3. (16 points) Consider the following two period general equilibrium model with a representative firm and representative household. The representative household solves max U(X1, X2) = In(Ct) + 0.8In(Ct+1) Ct, Ct+1 Such that C+ + : Ct+1 "it+1/Pt+1 1+r Pt 1+r The firm solves Tit+1/Pt+1 max + It Pt 1 + it = 4K - It, Pt Tit+1 = 4K1/2 t+1 Pt+1 Kt+1= It +(1 -d)Kt The markets clear Ct + It = 4K)/2 Ct+1 = 4Kt+1 1/2 + (1 - d)Kt Suppose Kt = 4, d = 1, Pt = Pt+1 = 1. a) Calculate the general equilibrium values of Ct, Ct+1, It, Kt+ 1, It. List clearly five equations associated with these 5 endogenous variables. (6 points) b) Suppose now there is a productivity shock so that At increases from 4 to 6. What is the new equilibrium interest and the new equilibrium consumption Ct, Ct+1? (10 points)