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 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.