We study the welfare properties of a New Keynesian monetary economy with an essential role for risky bank lending. Banks lend funds deposited by households to a financial accelerator sector, and face penalties for maintaining insufficient net worth. The loan contract specifies an unconditional lending rate, which implies that banks can make loan losses. Their main response is to raise lending rates to rebuild net worth. Prudential rules that adjust minimum capital adequacy requirements in response to loan losses significantly increase welfare. But the gains from eliminating limited liability and moral hazard would be an order of magnitude larger.