A monopolist does not necessarily have the power to charge different prices to different people

A monopolist does not necessarily have the power to charge different prices to different people. It depends what good is being sold and how easy it is to identify and keep separate members of the two (or more) groups. If the good is such that one consumer can sell it to another after purchase at trival cost in time and trouble, then discriminate is not possible, for any attempt to charge a higher price to one group would result in their having members of the lower price group make their purchases for them. If we assume that our two groups can be identified, and that the good is such that they can be kept form retarding it between them, it will pay the monopolist to charge them different prices.

The slope of the total revenue curve is equal to marginal revenue and just as the slope of the long-run total cost curve is equal to long-run marginal cost, so the area under the marginal revenue curve measures total revenue and the area under the long-run marginal cost curve measures long-run total cost. —Eqn 12.2

If to maximise profits a discriminating monopolist is to equate marginal revenue between two markets, then the higher the absolute value of the elasticity of demand in either one of them, the lower will be the price.