Assume I am an individual household or small firm, and that I have perfectly flexible prices. How am I affected if all the other households and firms around me have sticky prices, and there is a monetary shock that causes a recession? To what extent can my adjusting my own prices optimally insulate me from the recession around me?
I think that in a world of small, continuous changes, the ability of a small agent (household or small firm) to insulate itself by making small price changes ought to be nearly complete. However, I do not believe that we live in such a world. I think we live in a lumpy world with discontinuous changes. Individuals and firms tend to remain as stable as possible, and then when their actions become unsustainable they make large changes. In some sense, there is under-reaction to small events until problems cumulate and we observe larger actions.
If you are a home builder in Nevada in 2008, a small price cut will not insulate you from the problems that have accumulated. If you are a worker for whom a newly-invented capital good can substitute at much lower cost, a small wage cut will not help you. And so on.