I have some issues in deriving the NKPC in Clarida, Gali & Gertler (2002) that you can find here. I'm asked to derive the NKPC by combining the log-linearized optimal price setting rule (22) with the price index (24), but I don't get the same result (equation 46). Besides, I'd also make the same applying Rotemberg rather than Calvo, with the following two formulas:
I assume equation 24 to be of this kind given that in Rotemberg every firm changes its prices every period. However, the result I get after having log linearized these two equations is weird. In fact, I don't get anything similiar to what is written in the paper. Specifically, I can't cancel out the price and I don't get inflation expectations.
Please, let me know what you get in computing the NKPC in this case.
Thank you in advance.
P.S. Maybe I forgot a in the second term in 1, but I'm not sure about that.