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In marketing, it is well known that social needs play an important role in the purchase of conspicuous products such as high-end luxury fashion labels. In this paper, we analytically study the optimal advertising and pricing decisions for luxury fashion brands in a market that consists of two consumer groups with contrasting social needs for fashion products, namely, the leader group (LG) and the follower group (FG). We consider a situation where the LG consumers have the desire to distinguish themselves from the FG consumers, whereas the FG consumers would like to assimilate themselves with the LG consumers. We first develop an original optimization model for this problem. We then explore the optimal solution scheme by separating the problem into tactic-based subproblems and conduct an extensive sensitivity analysis. Our analysis reveals that the optimal strategies follow different scenarios, and it can be optimal for a brand of conspicuous product to do the following: 1) Advertise to only one group while sell to the whole market; 2) advertise and sell to the FG only; and 3) advertise and sell to the LG only. Important insights are also reported.