Are monopolies more efficient than firms under perfect competition?

Monopolies are the sole suppliers in a market, who are price makers, can create barriers to entry, create a unique product, and face a downward sloping demand curve. Under perfect competition, there are many firms who create a homogenous product, are price takers and face a perfectly elastic demand curve due to the nature of their product - since charging higher would cause consumers to purchase the good elsewhere, and charging lower would result in a loss. In addition, there are no barriers to entry and exit under perfect competition.Firms under perfect competition are both productively and allocatively efficient. In terms of productive efficiency, which is where a firm produces at the bottom of its long run average cost curve, firms under perfect competition achieve this. This is because any abnormal profits in perfect competition attract new firms to the market, shifting supply outwards and lowering price. However, any losses in perfect competition cause firms to leave, shifting supply inwards and raising price. The point at which price is equal to the lowest point of the long run average cost curve is where firms are making normal profits and thus are neither entering nor exiting the market. In terms of allocative efficiency, this is also achieved; this is the point where the price of the good (the cost to society) is equal to the cost of production, and thus where P=MC. since MC intersects AC at its lowest point by nature, this long run equilibrium creates both allocative and productive efficiency. However, monopolies do not create either of these efficiencies. Monopolies are price takers, and do not charge a price which corresponds to the bottom of their average cost curve. Monopolies can maintain abnormal profits in the long run due to the existence of barriers to entry, such as sunk costs. This also means that monopolies do not operate at the point where P=MC; monopolies profit maximise by producing at the point where MC=MR. However, monopolies may be more dynamically efficient, since abnormal profits made can be re-invested into research and development which may shift the long run average cost curve downwards.Overall, the extent to which firms under perfect competition are allocatively efficient depends on the existence of externalities, since these distort the costs to society of consuming a good by introducing costs separate from price. In addition, it also depends on the extent to which monopolies use their abnormal profits to re-invest in research and development; they may use it, for example, to pay out dividends to shareholders instead.