A firm can never achieve allocative efficiency if it is a monopoly. It will always produce too few of its good or service and will always charge too much for it/them.
In perfect competition, firms produce the number of goods/services where the price for each unit of the good or service is equal to the marginal cost (MC) for the last unit produced. When this happens, firms are producing the quantity of goods and services that the market demands at the lowest possible price. In a monopoly, a firm can produce a quantity of goods/services where the price is greater than the MC. This quantity will be lower than what the market demands and the price of each good or service will be higher than necessary.
If a firm did this in perfect competition, other firms would enter the market, driving the price down and driving up the quantity of goods or services produced. In a monopoly, other firms are barred from entering the market. Therefore, the monopoly remains free to charge the higher price and produce the lower quantity.
It will not as there would not be much competition against it and so the monopoly is free to charge more for an item, or limit the quantities of the product at their own discretion.