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What actually raises the price of milk is the farmer uses his profits to buy up other local dairy farms consolidating their position in the market. They then sign exclusivity deals with both grocers and further milk processors (who are also consolidating) to prevent competing in the market, driving their competitors to either sell for cheap or go out of business. https://theconversation.com/americas-dairy-farms-are-disappearing-down-95-since-the-1970s-milk-price-rules-are-one-reason-why-237439#:~:text=Across%20the%20country%2C%20the%20dairy,per%20farm%20%E2%80%93%20has%20been%20rising.

Because "farm Inc" has a massive horde of wealth, they can stamp out competition by either buying them out, cutting them out, or driving them out of business with prices a small farmer can't handle. After that, they get to set and raise prices at will with the now smaller pool of big name "farm Inc".

This literally happens every time a market is poorly regulated and businesses allowed to grow too big. It's the natural end state of capitalism.