Increasing returns, entrepreneurship and imperfect competition

We study a simple bilateral oligopoly model in which individual agents, who are initially endowed with capital, decide sequentially (i) whether they want to act as producers (entrepreneurs) or as capital lenders (rentiers) and, then (ii) which quantity of capital they would like to borrow or lend, though exchange of capital units against units of the produced good. Production takes place under increasing returns to scale. We show the existence of "natural equilibria", at which wealthier capital owners become entrepreneurs while the remaining ones decide to be rentiers. We also study the efficiency of equilibria which is shown to increase by replication of the economy, but sometimes to decrease as a consequence of wealth redistribution.