Consider the new Keynesian Phillips curve with indexation, (equation 7.76 Page 344 of the reading material), under the a

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Consider the new Keynesian Phillips curve with indexation, (equation 7.76 Page 344 of the reading material), under the assumptions of perfect foresight and β = 1, together with our usual aggregate demand equation, yt = mt - pt.(a) Express pt+1 in terms of its lagged values and mt.(b) Consider an anticipated, permanent, one-time increase in m: mt = 0 for t < 0, mt = 1 for t ≥ 0. Sketch how you would find the resulting path of pt. (Hint: Use the lag operator approach from Section 7.3.)