NotesECN741-page21

NotesECN741-page21 - ECN 741: Public Economics Fall 2008...

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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 ) ≤ t,st t,st i 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 ). Feasibility 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. 21 ...
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