'Time inconsistency': The Phillips curve example (an analysis for intermediate macroeconomics)

This paper provides the algebra and a panel diagram to attempt to examine the so-called inflation- unemployment (or Phillips curve, or aggregate supply) example, the most popular example in the literature when introducing the concept of time inconsistency or dynamic inconsistency. The resulting panel diagram (along with the derivations presented in the appendices) is used to analyze the different possible outcomes, depending on the scenarios - rule or pre-commitment, cheating, and equilibrium - and find out whether there is indeed time inconsistency or dynamic inconsistency in the said example.