Cornell Law Professor Robert Hockett thinks Elon Musk's Tuesday tweet, which said that he was considering taking Tesla (TSLA) private, is legal, but may still spark an SEC inquiry.

"I could imagine [the SEC] looking into this not with a view to any possible wrong doing legally or otherwise on the part of Mr. Musk, but just from the point of view of market stability," Hockett said. "I could imagine the SEC and other policy makers might want to think about the possibility of excessive market turmoil maybe being caused by certain modes of communication, such as Twitter."

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