Profit-maximizing monopolists never produce in the range of output where MR is negative because

They wouldn't maximize profit.

Explanation:

Profit Maximizing Monopolists would always produce so long as Marginal revenue is positive because it would give them a chance to make more profit. If marginal revenue becomes negative, they would be making less than they did on the last product which would not be ideal to them.

This is so because the profit maximizing point is where marginal cost equals marginal revenue and as production increases, so also does marginal cost which means that for profit to be maximized, marginal revenue has to be positive as well to equal marginal cost.

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