Marginal Cost of Gali Chapter 8 Nonlinear

Hi everyone:
I derive the marginal costs of SOE following Prof.Dr Johannes Pfeifer chapter 3 nonliner derivation.
1. I derive the marginal cost which is equal to chapter 3, but the true marginal cost multiply by (TOT/REER), Why is this term there?
Marginal Cost equation of Gali chapter 8.pdf (95.4 KB)

2.Whether the relationship between isiosynacratic marginal costs and average marginal costs is identical to `(P*\P)^(-alpha*epsilon/(1-alpha)) in open economy.

Domestic goods have price P_H, while the domestic CPI is P_t. This term (or its inverse should pop up when you consider marginal cost expressed in terms of domestic prices. At the same time
\frac{{{\mathcal{Q}_t}}}{{{\mathcal{S}_t}}} = \frac{{{P_{F,t}}{P_{H,t}}}}{{{P_t}{P_{F,t}}}} = \frac{{{P_{H,t}}}}{{{P_t}}}