Oligopolistic competition in the banking sector and risk in the real economy are important characteristics of many economies. We build a model of monetary policy transmission that incorporates these characteristics which allows us to analyze the long-run consequences of variations in the degree of banking competition. We show theoretically that various equilibrium cases can occur, and that the effect of monetary policy varies greatly across equilibrium cases. We calibrate the model to the U.S. economy in 2016-2019 and find that monetary policy pass-through is incomplete under imperfect competition. Further, we show that a decrease in the policy rate during the calibration period would have increased expected welfare, but also bank default probability.