# Pareto Improvement with Monopolies

This may be one of the more 'elementary' questions on this site.. But I really can't wrap my head around it and a search on the web hasn't yielded much.

Given that Pareto efficiency is defined as when the allocation cannot make any party better off without making anyone worse off, it seems that something like breaking up monopolies is in fact not a Pareto improvement, as it's making the consumers better off by making the monopolist worse off?

I'm inclined to say that antitrust measures are (theoretically) a Pareto improvement, because that's moving closer to the allocative efficient level in a perfectly competitive market. However I don't know how to incorporate the definition of Pareto improvement into this.

Would be extremely grateful for any help!!

Many many thanks, Shine

In a monopol we know there exists a consumer who would be willing to pay a price for an additional unit of the good that is higher than the additional cost to produce that unit. Possibility of Pareto improvement: monopolist produces one additional unit and receives marginal cost from consumers. Giving away one unit for marginal costs does not make the monopolist worse off in the first case. But if the monopolist wants to sell an additional unit, he must lower the price not only for the last unit, but also for all remaining units. This is the result of one critical assumption: no perfect price discrimination. But from the perspective of a social planner one could produce an additional unit and find a trade where $$MC \leq P$$ by allowing the monopolist only to change price for its last produced unit. In absence of such a planner the monopolist falls back to the old logic.