A firms that is using resources to their maximum efficiency by producing their output at the lowest possible average total cost is productively efficient (AC=MC)
Allocatively efficient firms produce the right amount of output. There is neither under nor over-allocation of resources towards a odd. If the price was higher than the marginal cost, this is a signal that more output is desired, if price was lower than marginal cost, the signal from buyers to sellers is that less output is desired. Only when P=MC is the right amount of output is being produced. You could also write this as AR=MC.
In this diagram, the quantity at which should be produced to be productively efficient is Q1. Q2 would be the quantity which a firm should produce at to be allocatively efficient. But since a monopolistic firm produces at the quantity Q where their marginal revenue is equal to their marginal cost in order to maximize profit, it is neither allocatively efficient nor productively efficient. And they don't have to be because there is no one they have to compete with. This is the total opposite to perfect competition where firms are forced to be using their resources as efficient as possible.
In perfect competition, firms are allocatively and productively efficient when they're breaking even which all firms do in the long run. At this point, for the quantity Q MC=AC and MC=AR, and at the same time it still maximizes profits. This is only possible for firms in perfect competition due to their perfectly elastic demand curve. Since a monopoly has a normal downward sloping demand curve and another curve that represents the marginal revenue, it won't ever be able to be both allocatively and productively efficient.In conclusion, a monopoly is less efficient than a monopoly than a firm in perfect competition since a firm in perfect competition will eventually always become allocatively and productively efficient in the long run. While a monopolistic firm will only be able to be allocatively or productively efficient if the government regulates it.
This is due to the extremely high costs that only very big companies can face. Furthermore, it is more efficient when only one single firm produces the product that is being demanded. This can be shown in an example. If there are 8 firms in the market for nuclear power plants and each of those firms produces one nuclear power plant, each firm faces costs of 150 million $ while when there are 2 firms each producing four nuclear power plants, the costs faced by the each firm would only be 40 million $. But when there is only one single firm producing eight nuclear power plants, the costs for this firm are only 40 million. The difference between 1200 million $ (8x 150 million $) and 320 million $ (8x 40 million $) shows the inefficiency of more than one firm operating in such a market. This is the main feature of a natural monopoly. Furthermore, if more than one company would be in such a market, the new firm would take parts of the demand of the firm that was already in the market and thereby shift the demand curve down which would cause a decrease in price for both firms or losses for both.
Furthermore, in a monopoly the law of demand still exists which says that in order to increase the demand, the firm has to lower its price which is shown by the downward slope of the demand curve. Therefore, a monopolistic firm can't just charge any price, but has to adjust the price to the demand for the product it is selling which also effects the output the firm can make. But what - just like every other firm - a monopolistic firm really wants to do is to maximize its profits. The profit-maximizing point is where the firm's marginal cost is equal to the firm's marginal revenue. Then the firm will produce at the quantity/ output Q1.
But there is also another reason for the rigidity of the price in non-collusive oligopoly: the shape of the MR curve for an oligopoly. The MC curve has a vertical section. This means that if marginal costs were to rise then it is possible that MC would still equal MR and so the firms, being profit maximisers, would not change their prices or outputs. Due to the shape of this MR curve, the MC could rise from MC2 to MC1 and the firm would still be maximizing profits by producing at Q and charging P.
