Macro Model with Government and Trade
Macro Model with Government and Trade
Tax rate
Tax rate
In[]:=
ClearAll["Global`*"](*completelyclearglobalsymbolstostartfresh*)
In[]:=
eq=y==c0+c1*(1-t)*y+f+g+x-m1*y(*fstandsfortheinvestment*)
Out[]=
yc0+f+g+x-m1y+c1(1-t)y
In[]:=
PIB=Solve[eq,y]
Out[]=
y
c0+f+g+x
1-c1+m1+c1t
In[]:=
Multiplier=D[PIB,g]
Out[]=
0
1
1-c1+m1+c1t
In[]:=
Multiplier=D[PIB,g]
Out[]=
0
1
1-c1+m1+c1t
In[]:=
partialm1=D[Multiplier,m1]
Out[]=
0-
1
2
(1-c1+m1+c1t)
In[]:=
partialt=D[Multiplier,t]
Out[]=
0-
c1
2
(1-c1+m1+c1t)
In[]:=
partialc1=D[Multiplier,c1]
Out[]=
0-
-1+t
2
(1-c1+m1+c1t)
Numerical exercise
Numerical exercise
In[]:=
c0=100;c1=0.8;t=0.2;f=1000;g=100;x=500;m1=0.25;
In[]:=
PIBMultiplierpartialm1partialtpartialc1
Out[]=
{{y2786.89}}
Out[]=
{{01.63934}}
Out[]=
{{0-2.68745}}
Out[]=
{{0-2.14996}}
Out[]=
{{02.14996}}
Lump-sum Tax
Lump-sum Tax
In[]:=
ClearAll["Global`*"](*completelyclearglobalsymbolstostartfresh*)
In[]:=
eq=y==c0+c1*(y-t)+f+g+x-m1*y(*fstandsfortheinvestment,tisnowalump-sumtax*)PIB=Solve[eq,y]Multiplier=D[PIB,g]partialm1=D[Multiplier,m1]partialc1=D[Multiplier,c1]
Out[]=
yc0+f+g+x-m1y+c1(-t+y)
Out[]=
y
c0+f+g-c1t+x
1-c1+m1
Out[]=
0
1
1-c1+m1
Out[]=
0-
1
2
(1-c1+m1)
Out[]=
0
1
2
(1-c1+m1)
Numerical exercise
Numerical exercise
In[]:=
c0=100;c1=0.8;t=101;f=1000;g=101;x=500;m1=0.25;
In[]:=
PIBMultiplierpartialm1partialc1
Out[]=
{{y3600.44}}
Out[]=
{{02.22222}}
Out[]=
{{0-4.93827}}
Out[]=
{{04.93827}}
Balanced budget multiplier (Haavelmo)
Balanced budget multiplier (Haavelmo)
In[]:=
c0=100;c1=0.8;t=100;f=1000;g=100;x=500;m1=0.0;
In[]:=
PIBMultiplierpartialm1partialc1
Out[]=
{{y8100.}}
Out[]=
{{05.}}
Out[]=
{{0-25.}}
Out[]=
{{025.}}
In[]:=
c0=100;c1=0.8;t=101;f=1000;g=101;x=500;m1=0.0;PIBMultiplierpartialm1partialc1