The Rich and the Poor in a Simple Model of Growth and Distribution

We consider a model of economic growth with altruistic consumers who care both about their consumption relative to others and the disposable income of their offsprings. We show that if the parameter accounting for the importance of positional concerns is lower than a certain threshold, then the wealth of all agents converges irrespective of the initial distribution of wealth. If, however, it is higher than the threshold, then all the capital is eventually owned by the households which were the richest from the outset.