Geographical Indications (GIs) are considered as upmarket products because they are based on tradition and convey information about their geographical origin. Otherwise, the limitation of the geographical areas devoted to GIs and the exclusivity they benefit on the product lead to suspicions of monopoly power. Quality and market power should however reflect a stronger attachment, making consumers less price sensitive than for standard goods. This research aims to compare theses conjectures to empirical measures concerning the French cheese market. Price elasticities are computed from a demand model on 21 products, 11 Protected Designation of Origin (PDO) products and 10 non PDOs. The results are counterintuitive, PDOs being as price elastic as or more price elastic than standard products. This finding thus challenges the widespread idea that PDOs systematically correspond to high quality. It also has important implications in terms of competition policy, showing that PDO cheeses suppliers cannot decide on price increases without suffering large reductions in demand.