Our main objective is to study the impact of consumption externality like keeping of with the Joneses on the properties of long-run equilibrium in the two-sector optimal growth model. Does this consumption externality lead to a new mechanism of local indeterminacy and endogenous fluctuations? We will see that, in two-sector growth models with exogenous labor and without technological externalities, if the representative agent is able to give more value to his social status than his own consumption, this is the keys of a new mechanism for endogenous fluctuations. Moreover, by opposition with the other endogenous fluctuation mechanisms, we will see that this one doesn't need to have restriction on the factor intensity configuration of the consumption sector.