The aggregate price level in this economy is defined by the price index: $$ P_t = [\theta P_t-1^1-\epsilon + (1-\theta) (P_t^ )^1-\epsilon]^\frac11-\epsilon $$ Log-linearizing this index around the steady state yields the law of motion for aggregate prices: $$ p_t = \theta p_t-1 + (1-\theta) p_t^ $$
In the basic Gali model, the real marginal cost is a linear function of output: $$ \widehatmc_t = \left( \sigma + \frac\varphi + \alpha1-\alpha \right) \tildey_t $$ Where $\tildey_t$ is the output gap (deviation from natural output). Solution Manual Gali Monetary Policy
provides detailed solutions for problem sets that cover the basic New Keynesian model and productivity shocks. Computational Replication (Dynare) The aggregate price level in this economy is