Why do DDoS attacks cost a fortune to stop?

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http://serverfault.com – This is a really newbie question regarding DDoS attacks so I hope this won't get down voted or closed. I have read so many stories that a major DNS attack is causing companies thousands of dollars to mitigate. I have two questions: Is this because they try to keep the servers accessible to real site visitors while an attack is going on? Does shutting the server down instead of trying to keep it up still cause money? In other words, instead of spending thousands of dollars to try to keep the server up why not just shut it down (concede from the attackers) and spend nothing. (HowTos)