In this paper we show that bank competition has an intrinsically ambiguous impact on capital accumulation. We further show that it is also responsible for the emergence of development traps in economies that otherwise would be characterized by unique equilibria. These results explain the conflicting evidence emerging from the recent empirical studies of the effects of bank competition on economic growth. We obtain them developing a dynamic, general equilibrium model of capital accumulation where banks operate in a Cournot oligopoly. More banks lead to a higher quantity of credit available to entrepreneurs, but also to diminished incentives to offer relationship services that improve the likelihood of success of investment projects. We also show that conditioning on one key parameter resolves the theoretical ambiguity: in economies where intrinsic market uncertainty is high (low), less (more) competition leads to higher capital accumulation.