The new Keynesian Phillips curve with partial indexation. Consider the analysis of the new Keynesian Phillips curve with indexation in Section 7.7.

Suppose, however, that the indexation is only partial. That is, if a firm does not have an opportunity to review its price in period t, its price in t is the previous period’s price plus γπt−1, 0 ≤ γ ≤ 1. Find an expression for πt in terms of πt−1, Etπt+1, yt, and the parameters of the model. Check that your answer simplifies to the new Keynesian Phillips curve when γ = 0 and to the new Keynesian Phillips curve with indexation when γ = 1. (Hint: Start by showing that [α/(1 − α)](xt − pt) = πt − γπt−1.)