Monetary policy is neutral even with fixed prices, if there is free entry and variety is determined optimally as in Dixit and Stiglitz (1977). When individual prices are sticky, entry substitutes for price flexibility in the welfare-based price index. In response to aggregate demand expansions, the intensive (quantity produced of each good) and extensive (number of goods being produced) margins move in offsetting ways, leaving aggregate production unchanged. Deviations from neutrality thus occur only when variety is not optimally determined (preferences are not Dixit-Stiglitz) or when entry is subject to frictions.