Why it’s a joke
The humor comes from a pun:
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The phrase "aus Kostengründen" means for cost reasons (because it’s too expensive).
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But here, the elephant named Klaus sounds very similar to "Klaus-t" → which plays with the word Kosten (costs).
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So the punchline is: Klaus must go “wegen der Kosten” (because of the costs), but it’s also a wordplay suggesting that Klaus himself is linked to the word Kosten.
It’s a classic example of a dad joke / Wortspiel (pun) in German: the setup makes you think it’s a financial reason, but the real "reason" is just the similarity in sound between Klaus and Kosten.