Free response question

IEO past paper: 2021 International Economics Olympiad, open questions

By the assumption made by many standard textbooks and models, zero is the lower bound of an interest rate, limiting the central bank's capacity to stimulate the economy through monetary policy loosening. This assumption has been disputed recently, as central banks of several countries have set interest rates at negative levels. Some economists tried to identify (at least theoretically) the interest rate which is, indeed, a lower bound for expansionary monetary policy. They have found that for an interest rate below some (probably negative) level, the further decrease may surprisingly be contractionary. This task will walk you through their reasoning.