Single-Valuedness of the Demand Correspondence and Strict Convexity of Preferences: An Equivalence Result

If preferences are rational and continuous, then strict convexity implies that the demand correspondence is single-valued (e.g. Barten and Böhm, 1982, lemma 7.3). We show that if, in addition, preferences are strictly monotone then the converse is also true, namely single-valuedness of the demand correspondence implies strict convexity of preferences.