I propose an AK model with households determining their subjective discount factors endogenously. It is assumed that the subjective discount factor of a household is, other things being equal, an increasing function of its relative well-being. At the same time, it is admitted that some other factors can influence the time-preference rates. I introduce the notion of sliding equilibrium path, prove an existence theorem and show that any sliding equilibrium path becomes balanced from some time onwards, and all the capital is eventually held by the household which is the richest at the initial state. It follows that the long-run rate of growth depends on the initial income distribution.