Consider the new Keynesian Phillips curve with indexation,under the assumptions of perfect foresight and=1, together with our usual aggregate demand equation,y_t=m_t-p_t.

(a) Expressp_t+1in terms of its lagged values andm_t.

(b) Consider an anticipated, permanent, one-time increase inm:mt=0 fort<0,m_t=1 fort0. Sketch how you would find the resulting path ofp_t.