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code for hw2q2.m

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+close all
+delta=0.025              %depreciation rate
+alpha=0.35               %capital share of income
+beta=0.99                %discount rate
+sigma=2                  %utility parameter
+
+
+nbk=20                 %number of data points int he grid
+nba=2                    %number of value for the shocks
+crit=1                   %convergence criterion
+epsi=1e-1                %convergence parameter
+
+
+PI=[phh 1-phh;1-pll,pll] %transition matrix
+pihh=0.977               %this is pi hh
+pill=0.926               %p ll
+ah=1.1
+al=0.678
+A=[ah al]                %stochastic matrix
+
+
+kmin=0.1
+kmax=5
+k=linspace(kmin,kmax,nbk)% k grid
+c=zeros(nbk,nba)
+util=zeros(nbk,nba)
+v=zeros(nbk,nba)
+Tv=zeros(nbk,nba)
+
+
+%%%%%%%%%%%%%%%%%%set up%%%%%%%%%%%%%%%%%%%%%
+
+while crit>epsi
+    for i=1:nbk
+        for j=1:nba
+            c=A(j)*k(i)^alpha+(1-delta)*k(i)-k
+            neg=find(c<0)
+            c(neg)=NaN
+            util(:,j)=(c.^(1-sigma))/(1-sigma)
+            util(neg,j)=-1e12
+        end
+        [Tv(i,:),pl(1,:)]=max(util+beta*(v*PI))
+    end
+    crit=max(abs(Tv-v))
+    v=Tv
+    i=i+1
+end
+
+plot(v(:,1))
+hold on 
+plot(v(:,2))
+
+