Conventional wisdom is that inflation makes people spend money faster, trying to get rid of it like a 'hot potato', and this is a channel through which inflation affects velocity and welfare.  Monetary theory with endogenous search intensity seems ideal for studying this. However, in standard models, inflation is a tax that lowers the surplus from monetary exchange and hence reduces search effort.  We replace search intensity with a free entry (participation) decision for buyers - i.e., we focus on the extensive rather than intensive margin - and prove buyers always spend their money faster when inflation increases. We also discuss welfare.