Scrap the CAP!

A friend of mine sent me an unintentionally amusing article from the Guardian (emphases mine; she reads it so I don't have to!):

Because China has no tradition of dairy farming, there is a shortage of home-produced milk. A third of all the milk produced worldwide is now being transported to China, much of it from the EU and a significant amount from Germany, which produces 27bn litres a year.
EU dairy farmers would like to increase production to cope with a current shortfall, but are prevented from doing so by EU milk quotas, imposed in 1984 and in force until 2015. Instead German dairy farmers have taken the obvious step of putting up their prices, which they have long claimed were artificially low. Blaming the Chinese has helped to deflect criticism from the farmers.
[...]
Now outraged consumer groups and politicians have called for the government to raise unemployment benefit to cover the rise.
[...]
The only effective way to increase global milk yields without breaking the milk quotas, according to experts, is to encourage the breeding of cows outside the EU.

This is simply hilarious! China wants more milk, EU farmers would be more than happy to offer it to them (presumably this increased demand would help the European agricultural sector, which the CAP is supposedly meant to protect), but since the farmers are not allowed to produce more, prices are skyrocketing. What's the German solution? Raise unemployment benefits! Wouldn't it just be easier (and more beneficial) to remove the milk quotas?