We define an intertemporal equilibrium where agents optimize a functional of utility on consumption and final wealth on nominal terms as proposed by [J. A. London͂o, J. Appl. Probab., 46 (2009), pp. 55--70]. The equilibrium obtained is a Duesenberry Equilibrium in the sense that at the optimal choices, heterogeneous agents have utility values for consumption and wealth that can be seen as a functional on utility on relative consumption and wealth (relative income hypothesis). We characterize these markets under a weak condition, provide existence and uniqueness results, and develop some simple examples. Also, we show the behavior of the proposed model to explain classical puzzles, and we suggest a possible extension. The theoretical framework used is a generalization of markets when the processes are Brownian flows on manifolds.