Subsidizing isn't just throwing money at the farmers, it's supposed to keep them in agriculture. Let's face it, agriculture isn't the most appealing job and young people will try to do something else unless money's good. Ask a child of a farmer, would he/she rather make 10,000 euros a month working on a farm or the same amount from working in an export/import company in a big city...
You need to keep that land worked and you need to keep people there. Even in the most advanced countries significant number of people still work in the agricultural sector, most of them aren't educated for many other jobs. In the long run it's cheaper to subsidize them then to give them a new education or give them unemployment money. Food is produced, people have jobs, land is worked. It's not a coincidence all developed countries in the world subsidize agricultural production...
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