We study how market power affects investment and welfare when banks choose between restricting loan sizes and monitoring, in order to alleviate an underlying moral hazard problem. The impact of market power on aggregate welfare is the result of two countervailing effects. An increase in banks' market power results in: (i) higher lending rates, which worsens the borrower's incentive problem and reduces investment by unmonitored firms, (ii) higher monitoring effort, which reduces the proportion of credit-constrained firms. Whenever the second effect dominates, it is optimal to provide banks with some degree of market power.