The world is described by individuals that maximize intertem- poral utility by choosing between physical capital, bonds, real money balances, leisure and consumption. The intertemporal utility function is given by ZtopU(Ct, mt, l) where p > 0, Ct is consumption, my is real money balances, and 4 is leisure. Firms maximize profits choosing labour and physical capital. Produc- tion is constant returns to scale and it is given by Y= AK NI-, 0 0 where, Nt, is labour and, Kt , is physical cap- ital. Under some assumptions the equilibrium outcome of such a model is given by the following IS-MP-PC model: Tit = nt+ 7(yt - yi ) + et (1) yt = y*- a(it - nt - r*) + ex (2 ) it = r* + n* + Bo ( It - *) (3 ) yt = y* - a(B. - 1) (nt - * ) + ey (4) where B, > 0, a > 0, 7>0. (i) State and explain briefly the assumptions under which the model in the description of this question results to equations (1)-(4). (5 marks) (ii) Find the effect of a permanent decrease in productivity in the short-run and long-run output, employment, wages and inflation. Provide diagrams and brief economic interpreta- tion. (10 marks)(iii) Assume that 11'? = Tl't_1. Let's assume that due to the high duration of the CovidIQ pandemic people became, temporarily, less patient. Find the effect of this incidence on the shortrun and longrun output and inflation by us ing equations (1](4], and the diagrams of the lSMPF'C model. Provide brief economic interpretation. (10 marks] (iv) Plot the time paths of output and inflation and comment on how this situation would differ if central bank preferences for inflation were stricter. (5 marks]