Systemic banks and the lender of last resort

We propose a model where systemic and non-systemic banks are exposed to liquidity shortfalls so that a lender of last resort policy is required. We find that it is socially optimal to override the decision of the central bank by the unconditional provision of liquidity support when the shortfall is large enough, i.e. in crisis times. The existence of systemic banks provides a rationale for the central bank to act as lender of last resort for non-systemic banks in a larger range of their liquidity shortfalls. However, the impact of systemic risk on the optimal allocation of the lender of last resort responsibilities for systemic banks depends on the relative size of counteracting effects.