without taxes
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7/25/2019 Without Taxes
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Optimal Taxes without Commitment
On this section we introduces lack of commitment to future policies,government will reoptimize its choices in every period. The choices will befocused on the government needs for the period it belongs. This generatedistrust in households on the government's commitment in the application of
taxes and the debt default.
ub!ect to"
MAX:t=0
t[U(Ct1 , Ct2 , lt)+V(g t)]
#mplementability condition"
:t=0
t[U1 (t)Ct1+U2Ct2+Ul(t) lt]=K
CO$%#C#O$ %& (CT#)#*#%(%"
t:Ct1+Ct
2+Kt+1(1)Kt+gt=f(Kt, Lt)
#ncentive compatibility constraint"
t=s
t s [U(Ct1 ,Ct2 ,l t)+V(g t)]W(Ms s )
+amsay Taxation characterization without Commitment
LRS=
t=s
{t[U(Ct1 ,Ct2 ,lt)+V(gt)]+t=0
t[U1 (t)Ct1+U2Ct2+Ul( t) lt]+t[ f(Kt, Lt)Ct1Ct2Kt+1+(1
ouseholds utility by
the government
olicies without
-aximum utility of the
households on the worts in
the worst case scenario
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7/25/2019 Without Taxes
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The following derivatives are the caractization of the solution for the +amsay
Taxation Commitment"
LRs
Ct1=
t
U1(t)+ t
[U11 (t)Ct1
+U1 (t)]+s=1t
t s
U1(t) st=0
/012
( tsU2(t)W1) st=0
LRs
Ct2=tU
2(t)+ t[U22(t)Ct2+U2(t)]+
s=1
t
./312
LRs
lt =t
Ul( t) 4 t
[U (t) lt+Ul(t)]+s=1t
ts
Ul (t) s+t(t) 56
../712
LRs
kt+1=t+t+1 [ fk(t+1 )+(1)]=0
/812
LRs
gt=tVg (t)+
s=1
t
ts
Vg (t) st=0
/912
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