This paper characterizes the optimal fiscal policy when it is assumed that there exists a minimum wage below which no worker can be hired. The rigidity due to the minimum wage legislation can lead to equilibria in which the supply side of the labor market is rationed. One of the main results of the paper is that allocations in which the worker is involuntarily unemployed can be found to be optimal. The main conclusion with respect to the stabilizing properties of the optimal policy is that it should not be used to offset the negative effects of the cycle in the economy.