To a small extent, you're in the right ballpark. But mostly, you're wrong. Let's say the demand was 12 billion units of whatever product it is that farmers produce. You realize that their production doesn't happen overnight, right? It takes many months between planting & product ready to go to market. For national security, it makes little sense to aim for close to or barely over that 12 billion units. All it takes is a drought, a large flood, etc., and you could lose a significant portion of that crop. Then what? Are you willing to put up with occasional food shortages?
You make my point for me which is to illustrate how subsides basically increase the cost of crops and food stuffs over the long term.
Government sets higher prices for corps then the market would allow to ensure that farmers over produce and grow more crops then what is needed to offset difficult periods of little demand, increased demand and/or as you stayed periods where natural disasters such as prolong droughts etc.
In the end however the result is that prices for crops via subsidies are set at a unrealistic price point which is not in line with what the market would offer or bare thus this is why we see a verifiable and notable rise in food prices over a long period of time with any kind of food/crop subsidies (which includes the food stamps program).
Also, farmers are good at what they do. Damn good. Milk production is so good that the farmers, competing against each other, would be able to run each other out of business by over-production & forcing the price too low. You really can't consolidate all milk production into too centralized of farms; it works better to have a lot of farms more spread out.
Again you make my point for me here as well.
Farmers would be forced to compete in the market without subsides and this competition would then drive down prices because efficiency brought to bare in market prices and farmers would seek to sate the demands and needs of consumers at prices both parties are willing to accept and which allows farmers to be able to compete with each other.
Furthermore monopolies that would occur naturally in the market would only exist so long as the monopoly in question is able to provide their goods and services at a low enough price level to sustain their dominance over others in the market. Thus prices for crops and food in general would decrease over time. In addition not all monopolies are inherently "bad" for the economy. If these monopolies occur naturally and without the aide and support of government intervention due to competition and lower prices then it is a benefit to the consumer.
However if these monopolies originate or are in part due to government action via regulations and/or subsides then their benefit is not seen by the consumer as these types of monopolies have no incentive to set their prices lower as they are partly maintained and sustained by government influence in the market which has the effect of removing any competition that would attempt to undermine their control by undermining them via lower prices.