I've been mulling this over for the last couple of weeks. I haven't really come up with a clear answer. So I thought I would just throw it out there.
I've got three questions. The most important question is the third question.
1. 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?
2. Assume my country is a small open economy with sticky prices, and an independent monetary policy with flexible exchange rates. How is my country affected if all the other countries around mine also have sticky prices, and there is a global monetary shock that causes a global recession? To what extent can my country's adjusting its own monetary policy optimally insulate my country from the recession around it?
3. Do questions 1 and 2 have essentially the same answer?
My hunch is that the answer to question 3 is "yes". But I'm not sure. What is the difference between questions 1 and 2?
Update: to be a little more specific, my hunch is that the answers to both 1 and 2 are: "Even if I respond optimally, I will be worse off, because my terms of trade will deteriorate." But I'm not sure if I'm missing something, and if those standard answers are correct. My focus is on 3, not on 1 and 2 per se.