Will a monopoly ever provide a Pareto efficient level of output on its own?

No, a monopoly will not provide a Pareto efficient level of output on its own. This is because a monopoly has the market power to set prices and output levels that are not socially optimal. A Pareto efficient level of output is one where it is not possible to make any one person better off without making someone else worse off. This is not possible in a monopoly, as the monopolist can set prices and output levels that are not socially optimal.