Brand Image and Brand Dilution in the Fashion Industry

We develop a dynamic optimal control model of a fashion designer's challenge of maintaining brand image in the face of short-term profit opportunities through expanded sales that risk brand dilution in the longer-run. The key state variable is the brand's reputation, and the key decision is sales volume. Depending on the brand's capacity to command higher prices, one of two regimes is observed. If the price mark-ups relative to production costs are modest, then the optimal solution may simply be to exploit whatever value can be derived from the brand in the short-run and retire the brand when that capacity is fully diluted. However, if the price markups are more substantial, then an existing brand should be preserved. It may even be worth incurring short-term losses while increasing the brand's reputation, even if starting a new brand name from scratch is not optimal.