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Unformatted text preview: ECN 741: Public Economics Fall 2008 sub. to
p(st ) wt (st )(1 − τ (st ))y (st ) + R(st )k (st−1 ) − T p(st ) c(st ) + k (st ) ≤
k i (s0 ) = k0 is given in which R(st ) = 1 + (1 − κ(st ))(rt (st ) − δ ) and T = t,st p(st )T (st ) is present value of
lump-sum taxes. Note that there is heterogeneity in skills θi as well as initial capital holding
k i (s0 ).
Let L(st ) = i π i y i (st ), C (st ) = i π i ci (st ), K (st ) = i π i k i (st ). Then feasibility is C (st ) + K (st ) + g (st ) = F (K (st−1 ), L(st ), st , t) + (1 − δ )K (st−1 ) (29) Govern met
Government has exogenously given sequence of expenditure g (st ) to ﬁnance. It can levy
linear tax on capital income κ(st ). It can also levy the following tax on income
τ (st )wt (st )y i (st ) + T (st )
Government budget constraint is
p(st ) τ (st )wt (st )L(st ) + κ(st )(rt (st ) − δ )K (st−1 ) p(st )g (st ) ≤ T +
t,st (30) t,st F irms
As usual the ﬁrm’s problem is static and implies marginal product pricing
rt (st ) = Fk (K (st−1 ), L(st ), st , t) (31) wt (st ) = FL (K (st−1 ), L(st ), st , t)
Equilibrium is deﬁned the usual way.
Next we derive the implementability constraints. Werning (2007) develops a methodology
that incorporates the fact that labor income taxes are uniform across types (so no extra constraint needs to be added to the optimal taxation problem). Also, he shows implementability
constraints can be written only in terms of aggregates.
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- Fall '10