I was reading this article on advance purchase discounts and pricing in which the author uses the monotone hazard rate assumption. Why does the author use it?

The article is Advance-purchase discounts as a price discrimination device (PDF) by Nocke Peitz and Rosar

Below you can find a screenshot of the part in question.

Thank you very much!

enter image description here

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The motivation for this assumption is to have a unique solution. In this article, it is necessary to prove the 1st lemma, i.e. the quasi-concavity of the profit function. You find a similar motivation in Tirole’s book (Industrial Organization, p. 156).

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