A Question about NK model assumption


I am studying a simple New Keynesian model. I have one small question. Could you please let me know?

When a firm reoptimizes the price P*, it only considers that P* will go on forever.
Therefore, we just differentiate that case only when the probability theta repeats.

But I think it is possible P* can also exist. For example, if P* remains two periods and then the firm reoptimzes at that time. This kind of cases could be countless.

I do not understand why Gali’s book does not consider those cases.

Thank you.

The firm optimizes keeping in mind how long it won’t be able to change prices. So it covers all possible cases.

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Ok, thank you for your time and answer.

Exactly, all branches of the probability tree where the firm reoptimizes are irrelevant for the price setting decision today. All branches with finite time where the firm is stuch with today’s prices are considered in the FOC.