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In fact, if a brand uses price promotions on a regular basis, this trains brand buyers to hold off buying when the brand is at full price, and wait until it at a discount again. This destroys profit and is likely to damage brand appeal.

Here's a link to the paper by Slotegraaf and Pauwels; Table 4 on page 300 is key. The paper also shows that having stronger brand equity makes it more likely for a brand to see a long-term benefit from price promotions.

Here's the link to Kantar report with the data used in the witch's hat graphic.

What to learn more? Try asking Virtual Dan White.