# Gali (2015) Chapter 8 Symmetric Steady State

In Chapter 8 (small open economy) of Gali's 2015 version of Monetary Policy, Inflation, and the Business Cycle, he often performs log linearisations around a symmetric steady state like below:

My questions are: 1. What exactly is a symmetric steady state, 2. How do we know that it exists 3. How do we know that $$P_H = P_F = P$$ in steady state? (I know from S=1, that I can infer that $$P_H = P_F$$, but I'm confused about whether S=1 is the cause for $$P_H = P_F$$ or a consequence of $$P_H = P_F$$).

Thank you very much for your time in advance!

1. The steady state is "symmetric" in the sense that terms of trade with all other countries are equal to $$1$$, with respect to the home country. It would be non-symmetric if for some of them terms of trade were not equal to unity.
3. $$S$$ is the ratio of two price levels. Logically then, it is a derivative measure of these two, so the price levels are the underlying forces.