In the human capital literature, it is usually assumed that human capital is paid according to its marginal productivity. Nevertheless, in the real world labor compensation is linked to a fixed hierarchy due to the division and labor organization. Access to privileged positions in the hierarchy depends on schooling credentials, which in turn are a function of individual learning abilities and of individual spending in education. People compete in education in order to achieve the best job positions: positional competition is like a rent-seeking activity, based on the different levels of credentials. In this paper, a simple OLG economy with two agents and two kind of jobs is modeled, and the strategic solutions are analyzed. The model shows different outcomes depending on the hypotheses regarding the type of strategic interaction (sequential or simultaneous) and the characteristics of the capital market. In the sequential equilibrium, the presence of credit market imperfections and risk-aversion makes the asymptotic wealth distribution dependent on initial conditions (non ergodicity). In the simultaneous equilibrium, a non monotonic relationship between income inequality and long run growth is shown; in the long run, job allocation is mainly determined by the innate learning abilities and it is unrelated to the initial wealth distribution (ergodicity).