microeconmics: can a monopolistic firm be profitable if its marginal revenue is negative?
As a counterexample to the statement, consider the following:

Let demand be $p=10-q$, so that $MR=10-2q$. Suppose there’s no cost, so that profit equals revenue. If the monopolist produces at $q=6$, $MR=-2&lt;0$, but $TR=(10-6)6=24&gt;0$, thus contradicting the statement.