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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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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