In recent times, central banks have attempted to stimulate their economies by resorting to forward guidance, which are announcements that monetary pol- icy will be expansionary not now but in the future. We will argue that the effectiveness of forward guidance depends crucially on the specification of ag- gregate supply. Current formulations of aggregate supply are versions of the New Keynesian Phillips Curve: It = BE+ Tt+1 + kyt + up (7) where S and & are positive constants, * denotes inflation, yt output (or the output gap, but here there is no difference, as we will assume that the natural level of output is fixed), and up an exogenous shock. Also, Ett+1 denotes, as usual, the expectation of 7+1 conditional on information available in period t. A previously popular formulation of aggregate supply was the Lucas supply curve, which had the form It = Et-17+ + kyt + up where Et-17+ is the previous period's expectation of today's inflation. To examine forward guidance, assume up = 0, and that at some time t the central bank announces a policy change that will raise demand one period later (i.e. the policy does not affect yt but raises Etyt+1). (i) Show that the announcement has no impact on inflation or output at time t under the Lucas supply curve. (ii) If, instead, aggregate supply is given by the New Keynesian Phillips Curve, show that the announcement of the previous question must raise It.(iii) "Forward guidance can provide a current stimulus by changing expec- tations about future demand." Comment briefly on this statement on the basis of your answers to (i) and (ii)