Why did the price of prerecorded cassettes fall dramatically when compact discs became widely available in 1991?

Because CDs are better than tapes (for a multitude of reasons). Before CDs, manufacttureres could sell tapes at high prices because there was no better alternative. However when CDs were invented, if taped had stayed at the same inflated prices, nobody would have bought them, so the price had to come down or manufacturers would have loads of tapes priced really high, competing with (better) CDs.