In the fashion industry the brand integrity of a product is of crucial importance for its economic performance. In the fashion survey of the Economist (March 6-12, 2004) it is stated that brand integrity is "analyst-speak for that indefinable aura that convinces a consumer to pay a lot of money for something he, or more likely she, could buy much more cheaply elsewhere."
The destroyer of brand integrity is brand dilution, which arises when the product is "too popular". "If too many people have a supposedly exclusive Fendi handbag or Hermès scarf, it is no longer exclusive, and therefore, in the customer's view, no longer worth its vertiginous price. A fashion firm dealing with brand integrity and brand dilution thus faces the following trade-off: on the one hand selling a lot of products is good for immediate revenues, but on the other hand this reduces brand integrity and thus is bad for future profitability of this product. This trade-off is the subject of our analysis, which departs from an optimal control framework. We try to answer questions like: i) under what circumstances is it worthwhile to build up brand integrity, or ii) when will a fashion designer exploit his current high brand integrity by selling many of his products against high prices but at the expense of future profitability.