Optimal central bank lending

We analyze optimal monetary policy in a sticky price model with open market operations. The central bank sets the policy rate and can, additionally, control the amount of money by rationing money supplied against eligible securities. Optimal policy under money rationing is shown to enhance welfare in the long-run and in the short-run compared to a conventional optimal policy regime where money supply is not rationed and satiates money demand. Specifically, this property is shown to apply when privately issued debt is eligible in open market operations, which allows the central bank to separately alter costs of borrowing and the size of transactions for which money is required.