# New Keynesian Phillips Curve (NKPC) derivation in Clarida, Gali & Gertler (2002) using Rotemberg

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:

1. $P_{h,t}^{o}Y_{t} -MC_{t}Y_{t}(1+\mu) -\frac{\psi}{2}\left(\frac{P_{h,t}}{{P__{h,t-1}}}-1\right)^2 P_{h,t} =0$

2. $P_{h,t}^{o}= P_{h,t}$

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 $P_{h,t}$ and I don't get inflation expectations.

Please, let me know what you get in computing the NKPC in this case.
P.S. Maybe I forgot a $P_{h,t}$ in the second term in 1, but I'm not sure about that.