Problem: Derive the log-linearized version of the NKPC. For the derivation of the NKPC you can take the optimal Calvo pricing problem (from Part of the lecture dealing with the NKPC) as given. Your grade on this question will depend on the degree to which you demonstrate mastery and understanding of the intermediate steps in the derivation.
That is, simply copy pasting or copying by hand from the lecture slides will not constitute an adequate answer. Provide economic intuition wherever applicable (e.g., why do firm-level marginal costs depend on aggregate variables?). Throughout your derivations, highlight the role of nominal and real rigidities in determining the slope of the NKPC.