This paper presents a model in which the effect of monetary policy depends on the state of bank net worth. When banks are flush with equity, changes in the central bank's policy interest rate pass through fully to bank lending rates. When banks have low equity, there is no such pass-through. Banks in the model are local monopolists for borrowers near them. When they have lots of equity, they compete for customers at the edges of their markets. When they have little equity, they retreat and exploit the monopoly power over their local customers. With very low equity, banks may even raise lending rates after a drop in the policy rate. The model posits novel connections between aggregate bank net worth, bank competition, and the effectiveness of monetary policy.