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 indepedendently
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.