Monopoly doubt

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Monopoly doubt

VanHelsing
For third degree price discrimination, the monopolist charges a lower price in the market which has more elastic demand. My question is: can we infer anything about the quantities sold in the two markets ? I worked out a few numericals, and in all those I am getting that the monopolist sells a higher quantity in the market with more elastic demand, but is this ALWAYS true ? In case of identical demand curves, it would obviously be so, but the whole point of price discrimination is non identical demand curves.
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Re: Monopoly doubt

Asd1995
It is always true. I'm sure you can prove it mathematically.