Demand Cycles and Heterogeneous Conformity Preferences

We explore the dynamics of demand for n designs of a good when agents have preferences for (anti-)conformity. Agents differ in their social status and each agent seeks to imitate those of higher status and to distinguish herself from those of lower status, relative to her own status. In each period, every agent chooses a design given each agent's demand in the previous period. We show that demand dynamics resemble fashion cycles: Total demand for each design over time is repetitively bell-shaped, and, when positively demanded, a design trickles from high- to low-status individuals. At least for n=3, the demand dynamics converge to a unique limit cycle. We obtain a similar (though weaker) convergence result for n=4, and simulations suggest that the result holds for n=4 and 5