In this paper, we analyze the implications of price setting restrictions for the conduct of cyclical fiscal and monetary policy. We consider an environment with monopolistic competitive firms, a shopping time technology, prices set one period in advance, and government expenditures that must be financed with distortionary taxes. We show that the sets of (frontier) implementable allocations are the same independently of the degree of price stickiness. Furthermore, the sets of policies that decentralize each allocation are also the same except in the extreme cases of flexible and sticky prices, where the sets are larger but still include that common set of policies. In this sense we establish an irrelevance or equivalence of environments. We also describe the minimal set of instruments, in the different environments, and thus discuss equivalence and neutrality of fiscal and monetary instruments. In particular we show that state contingent debt is not necessary, provided there are both consumption and labor income taxes.