the economic choice for the individual farmer is to plant the former. If the claims that HFCS contribute to obesity are founded, then it is in the public interest to produce less of it, and more alternative foods. Given that a market rather than a planned economy is desired, this cannot be achieved by decree, but rather money is used as an incentive. In the long term, this investment may very well pay off through reduced health care costs, so it is a rational economic decision from the state's point of view. In a world where all actors make decisions that are fully in their self interest, in principle subsidies would not be needed as consumers would demand healthy rather than cheap foods, and market mechanisms would provide these.