On the performance of the representative agent during out-of-equilibrium dynamics

This note contributes to the discussion about the representative agent's ability to characterize the collection of agents. We perform two exercises in context of a fairly general environment and show that even if the representative agent is powerful enough to describe the society in equilibrium, she might fail in describing the out-of-equilibrium dynamics of the system. It is established that this feature is not specific to the systems with or without interacting agents.