Why are monopolies inefficient?

Monopolies happen when a single firm or a single producer is the only supplier in the economy. It is thus able to fix the price of its products/ goods and/or choose the quantity that will maximise its profits. The solution to the maximisation problem faced by a monopoly is the quantity and price for which the marginal revenue = marginal cost, this will give Pm and Qm. However, under perfect competition the solution to the maximisation problem is found by equating the marginal cost with demand (average revenue) which gives Pc and Qc. What we observe is that quantity under monopoly is lower and the price is higher. By charging a lower price, consumers would be willing to buy more, until Qc. Monopolies charge a price higher than marginal cost such that they realise abnormal profit whereas under perfect competition, the competition pushes down the price to marginal cost. Monopolies are inefficient because they fail to provide the resources desired by the market (at any other price people would be willing to buy) and thus create a deadweight loss, which is also a loss of welfare for the economy.