This paper introduces variable mark-ups in a horizontal-differentiation growth model by considering a larger class of preferences that nests the classic “CES” specification usually present in the workhorse love-for-variety models. Our first result is to obtain a generalized characterization of the Euler condition for this broader class of utility functions: in our model, the Euler rule features a supplementary term aiming at compensating the consumer for variations in the preference for variety along the consumption level. We are then also able to demonstrate that in our generalized framework, the economy’s balanced growth path displays both endogenous markups and a strictly positive growth rate of the number of available varieties (being the engine of growth). Finally, we show that under endogenous markups, the economy’s growth rate and firms’ market power can display a negative correlation, as opposed to the standard result obtained in the CES framework.